UNITED STATES DEPARTMENT
OF THE INTERIOR
Water and Power Resources
Service
Denver, Colorado 1980
Transmission Line Design Manual
bY Holland H. Farr
A guide for the investigation,
development,
and design of power transmission
A Water Resources Technical
lines.
Publication
As the Nation’s principal conservation agency, the Department of the Interior has responsibility for most of our nationally owned public lands and natural resources. This includes fostering the wisest use of our land and water resources, protecting our fish and wildlife, preserving the environmental and cultural values of our national parks and historical places, and providing for the enjoyment of life through outdoor recreation. The Department assessesour energy and mineral resources and works to assure that their development is in the best interests of all our people. The Department also has a major responsibility for American Indian reservation communities and for people who live in Island Territories under U.S. administration.
On November 6, 1979, the Bureau of Reclamation was renamed the Water and Power Resources Service in the U.S. Department of the Interior. The new name more closely identifies the agency with its principal functions - supplying water and power. The text of this publication was prepared prior to adoption of the new name; all references to the Bureau of Reclamation or any derivative thereof are to be considered synonymous with the Water and Power Resources Service.
SI METRIC
UNITED
STATES
GOVERNMENT DENVER:
PRINTING
OFFICE
1980
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington DC 20402, and the Water and Power Resources Service, Engineering and Research Center, Attn D-922, P 0 Box 25007, Denver Federal Center, Denver CO 80225, Stock Number 024-003-00135-O
PREFACE The
purpose
followed
in the
of the line
Interior.
design,
such
of this
manual
is to outline
design
of power
transmission
Numerous
are included
aspects
protection,
spotting.
of the
National
problems
with
as selection clearance
structure
design
patterns, Safety when
the
sixth
some 16 000 circuit to properly distribute
made
other
codes
edition
are made
of NESC
as required.
lightning charts,
of the
are so noted;
sparce
by
and
Interpretations
Some
and
concerning
guying
construction.
considered
voltages engineers
of transmission
insulation,
and
to he
Department
is presented
was current,
while
of lines having power, Bureau
procedures U.S.
tensions,
limitation
to wood-pole
the aspects
Information sags and
structure
are limited
and
on specific
applications.
of NESC. of the Bureau, miles this
of Reclamation,
been
conductors, and
for,
Bureau
conductor
examples
most examples use the 1977 edition The transmission line network encompasses In addition,
have
of their
Code
requirements
by the
of construction,
design
developed
which
galloping
Structure
various
lines
explanations
of type
Electrical
were
studies,
the
some
up to and including have also designed
example however,
standards,
500 kilovolts. and built some
300 substations and switchyards. This total transmission system represents an installed transformer capacity of approximately 22 million kilovolt amperes. In many areas, a Bureau line is the only source of electricity and, if an outage occurs, an area may be completely without power. The vast land area covered
by
Bureau
lines
offers
almost
every
conceivable
type
large percentage of lines are in remote areas-maintenance Therefore, the line designs shown in this manual are more ordinarily be considered. The
Bureau
of Reclamation
recognized
the
need
for
this
of climatic
condition,
and
complete be readily
the manual available
engineers designing new This manual contains
manual
and
consequently
initiated
so that the design expertise gained through years of practical to other organizations as well as being a technical guide
lines and maintaining the engineering tools
many years of transmission line reference and guide for Bureau
design by the Bureau. designers. In keeping
metric units have been shown throughout the There are occasional references to proprietary not be construed in any processes of manufacturers other
facilities. that have
proven
its
of Energy in transmission to have the experience for Bureau
to be successful
over
The manual is not a textbook, but a useful with the Metric Conversion Act of 1975, SI
manual in addition to U.S. customary materials or products in this publication.
way as an endorsement, as we cannot or the services of commercial firms
units. These
must
endorse proprietary products for advertising, publicity, sales,
or or
purposes.
The author, as an electrical contributions Area
the remaining and concepts
a
is both difficult and time consuming. conservative than designs which might
preparation. With the advent of the Western Area Power Administration, Department October of 1977, many of the electrical power features of the Bureau, including most lines, were transferred to the jurisdiction of Energy. However, it was deemed prudent Bureau would
because
Power
Mr. Holland H. Farr, has more than 30 years of transmission line design experience engineer with the Bureau of Reclamation. He gratefully.acknowledges the many to this manual by the personnel of both the Bureau of Reclamation and the Western Administration.
Special recognition to H. J. Kientz for
suggestions, and consultation; R. D. Mohr who provided the technical Bureau of Reclamation, U.S. Department
is given to F. F. Priest his computer treatment
continuity. This of the Interior,
Cdlorado. . ..
111
for his encouragement, of the concepts; and
manual was prepared and Engineering and Research
published Center,
to
by the Denver,
ABBREVIATIONS ACSR
aluminum
conductor,
AIEE Alcoa
American
Institute
Aluminum
AND SYMBOLS steel
of Electrical
Company
ANSI
American
National
,4WG
American
Wire
BIL
basic
impulse
Standards
insulation
level
International extra
IEEE
Institute
K
conductor
loading
LP
low
(distance
MS1 NBS
maximum National
Bureau
NESC
National
Electrical
OGW SAS
overhead ground sum of adjacent
UHV USBR
ultra high voltage U.S. Bureau of Reclamation gigapascal
GPa Hz kcmil
hertz thousand
kPa kV*A
kilopascal kilovolt
kWh MPa
kilowatt
N/m N*m
Institute
Gage
EHV
point
Engineers
of America
CIGRE
high
reinforced
Conference
on Large
Electric
Systems
voltage of Electrical
and
Electronic
Engineers
constant between
low
sag increase of Standards Safety wire spans
circular
mils
ampere hour
megapascal newtons per meter newton meter
iv
Code
points
in adjacent
spans)
CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preface :\bbrc\
ialions
and
CHAPTER
syn~hols
I. BASIC
Field
data
Safety Cost
6 7 8 9 10
CHAPTER
.....................................
of type Single
wood-pole
(b)
H-frame,
(c) (d)
Single-circuit Double-circuit
(e)
Structures
(f)
Transpositions
structures
...................
4
steel structures steel structures
.................... ...................
s
................... long-span construction ..................... and effective spans ............................. Selection of conductors ................................ Stress-strain curves The parabola and the catenary ........................ Design
instructions
Transmission
data
II. CONDUCTOR
srnnmary
tension
calculations
19 20 21
9 10 14 21
form
23
...................
2s
................................
charts Preparation
........................................ of sag template
Inclined
spans
using
Coppcrwcld
sag calculating 29 32
..........................
38 SO
.................................... ............................... conductors
Galloping Broken
conductors
Insulator
effect
III.
7
SAGS AND TENSIONS
Sag and
Spans
7
................................
line
12
CHAPTER
6 6
Special ruling,
ion
18
6
..................
special conditions ..............................
informat
16 17
.4
structures
wood-pole
for
4
....................... .....................
of construction
(a)
General
1S
2
....................................
11
13 14
1 2
......................................
estimates
(g) Normal,
with
iv
DATA
codes
Selection
5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
... III
56
................................ on sag and
concentrated
tension
in short
spans
...........
........................
loads
77 99
INSULATION, LIGHTNING PROTECTION, AND CLEARANCE PATTERNS
Insulation
coordination
Lightning Conductor
protection clearance
............................. ............................... ......................... patterns
V
103 106 111
TRANSMISSION
vi
CHAPTER
22
LINE DESIGN MANUAL
IV. STRUCTURE LIMITATION GUYING CHARTS
AND
127 127
General
........................................ .............................. Components of charts ............................... Preparation of charts
23 24
CHAPTER 25
V. ADDITIONAL Stresses Structure
26
in wood-pole spotting
266 266
required .................... ...........................
(c)
Determining
...........................
26%
(d) (e)
Insulator General
........................... ..........................
268 273
Kight-of-way Armor Corona
uplift sideswing instructions
and
building
clearance
sag data
(a)
Sag tables
(b)
Sag and
Transmission
274 282 284
......................
.................................
292
.................................
292 292 300
insulator
line
266
.....................
rods and vibration dampers ........................................
Stringing
Bibliography
213
........................ structures .................................
Data and equipment Process of spotting
28
31
DATA
(a) (b)
27 29 30
127
offset
equations
data
for
inclined
spans
........
...........................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
303
APPENDIXES A.
A method for computing transmission spans adjacent to a broken conductor
B.
Useful
C.
Conductor
Index
figures
and and
tables
overhead
line
sags and ..................
tensions
307
............................ ground
wire
data
tables
in
............
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~....
339 441 479
CONTENTS
1
Conductor for
and
USHR
Mathematical
transpositions calculation
form
(metric)
tension
calculation
form
(U.S.
Stress-strain furnished
by
tension
parabolic
and
and and
and curve
catenary showing
length
line data of standard
13 I-I
Typical
sag template
15
Sag and
tension
origin
16
template Sag and
form
for (metric)
form
for
on
example
on
construction
calcldation
span tension
Sag on inclined
span-parameter
of cxampk
% method
problem
on
22
parameter Conductor
23
Conductor
24
problem Overhead
25
example Overhead
26
IIalf-sag
sag
Zmethod sag and
(U.S. customary) tension calculation
galloping sag and
conductors
24 33
......
34 sag 36 problem
on
sag
..............
38
.............. ................
39 44
using 47
span using ..................
form
(metric)
ellipses
on
for
calculation
on
for
,49
example
................
galloping example
form
52
example ........... on galloping conductors (U.S. customary) ground wire sag and tension calculation form for .......... problem on galloping conductors (metric) ground wire sag and tension calculation form for problem
tension
form
problem
an inclined span ........................
21
example
18
36
method method
parameter %method (metric) Results of example problem on an inclirled
on
18
......................
span-equivalent span-average
problem
15 16 17
22
inclined Sag on inclined Restllts
as
...................
form tension
..........................
on
I4
problems ............ curves (U.S. customary) percentage relationship between
summary sag and
12
used
example problems ..................
customary)
Sag
of values
......................... .........................
calculation form for example ................................. (metric) tension calculation form for example (U.S.
11 ....
..................................
Transmission Explanation
template
.......... customary)
for an ACSR, 26/7 conductor ................. Association
curves
calculation
7
........................
equations equations
catenary
tension
span
illustrating
calculations
calculation
and
parabolic Catenary
curves
and creep curves the Almninum
Sag and Sag and
creep
tension
9
19 20
3
tension
and
criteria
..................
sag and
curve curve
18
design
sag and
Parabolic Catenary
17
for
ratenary
Standard
7 8
12
wire
.........................
Standard
in sag and
10
ground lines
solution
Stress-strain
6
overhead
transmission
vii
conductors problem
on
for
(U.S. galloping
customary) conductors
53 54 .... ...
54 55
. .. VIII
TRANSMISSION
LINE DESIGN
MANUAL Page
b'igrrw
Profile
28
Sag and problem
tension calculation form for ................................. (metric)
broken
conductor
29
Sag and
tension
broken
conductor
30 31
of spans
used
for
broken
calculation
form
Curves
for
broken
Sag template
for
33
Conditions condition
for
problem
problem
conductor
60 61
tension
for equilibrium before ......................................
(U.S.
to broken
and
after
68
sohltion
of unbalanced
condition
(metric)
Graphical
solution
of unbalanced
condition
(U.S.
36
Nomenclature
37
tension Sag and
39 40
tension
(U.S.
customary)
calculation
Spans Graphical
rnethod
43
conductor Reduction
required of angle
with
structure
concentrated
height
(metric)
tension
effect
for
insulator effect
problem
problem
(U.S. 94
........................
determining
additional
100 length
of ..........
for concentrated load problem of protection against lightning patterns
according
tension
the
three
types
to
of voltage 112
clearance
pattern
problem
calculation form for .................................
clearance
pattern
problem
form
113
for
side
view
114
of structure
at conductor 121
...................................... structure
49
Clearance
pattern for a 30s ......................................
tangent
structure
so
conductor Clearance
pattern
angle
for
101 110
for
pattern for a 30s tangent ......................................
Clearance conductor
effect
90
insulator
Clearance conductor
51
problem
for
47
conductor
problem
85
form
calculation
(U.S. customary) Assrmled dimensions
18
effect
.......................................
Sag and
elevation
insulator
..................................
16
76
on sag and 78
insulator
loads
for
Superimposed clearance stresses ............................................. Sag and
for
75 ...
81
Tension-temperature curve for customary) .....................................
42
4.5
form
effect
.......... customary)
.................................
41
44
determining insulator .............................. spans
Tension-temperature curve for (metric) ....................................... Sag and
67
unbalanced
Graphical
38
66 .....
conductor
35
(metric)
.......
customary)
due
34
in short tension calculation .......................................
6.5
.............
(metric)
problem
reduced
for
57
...........................
problem (U.S. customary) Curves for broken conductor
32
conductor
..........
27
a 30A
with
single 122
with
duplex 123
structure
with
single 124
...................................... pattern for a 30A angle .......................................
structure
with
duplex 125
CONTENTS
52
Condnctor
sag and
problem 53
on steel
Condnctor
iX
tension
calcnlation
form
for example
strnctnre
limitation
chart
(metric)
tension
calcnlation
form
for example
structure
limitation
chart
(U.S.
sag and
. . . . . . . . .
13s
. . .
136
54
Center
phase
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of a steel structure limitation chart (metric) . . . . . . . . .
137
5s
angle Example
56
Example
limitation
chart
. .
148
57
Conductor problem
sag and tension on wood-structnre
calculation limitation
form chart
for example (metric) . . . . . . . . .
IS0
58
Conductor
sag and tension on wood-structure
calculation limitation
form chart
for example (U.S. customary)
59
Type
HS
Type
HSB
problem
on steel
of a steel
problem 60 61
for
type
structure
wood-pole
3OS steel
structure
(U.S.
no line
customary)
. .
. . . . . . . . . . . . . . . . . . . . . . . . .
wind force ground wire
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sag and tension calculation form for
158
example
problem
on
wood-structure
. .
160
Overhead
grourld
wire
example
problem
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sketch of one pole of a type FIS wood-pole
161
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161
wood-pole structure sketch of wood pole
sag and
limitation
tension
chart
calculation
on wood-structure
chart
65 66
Single-line
67
structure with X-brace Force triangle showing
68
Force
69
limitation chart (U.S. Force triangle showing
70
Type
3A
71
Type
3AB
72
Type
3TA
73
HalfHalf-
and and
full-sag full-sag
ellipses ellipses
for for
type type
HS wood-pole HSB wood-pole
Half-
and
full-sag
ellipses
for
type
3AC
structure
sketch
limitation
chart
triangle
angle
of top
portion
HS
for (U.S.
wood-pole
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . angle of bias lines for wood-structure
163
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
(metric)
showing
of a type
(metric)
form
limitation
customary) Single-line
angle
of bias
for
wood-strncture
. . . . . . . . . . . . . . . . . . . . . . conductor force due to line
168
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
169 177
. . . . . . . . . . . . . . . . . . . . . . . .
178
wood-pole
customary) resnltant
lines
structure
wood-pole
structure
wood-pole
structure
. . . . . . . . . . . . . . . . . . . . . . . .
wood-pole
. . . . . . . . .
189
structure
. . . .
191 193
F&sag ellipses for type 3TA 4267-mm (14-ft) pole spacing
wood-pole structure, tangent, . . . . . . . . . . . . . . . . . . . . . . . .
77
Half-sag
wood-pole
4267-mm Full-sag angle,
ellipses
for
(14-ft) ellipses 11 278-mm
type pole
for
3TA spacing
type (37-ft)
3TA pole
structure,
spacing
structure,
187
tangent,
. . . . . . . . . . . . . . . . . . . . . . . . wood-pole
180
structure structure
76
78
151 154 1ss
compute Overhead
strncture
147
157
63
74 75
with
. . . . . . . . . . . . . . . . . . . . . . . .
62
wood-pole
customary)
strnctnre
. . . . . . . . . . . . . . . . . . . . . . . . showing values needed to
Type 3AC Single-line
64
V-string
90°
194
line
. . . . . . . . . . . . . . . . . .
195
TRANSMISSION
X
LINE DESIGN MANUAL
FigUIV 79
Page Half-sag
ellipses
angle, 80 81
Full-sag angle,
ellipses 4267-mm
Full-sag
ellipses
angle,
8230-mm
82
Half-sag
ellipses
angle,
4267-mm
83
Half-sag
ellipses
84
angle, Full-sag
85 86 87
angle, Half-sag angle,
88
for
11 278-mm
type (37-ft)
for type (14-ft) for
type
(27-ft) for
type
(14-ft) for
3TA
wood-pole
structure,
spacing
..................
pole 3TA pole
90 O line 196
wood-pole structure, spacing ....................
60’
3TA
wood-pole
60°
line
pole
spacing
structure,
60°
line
.................... structure,
60°
line
3TA pole
line 197
structure,
198
....................
wood-pole spacing wood-pole
199
type
3TA
8230-mm ellipses
(27-ft) for type
pole 3TA
spacing .................... wood-pole structure,
45 o line
angle, Half-sag
6096-mm ellipses
(20-ft) for type
pole 3TA
spacing .................... wood-pole structure,
45 o line
angle,
6096-mm
(20-ft)
Full-sag
ellipses
pole
spacing
type
3TA
wood-pole
4572-mm ellipses
(IS-ft) for type
pole 3TA
spacing .................... wood-pole structure,
4572-mm
(15-ft)
pole
spacing
for
200 201
.................... structure,
202 30 O line 203 30°
.................... limitation chart ...... chart (metric) ........ chart (U.S. customary)
89
Instructive Example
example of a wood-structure of a wood-structure limitation
90
Example
of a wood-structure
91
Additional
92 93
Example Example
94 95
Standard guying arrangement for type 3TA structure 29-m type HS 230-kV structure with class 2 Douglas
96
95-ft
97
(one X-brace) 29-m type HSB
98
poles (one X-brace) Free body diagram
99
Free
data
chart
required
limitation for
the
line
wood-structure
customary)
(one
chart chart
crosstie body
HS
structures structures
class
example of pole
2)
(one X-brace) .................................... Free body diagram of pole above
plane
102
Free
customary
customary
example
of pole
2 Douglas
fir
2 Douglas
209
211
poles fir 219
of inflection
and
to the
example between
221
planes
101
diagram
......... fir poleg
.......................... between
with
(U.S.
class
............................... of pole above plane
example 2) ..................................... 95-ft type HSB 230-kV structure
body
.......
217 with
100
crosstie
(metric) (U.S.
214 with
................................... 230-kV structure
diagram
207
210
................................... 230-kV structure
(metric
206 . .
208 wood-pole wood-pole
.....................................
X-brace) type
for for
205
limitation
......................................... guying guying
204
of inflection
(metric 223
class
2 Douglas
fir
poles 232
of inflection
and
to the
2)
.................... planes of inflection
2) ., .............................
234 (U.S. 235
CONTENTS
29-m
type
poles 104 105
HSB
(two
230-kV
3)
107
(two X-braces) Free body diagram
type
crosstie
HSR
(U.S.
230-kV
fir
243
customary
109
customary example Typical sag template
110
Typical
plan
and
111
superimposed Typical plan
and
diagram
profile
114
Average
and
Sag and insulator
example
3)
between
bundles
poles
(II)
snow
of inflection
(U.S. 2.59
spotting conductor
sag template
269 showing
use of sag template 271
284
fair
287 weather
with
different
................................
form
.................. voltages free running stringing
120
insulator offset Profile of spans
121
sag correction ................................... Stationing equation for common survey,
assumption
122
Stationing
equation
123
survey, Station
assumption designations
calculation
form
sheaves
insulator operations
offset and ...............
for
problem ...............
on
problem
on .........
sag correction
Sag and
example (metric)
for
and sag correction for example problem
example
(U.S. customary) on insulator offset
293 297
298 line
common point on a transmission No. 2 ........................... when station back is greater than
line
1
Station
back
designations
point
...........................
301
for
when
station
.........................................
297
and
on a transmission
No.
...
288 290 293
sag
301 station
ahead ......................................... 124
267
......
structures
..........................
119
tension
2S7
....................
with
loss under
for different when using
and
to the
waves in a conductor (A) fair weather, (B) rainfall,
calculation
offset
and
...............
required for calculating data during stringing tension
of inflection
planes
drawing
of corona
Corona loss curves Conductor tensions Dimensions correction
fir
..............................
Schematic of vibration Corona loss curves for
conductor
1 Douglas
255 plane
................................... profile drawing
113
valrles
class
3) .............................. (plastic) used for
uplift
hoarfrost,
with
above
of pole
in determining
(C)
247
structure
of pole
Free
body
24.5
..................................
108
118
1 Douglas
.....................................
95-ft
116 117
class
body diagram of pole above plane of inflection and to the crosstie (metric example 3) .......................... Free body diagram of pole between planes of inflection (metric
106
115
with
..............................
Free
example
112
structure
X-braces)
xi
302 ahead is greater
than
stat&n
302
TRANSMISSION
xii
NESC Functions P curve
conductor P curve conductor 6
H
curve
conductor 7
11 curve conductor
.................. loading constants (K) ......................... sag template of % ...................................
27 37 41
for
computations
for example problem ................................
(metric) computations
example problem .......................... customary)
(U.S. computations
for
computations (U.S.
example problem .......................... customary)
No.
l-broken
I he
computations
for example ................................ for
No.
2-unbalanced
example problem ..........................
No.
2-unbalanced
11
P
curve full-load
computations condition
13
H curve
computations
14
full-load II curve
condition computations
no-load
conditiou
15
H
16
no-load Insulation
conditiou selection
17
Insulatiou
selection
18
Insulation Minimum
curve
(grade
computations
69 No.
2-unbhanced
example problem ..........................
No.
2-unbalanced
for example problem .......................... (metric)
No.
2-unbalanced
problem No. ....................
2-unbalanced
No.
2-unbalanced
problem No. ....................
2-unbalanced
customary)
H
69
problem
for
12
64
problem
10
(U.S.
63
for
condition (U.S. customary) P curve computations for example ................................ condition (metric) condition
63 l-broken
9
computations
l-broken
No.
computations (metric)
curve
No.
................................
Line data condition data
l-broken
problem
(metric)
example
No.
62
for
8
I9
MANUAL
conductor
Calculations
5
LINE DESIGN
for
example
70 70 71
(U.S. customary) for example problem ........................... (metric) for
example
72 73 74 107
(U.S. customary) for 34s kV ........................ ........................ for 230 kV
108
20
Conductor clearance surface-wood-pole
to pole ground wire or crossarm ....................... construction
21
Angular
of suspension
22
USBK Minimurn
23
109
........................ selection for 115 kV factors of safety for wood-pole construction R) .......................................
limitations
wood-pole structures factors of safety for ...................................... California
Conductor clearance surface-wood-pole
insulator
swing
for
129 129 standard 129
.......................... wood-pole
construction
to pole ground wire or crossarm .............. construction in California
in 131 131
. ..
CONTENTS
21-
Stttntttary
of loads
lertgths 2s 26
and
Stttntttary lengths Stttnrttary
of loads and
Sttrntnary Minimum NESC
29
Mirtirttttrtt NESC
irt structure
low-point
of loads
lengths 28
tttetnbers
distartces
and
in slrrtctttre
for for
242
3) . . . . . . . . . .
254
spatt
light,
clearartce
rttedittrn,
and
to buildings-USBR heavy
loading
. . .
266
startdard for . . . . . . . . . . .
275
cxatttple
horizontal clearance to buildings-USBR and heavy loading (rttetric) light, tnedittrn, horizontal
standard
(U.S.
2)
span
various
customary
231
. . .
various
exarttple
tttetnbers (U.S.
span 2) . . . . . . . . . .
for various span cttstorttary exatnple
(metric.
distartces
various
exarttple
rnerttbers
distartces
low-point
for
(rttctric
of loads iii structure rttetttbers artd low-point distartcrs (U.S.
lengths 27
itt structure
low-point
x111
crtstorttary)
3)
for . . . .
275
30
Right-of-way
values-NESC
light
. . . . . . . . . . . ,
276
31 32
Right-of-way Right-of-way
values-NESC values-NE%:
light loading (U.S. crtstotttary) . . . . , rnedittrn loadirtg (metric.) . . . . . . . . .
277 278
33
Right-of-way
values-NESC
ntedirtrtt
. . .
279
34 35
Right-of-way Right-of-way
values-NESC values-NE%:
heavy heavy
(metric) . . . . . . . . . . . (U.S. rttstotnary) . . . .
280
36
Data
frottt
correctiott 37
Data
1% I
problettt
(metric)
front
correction
example example (U.S.
loading
(metric)
loading loadirtg loading
ott insulator
(U.S.
offset
cuslorttary)
and
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . problettt crtstornary)
281
sag 299
on insulator offset artd sag . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . .
340 341
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
342
township showing sectiort rtttrttbering lartd section showing corner and l/l6
. . . . . . . . . . . . . .
B-2
Typical Typical
13-3
Azirttitth
H-4
I~eveloprttertt of forttirtla for rnaxirnttrrt rtiorttertt of resistance ort wood poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
343
13-s
Grottnd
344
chart
resistivity
in the
Urtited
States
desigrtatiotts
. . . . . . . . . . . . . . . . . . .
TRANSMISSION
xiv
LINE DESIGN
TABLES
IN
MANUAL
APPENDIXES
Pa&?
Table
B-l
Maximum ground
B-2
moment line-USBR
of resistance standard
for pole circumferences .........................
at
moment
of resistance
for pole circumferences ..........................
at
Maximum ground
line-ANSI
standard
B-3 B-4
Pole
circumferences
for
Douglas
fir
Pole
circumferences
for
western
red
B-5
Permanent
set values
for
Alumoweld
B-6
Permanent
set values
for
steel
B-7
Flashover
characteristics
B-9
Flashover Relative
B-10
Barometric
B-l
1
B-13 B-14
Pressure
Permanent
c-2
(metric) Permanent (U.S.
c-3 c-4 c-5
Conductor Conductor Conductor
C-6
Conductor
medium, medium,
pine
385
............... strand ....................
strand
of suspension
insulator
351 419 420
strings
and
air 424
Conductor sag-tension
C-l
southern yellow ................ cedar
.......................... values of air gaps ............... air density and barometric pressure .................... pressure versus elevation
B-12
Equivalent Selected
and
423
Mass per unit species used
B-15
348 ...
........................................
gaps.. B-8
345
volume and relative mass .............................. for poles
temperature computations
area
due
set, and and and and and and
427
to wind
and
for
final
normal 428
velocity
data for standard electrical ........................ conversions
set, creep, and initial ....................................... customary)
of wood
coefficients of expansion ...........................
on a projected metric SI-metric
density
426 426
...........
429 ......
conductors
431 moduhts
values 442
creep, and initial and .................................
final
overhead overhead overhead
.......... data (metric) data (U.S. customary) values for NESC light, ....................
heavy
loading
overhead heavy
ground ground ground
loading
wire wire wire
(metric)
ground (U.S.
430
wire
values
customary)
modulus
for
values
NESC .............
452 462 ....
466 470
light, 474
(
I
BASIC DATA 1.
Field
necessary
Data.-Before to gather
construction, establishment
design
certain
requirements
preliminary
for
a transmission
information
prior
line
can
be formulated,
to establishing
and the desired conductor and overhead ground wire of the voltage on major transmission lines, the number
the
sizes and and type
it is
voltage,
type
of
types. Usually, of lines required
the in
a given area, and the type of construction to be used depends on a comprehensive system study. This study would include the size and location of generators and loads, and the possibility of using existing transmission facilities. After a system study has established the required voltages and the end points of the transmission and
lines,
to prepare a. Operating b. Average
the following
designs: voltage and peak
information
is required
of the line. loads to be transmitted
over
the
to establish
line,
or the
the
peak
details
load
of construction
and
estimated
load
factor. c. per
Value in mills per kilowatt hour of the month or year of capacity to be served.
d.
A summary of local climatic (1) Maximum and minimum (2) (3)
e.
and
muskeg.
A map
showing
substations. g. The The
length
velocities with of ice expected
general
route
navigation
from
a., b., and
is used
mainly
specifications
clearance c., is used
to establish
prepare
h.
Whether
i.
Date delivery of power is required. Delivery points for Government-furnished
i material required k. Key map, 1.
Drill
logs
line
and
of the
To
the
will
and
a summary
designs,
the
sheets, of footing
and
line,
for,
to determine
the
required
following
the
value
special
1
river most
and
lake
economic and
per
kilowatt
and
drawings.
for
tower
and
agents,
intermediate
crossings. conductor
size.
The
requirements
is required:
forces:
the
crossing
corrosive
structural
information
or Governrnent
steel
or other
of terminal
additional
materials,
conditions
alkali
mechanical
by contract
and
sand,
locations
requirements
the
be constructed
at each point. plan and profile
and
and without ice. on the conductors.
smoke or fog atmospheres. that is, the presence of rock,
of, and
information
other information for the line.
the
to be transmitted,
conditions including: temperatures.
(4) Presence of corrosive A summary of soil conditions,
swamps, f.
Maximmn wind Radial thickness
energy
proportion
lines
or special
of each
steel
item
structures.
of
TRANSMISSION
2 2.
Safety
National
Codes.-The
Standards
NESC
Institute),
supply
and communication
where
it is not
certain
safety
rules
not
provide
The
from
code
specifies
structures,
circuits,
which
the
However,
design when
also be taken those
into
Loading the latest
by
than
Many
states
states
recognize
lines
in California
been
those and
prescribed
NESC
code
also
be based
line,
may
general
area.
cover
state
the force
for
of railroads,
weather
the
The
rules
important
to the
public.
supporting
thoroughfares,
geographic
or heavy
loading
and climatic
the use of heavier
that
construct
and
general
areas
in which
more and
conductors
the
medium,
We
of NESC.
for crossings
local
indicate
of the those
open
important
lines.
specifies
on light,
of electric
it is very
work
loadings
requirements
conditions
to line
(American
over
of these
intended
design
The
shall
for
the
have
as the
should
so noted.
in a code One climbing
general
special
standard
be designed
area rules
in which
regarding
for transmission in accordance
California
Public
It is imperative
have
clearances
areas
loading
in
conditions.
conditions
lines
the
line
electrical
should
conditions
and
is being
than
designed.
construction;
distribution
Utilities
Commission
however,
circuits.
Rules for Overhead Electric
with
3.
used
Cost
by
to make
the
most
Transmission
Line Construction,
[ 11.’
line,
construction.
They costs
making
types
of construction
on past
and
also
are also
system
A final Engineers the line, is prepared cost
in brackets
general
Preliminary
of various
when
certain
latest
refer
to items
state
at least
a minimum
allowable
and
that
often
types
to determine used
one
Ensure
of cost are the
to compare
of line
that
to assure
is too
that
code
and
NESC
all applicable design
overlooked,
all structures
in which
estimates
used
data
in the
and
Bibliography.
made, the
amount
of funds
of construction
the economy This
on current
are
to determine
the
construction.
are to be determined.
bid
be taken
applicable
that
cost For and
example, feasibility
is especially
Cost Estimate, based on the cost for each construction specification. and
of the
should
estimates
types
studies
editions
Care
have
factors
will
be met.
is the
the
safe
proper
climbing
codes.
Estimates.-Two estimate.
transmission
the
lines.
important factors of safety, for linemen on structures.
prescribed
engineers’
that
of transmission
been
of the most clearance
’ Numbers
maintenance
are
ANSI
are constructed
by fencing,
transmission
transmission
that
municipalities
for all designs
based
lines
by
maintenance
of the example problems in this manual were developed using the Sixth Edition of NESC [2]; most of the problems use the current 1977 Edition [3]. Problems using the old Sixth Edition
be used
compare
special
lines
for
General Order No. 95 of the
have
rather to the
circuits.
as local
NESC
issued and
conditions and conductor and overhead ground wire tensions shall be in accordance with edition of NESC with exceptions as shown on figure 1 or by specific heavier loading
conditions
Some however,
and
a particular
account
prescribed
Code),
installation
public
and
of construction,
communication
designing
the
transmission
construction
but
grades
of transmission
Safety
for
the general
of safety
requirements,
and
MANUAL
unless the regulations with NESC constructed are more stringent than
standpoint
clearances,
strength
power
from
specifications,
the
rules
overhead
in the
in accordance line is being
detailed
requirements
them
be observed
Electrical
safety
Because
to isolate
our transmission lines particular transmission do
(National
contains lines.
possible
LINE DESIGN
prices
a preliminary economic
to be requested these
comparisons
would
at voltages
as quoted
a final
voltages
and
of 230 kV
of a
budget
routes,
of all items involved Both the preliminary of materials
in the
on alternate
of different true
and feasibility
to
be used alternate
and
in the construction and final estimates by
for
and
manufacturers.
above. of are
CHAPTER
CONDUCTOR
AN0
OGW
FOR “SGN
FULL LO.9
Fii
LCunductor
I
CATENARY
DESIGN
TNAUSYISSION
LINES
CONDUCTOR NO LOAD
and overhead
From Dwg. 40-D-5169.
I-BASIC
ground
I
NO LOAD
I 1
wire’catenary
DATA
CRITERIA
O”ER”El0 FULL LOAD I
GROUND WIRE NO LOAD I “9
design criteria
for USBR transmission
lines. 104-D-1046.
TRANSMISSION
4 4.
Selection
of Type
a transmission
line,
to be used,
desired
or necessary
in the
according
to
structures
in a transmission
and methods
structures.
function:
lines,
special
are given All
40-D-
original
structures.
to design
conductor heights Brief
data
for specific
are on file
are supplied
Since the structure
Design
These
special
such
transmission Bureau’s
Denver
units
associated
with
on the basic
types
wood-pole
as standard
three
classes of the
hardware,
drawings
All standard
for general
design
limitation
and are given
104-D-
office,
and
reproducible
various
field
offices.
of structures
of materials
into
structures,
design
on
are to be used for all transmission
designs.
and loading conditions for transmission and types are varied to maintain efficient
discussions
availability
80 to 90 percent
as sag templates, lines
in the
the
type
are divided
Usually,
drawings
structural
drawings,
of conductors
and
Standard
and established ratings.
to be used
size and
line
(3) tension. class.
of construction
line,
of construction,
tangent
require
type
of the
in a transmission and
designed voltage
conditions
developed
drawings
been
for various
numbers.
are usually
drawings and
where
(2) angle,
the
voltage
costs used
are of the
have
lines
the
lengths,
structures
line
of installation
except
span
The
MANUAL
en selecting
to consider
(1) tangent,
use on transmission
tables,
of Construction.-Wh
it is necessary
to be used
LINE DESIGN
charts, or project prints
drawings and
sag
numbers.
of applicable
lines are often different, span lengths and economical use of the standard
are presented
in the following
paragraphs.
(a) Single Wood-Pole Structures .-The Bureau usually uses single wood-pole structures for voltages from 2.3 through 46 kV. In addition, where right-of-way is severely restricted, it is sometimes necessary to use single wood-pole construction for 69- and 115-kV 1ines. For lines up to and including 69 kV, two conductors,
types of single-pole structures are designated flattop and
are used
conductors triangular
are supported by a single crossarm and are arranged in the same horizontal plane. In the type, the middle conductor is supported at the top of the pole and the two outside
conductors are supported by a crossarm below both single-pole and H-frame construction. construction is used; however, crossarm are used. For 115-kV types
of single-pole,
which, with reference In the flattop type
triangular.
the For
top of the pole. Pin-type insulators 69-kV lines, a type of single-pole
suspension insulators with two lines, a single wishbone-type
single-circuit
structures
and
tangent, single crossarm small line angle, double
to the arrangement of the of construction, the three
their
conductors structure
nomenclature
suspended is used. The
are used triangular from the common,
= =
suspension, suspension,
SA SAT
= =
vertical conductor attachment suspension, medium line angle (up to 600), tension, large line angle (60 ’ to 90 ’ ), vertical conductor attachment
ST STR
= =
tension, medium line angle (0’ to 60 O), vertical suspension, transposition structure
crossarm
H-Frame
tangent be used 230-kV
structure which has a double-plank crossarm. Occasionally, for lower voltages where long spans cannot be avoided; lines. The use of X-braces between the poles is standard
the use of longer
Wood-Pole Structures .-The
conductor
(b) voltages
69 through
spans
161 kV.
and heavier
The
Bureau usually H-frame designation
conductors,
upper basic
are:
SS SD
from
in
and to support
attachment
uses H-frame, wood-pole structures for originates from the appearance of the this type of construction must however, it is sometimes used for on H-frame structures to permit
the structures
under
transverse
loading.
The use of wood poles longer than 27 m (90 ft) is not recommended, except for very special cases, because they are not economical and are difficult to obtain. For normal wood-pole construction, it is preferred that the majority of poles on lines with overhead ground wires should not exceed 19.8 m
CHAPTER (65 ft) in length;
and on lines
18.3 m (60 ft). Although we normally arise
(other
than
without
and
to permit
the
substation. The basic
to obtain
reduced types
HS 3AC 3A
and
high
(c) 161 kV.
Steel
clearance
for
on conductors
=
two-pole,
suspension,
=
three-pole,
suspension,
=
three-pole,
suspension,
=
three-pole,
tension,
and
H-frame
are also
many were
transmission line types: (1) tangent,
years used:
steel
used
for
structures
an SAL-type
climatic loading. In 1975, the the voltage;
system
steel
designate
the
voltages
under
long spans loadings.
is used
special
type to their system
Medium
D =
Double
Heavy Transposition
a 2 indicates
230
kV.
of the
number and
The
=
Suspension
X
=
Heavier
suspension
with
ST
=
Heavier
suspension
type,
A
=
phase dead-ended Angle (insulators in suspension)
T
=
Tension
Y D
= =
Tension with large line Dead end with variable
R
=
Transposition
small
to
for
second
is now
specific digit
such
used
is a design
as crossings spans
The
first
designator
designers to immediately letters are added to the
letters
designed
as a basic
into
in three line. For
identifying
structure
loadings.
above
for
light
designation digit
for
indicates
for a particular
identify two-digit
the basic number to
structure:
S
with
angle
suspension,
voltages
approach
in which
= =
Circuit
all
and are designed function in the
=
voltage
spans
are:
for for
H TR
a two-digit
approach
conditions
are required,
by a nomenclature
system permits the steel structure for any given line. The following
function
construction
M
and
For
angle
Tension Angle
a specific
towers.
angle
line
T = A =
for
situations
crossarm
Light
was changed,
exceed
angle line
a single-circuit,
to use steel
nomenclature
=
was
not
occasional
in the
L
designed This used
their
double-plank
medium
designated
wires
Suspension
=
for example,
series of towers. set of structures
were
structure
a set of structures
ground and
line
0 ’ to 90 ’
lower
it is necessary
should
183 m (600 ft) of a substation; therefore, to permit large line angles, where required,
overhead
small
of poles
up to 161 kV,
structures are usually of the self-supporting (2) an gl e, and (3) dead end, according
S
Thus,
all lines where
tangent,
Steel Structures .- Normally,
5
the majority
construction
over navigable streams where high clearance and substations and switchyards, and for extra-heavy Steel general
wires,
for crossings)
for
structures
DATA
to guy any structure within are used in these locations
tensions
Single-Circuit
ground
structures
of structures
3AB
3TA
overhead
use wood-pole
example, it is our policy not self-supporting steel structures
I-BASIC
line
small
line
no line
angle
(0’
angle angle
to 5 “)
(O’to
5O)
capability,
capability
angle (5’ to 30 “) capability line angle capability
capability outside
phases
in suspension,
center
6
TRANSMISSION
Thus,
a type
30s structure
The
limitations
in the
conductors
would
of a given and
LINE DESIGN
be a 345kV
suspension
set of structures
overhead
ground
wires,
MANUAL
structure
will
depend
and
the
with
upon
a design
conductor
loading
area
designation
size,
where
of zero.
maximum
the
structures
may
be used
tension are to be
used.
Double-Circuit
(d)
Steel Structures
necessary to place two cost of two lines along are arranged expected,
vertically the
on one
conductors
loading
are expected,
contact
between
may
(e)
of the
steel
structure.
be located
the conductors.
directly
to offset Contact
In
areas
above
the center
can be caused
structures
right-of-way, structures, where
one another; conductor
lines
for Special which
Conditions
and
however,
by galloping
ice loading
are
where
and
the
conductors
snow
possibility
or uneven
.-Sp ecial conditions frequently arise in the use of special structures. Special structures
the
not ice
of any snow
and
to use steel
Transpositions
.- To maintain
structures
to obtain
balanced
sufficient
conditions
phases of a transmission line, at least one terminals. However, it has been determined
designing of are required
a higher voltage line, (2) a branch and (4) long spans, such as those
require higher than normal structures to maintain navigational conductors. Where navigational clearances over rivers or lakes
necessary
clearances are required,
height.
of reactance
and
capacitance
on the
line
of uniform
configuration
three
transposition barrel should be placed between major that for less than 161 km (100 mi) between terminals,
the unbalance is not sufficient to affect the operation of the transmission line or the protective barrel, as used by the Bureau of Reclamation, refers to a section of a three-phase The term transmission
it is
For example, if the three conductors are located directly above one one of the lower conductors may drop its ice and spring up into the steel structures are constructed in the same general types as the
necessitate
for a river or lake crossing, or wider spacings between
(f)
snow
to minimize
where: (1) a lower voltage line is carried on the same structure below line takes off from a main line, (3) switches are required in a line,
it is usually
where
or if it is desired to reduce the the conductors for each circuit
structures.
Structures
transmission
side
it is desirable
ice loading on the conductors. another and covered with ice, conductor above. Double-circuit single-circuit
.-Double-circuit
transmission lines on a restricted the same route. On double-circuit
that
is divided
length by two transpositions arranged so that each one-third the length of the section. Specific instructions the design instructions for each transmission line.
into
conductor regarding
three
parts
of approximately
occupies each transpositions
relays. power equal
phase position for should be given in
The distances between conductors in a transposition must be studied to determine if adequate minimum electrical clearances will be obtained in a given case. If possible, it is helpful to set up model of the transposition. A model will give good results and will also present the whole problem in perspective. A problem thorough analysis. A model must
be made
to scale.
area in a transposition eliminates the possibility
A large
to hold the dowels in the desired an inexpensive way of duplicating conductors, between conductors Another
method
that
may
sheet
of plywood
may be difficult to locate of selecting the wrong area. for a base,
dowels
to support
correctly The model, the
without a of course,
conductors,
locations, and adequate string to represent the conductors various questionable line situations ‘such as clearances and structures, or between conductors and guys. be used
geometry to the problem. This method made and the problem areas determined. transposition problems.
to determine should The
be used formulas
these
clearances
is by
applying
a
screws provide between
descriptive
after an analysis of the whole system derived on figure 2 may be applied
has been to many
CHAPTER
I-BASIC
DATA
Dv v -=-
First
v= kS$=kD,
dD* dk =-2D,*+2k(Dv
D” -=S
Solution
S
kS
SHkS
derivative
7
of
D* with ‘+
respect
to k:
DH2)
of differential
equation:
2
ti=(S-kS@
=D,(I-k)
DH
D2=DH2-2D,*
(h2)*
D,* + D,*
D= ~kDv)2+[DH(I-k)]2 D*=
+ OH2 -2kD,‘+k*D,*
Dv2+DH4
D”*
D*=
D,* k2(Dv2+
For structures
at different
,/(Span)'+
(difference
13). where
rough
Special Long-Span terrain,
it is often
solution
Construction .-To necessary
5.
Normal, span lengths
Ruling, and Effective obtainable by using
take
to use spans
consideration. To obtain the required spacing may be used on single wood-pole structures, structures. For steel construction, the structures
the
-2DH4+DH4
+ D,.,’
conductors
e
on crossarm)
is the slope angle.
in elevation)*
Figure S.-Mathematical
(g)
+D,*)
elevations:
spacing) (-Ices Span
D,= V
v
D,*)
Remains the same (spacing between
D,= (Vertical
2
(D
D,*)~
(Dv *+ D,‘)
D* = D,2 -2kDH2+
D,
(D,*+
OH2 (Dv2+DH2)-2DH4+DH4
D*= k* D,* + (D, - kD,)* D2=k2Dy2
+
for transpositions.
advantage longer
104-D-1047.
of topographic than
are
normal
conditions for-
the
in areas voltage
under
between conductors for long spans, longer crossarms and greater pole spacing may be used on H-frame can be designed for any required conductor spacing.
Spans.-Th e normal span is used to determine and compare different structure heights. The normal span may be defined
of
8
TRANSMISSION
as the maximum level
span
ground.
seldom can
The
level,
attainable
with
usefulness
and
the
be calculated
a given
of the
actual
spans
the
following
from
LINE DESIGN structure
normal will
span
vary
MANUAL
height
and a given
is limited
because
considerably
from
conductor
the
the
clearance
transmission
normal
above
line
span.
The
profile
normal
is span
formula:
Normal span in meters (feet) = where:
P = height of conductor L = conductor clearance C =
ruling
D =
conductor
ruling
The changes spans the
span,
sag for
used
and
preparing
n spans
having
and
lengths
length
template,
ruling
which
level span
be defined
in temperature
span
for
above
the
ground,
normal
span
is to be calculated,
m (ft)
m (ft)
m (ft)
span may
of varying
support
as that
span
will
most
loading,
between
as a basis the
C, m (ft)
dead
ends.
nearly
agree
tables.
The
the
with
common
the
in the
average
sags and
ruling
span
dead
tension
definition
the conductor
L 1, L 2, Ls... L, between
of lengths
in which
A more
for calculating stringing
length
for
ends
tension
is that tensions,
any
may
conductor,
under
in a series
the
ruling
constructing
section
from
is
the
of transmission
be calculated
of
span
the
sag line
following
equation:
L,3
Ruling span = To
use this
is used
as a basis
structures the
equation,
lengths
the structure the
line
entire
exceptionally
rough tensions
due to variations
in sections
In
isolated
the
ruling
a structure.
If the
point
of the
the
conductor. the other, support
supports
conductor In this the
low that
spans, is made used for
point portion
the
case,
with
the
of the of the
the
middle
span
conductor conductor
by the
should
usually
and
short
spans
cannot
be avoided
a longer
or shorter
a change
ruling
spans tensions
of the
end
should
for of
be used.
because same
sections
canyons
with
because
occurs
by the
between
each
to the the
conductor
of a span
and
be closer
between
vary
of
be selected
span
span
do not result
strength
the
amounts
of different
which
are dead-ended
which
is supported
by
elevation,
the
span.
portion span
ruling
the
so that
span can be estimated
in ruling
or over
actual
is equal will
line
span
at each of the
is limited
span
before
a transmission
the ruling
crossings
to the
length
ruling
be estimated
for
ruling
where
as river
conductor
effective
span
Unbalanced
equal
must
structures
the
One
different
such
span
because
Therefore, long
point
to designate
is at the
case,
is the
at the
and loading.
long span
span is the term
low
this
of line
in temperature
end,
then
When
be dead-ended
spans.
Effecthe
will
profile.
must
where
However,
ruling
maximum
are located.
sections
+...L,
be known. the
The
+ .. . Ln3
+L,
to locate
requirements.
structures
for certain
must
practice
as possible.
the
+L,
sag template,
good
clearance
before
L,
locations
the
It is always
except
conductor
horizontal
than
calculating
and conductor accuracy
at each
structure
are as uniform
sufficient
ruling
for
are located.
span
The
the
i- L,3 + L,3
are at the
structure
actual
span.
to the lower structure
will
support
If one
support and
same
the
one-half
support and
low
each point.
is higher structure In effect,
of
CHAPTER considering
the
the
equivalent
low
point
conductor
load
of a level
of the
span
conductor.
To determine
on one equal
This
the total
spans;
6.
Selection
to consider
voltage
for
minimum depends
of the
it without
has assumed
no-load
conditions. the
sag and
initially.
When
values,
ru 1’m g s p an, the initial
(8.5 ft),
and
Bureau,
for
strength
(3954 to 3700 The
use of either point
the short
that
shorter
structures by
The
electrical
the conductor
with
conductor
losses
studies
to twice
it is necessary
on the
line,
corona
conductor
cost,
and is determined
of designs
type
or design amount
of conductor
before
instructions. of corona
loss;
Corona
loss
surface.
of 13 832
economical The
The
wind,
and
mm
(9.53
N (3110
lb) a t mimts
enough
and
using
short
spans
or very the
tension
sag with
small For
enough
some
small
are required.
structures can
standard height.
The
on a line
be supported structures
Section
may
15 describes
considerations.
conductivity to a temperature
of the conductor that
would
must cause
be high
annealing
enough
to carry
and consequent
N
no ice and no wind.
structures
to structure
is 17 580
the sag to increase
conductor
that
N/m
the immediate
structures.
of the
are
of 4.3782
and the
size conductor
permissible
in addition
tall cost
the
ultimate
conditions
lb),
cause
mm
by
of the
loading
18 ’ C with high
were
be 2594
N (7500
sag of the
increases
to use a larger maximum
the
they
as determined
will
excessively
will
a constant
ft),
assume
on a 213.4-m
percent
heavy
of 33 362
in the conductor
usually
considerations
NESC
tension
is 2906
without
either
condition,
loading
less than
no wind
is 33-l/3
factor
be high
that
more
load
no wind
spans
limiting
the initial
it will
conductor
no ice and
loading
for maximum
being
24/7
to
after under
is unloaded,
tension
conditions
transverse
to a full
must
The
maximum
strength
as specified
the
ice loads
conditions
ultimate
ACSR,
and
urlder
conductor
and
no load.
(4-lb/ft2)
wind,
wind
no-load
of the the
the
strength
specified
(0 OF) with lb).
initial,
to carry
kcmil),
loading
the creep
spans.
and
percent
(477
heavy
structures
longer
line,
conductivity,
by the permissible
When
N (4429
or tall
conductor
of power
system
under
18 ‘C
no ice and
sag is so great spans
galloping
galloping
0.19-kPa
long
from
greater
mm2
40 “F)
installation,
it becomes
limited the
NESC
conductor
for a transmission electrical
by ice and
sag being
a 242 19 700
use of reasonably
size conductors,
the
a tension
structure
structure.
of the ultimate
stretched.
be
ft) with
of the
is loaded
the conductor
after
(12.14
the
(3) 33-l/3
sag at minus
(0 ’ F) with
years
strength
to permit
sag, and
under ice,
loading
18 ‘C
Ten
mm
will
radial After
lb).
strength
40 OC (minus
(l/2-in) lb/ft).
sag at minus
the
tension conductor
at minus
13-mm (0.30
the this
is equal
be sufficient
(1) 50 p ercent
with
(700-ft)
must
ultimate
if we string
to consider
given
any of the
for preparation
sea level,
is permanently
example,
it is necessary
below.
the conductor
conductor tension
For
its final
selected
designers
conductor
of the
the
conductor.
above
exceeding:
and
for
vahte
determined
and
structure
span. the sum of the adjacent
side
is usually
altitude
of 46 kV
one-half
to one-half
of the conductor,
line
the
effective
supports
is equal
the conductor
is usually
structure
between
the
spans
on either
in the
each
distance
to be transmitted,
used
line
voltage,
(2) 25 percent
conditions, final
materials
strength
upon
conductor
load strength
of conductor
voltages
mechanical
conditions,
line,
the
is called
effective spans
only,
length
selecting
to the transmission
on the for
be imposed
adjacent of the
a transmission
diameter
is negligible The
of the
of the
is assigned
which
of the points
mechanical
availability
The The
voltage
interference,
the
the line
sum low
9
by any one structure,
supported
of Conductors.-When
the
and radio and
or the
to twice
supported
The
DATA
structure
span
length
effective
between
in length
conductor
on each side of a structure.
distance
of the
hypothetical
the spans the
side
I-BASIC
the load reduction
without in the
heating strength
to on be
TRANSMISSION
10 of the conductor voltage
drop
which, in the line
use of reactors, transmitted
over conductor
between
the
line
in greater
be limited
to about
synchronous
Usually,
size than
available
results
and
the line.
value
transmission
must
capacitors,
a larger
various
in turn,
LINE DESIGN sag and
reduced
of power
to control
to limit
heating
in the
conductor
and
the
will
result.
such
that
types
of conductors
minimum
above
this the
and voltage
annual
cost
as well
as determining
fixed
(reactive
volt
line is sufficient
drop.
A balance
charges
on
Comparison the most
the ground.
The
can be controlled
vars
losses in a transmission
is required
of losses
clearances
* however,
10 percent,
condensers
the value
MANUAL
must
to justify
must
the
by the amperes)
be obtained
investment be made
economical
in
the
between
the
size of any one type
of conductor. Since
1945,
has proved 1945, that
copper
(aluminum
conductor,
economical
than
other
were
that
copper
prices
aluminum
90 percent
ACSR
more
such
conductors
are now
of distribution
It is occasionally
being
steel
several
such
conductor specified
conductor, as copper
was more for nearly
because
of its lower
or Copperweld-copper.
economical all new
than
ACSR.
transmission
lines,
price, Prior
Records and
to
show
for about
lines.
necessary
to consider
the availability
it may be necessary to complete the transmission economical conductor. Once the route and length of a transmission conductor type and size selected to carry safely power,
reinforced)
conductors,
mechanical
considerations
line
of the different in a short
or distribution and economically
remain
which
may
time
types
of conductors
without
regard
because to the
most
line have been determined, and a the system voltage, current, and
influence
the
choice
of conductor
and
will definitely influence the installation methods. The designer must consider such factors as structure and ground clearances. Thus, the heights and locations, span lengths, conductor sags and tensions, designer must have detailed knowledge of conductor sag and tension as a function of span length, temperature,
and
weight
loading.
Most
of this
information
is supplied
by conductor
manufacturers
in the form of tables and graphs; however, the designer will usually have to prepare additional aids such as forms, charts, diagrams, and templates, that are related to a specific installation. Figures 3 and .4 show a standard form that USBR designers use for conductor calculations. This form is a Pa. [6]. Figure 3 shows metric variation of a form designed by the Copperweld Steel Co. of Glassport, calculations calculations 12, chapter
7.
for the conductor previously mentioned, for the same conductor. A detailed description II.
and figure 4 shows the U.S. customary of this calculation form is given in section
Stress-Strain
calculations
Curves.-Most of the mechanical properties required are determined by tensile testing. Wires used in the manufacture
conductors are tested in full section. The loads stresses based on an area of the original section:
determined
in a tension
for sag and tension of transmission line
test
are reported
as unit
Load Stress = Area Elongation elongation
is measured is then
determined
as the
increase
in length
of a gage-marked
as
(Final Length) - (Original Length) (Original Length)
length
on a test
specimen.
The
CHAPTER
DCm-578
I-BASIC
11
DATA
(3-78)
:“I’N’:“L’ SAGCALCULATIONS
LOADING
j T5!cp-\ LMST~ESSED LENGTH i
/3InIn Ice 0. 9/~~kP=Wl~(W”‘)~-/8.0, Permanent
No Ice.
Set 6 creep
NO Wmd
---.a--InIn 0.d!.#vsakPa Permanent
(W’)
1
-18 1 -1 15.5 12 __ 49
lo.
0.
0.000
15
999
O.RUfl 0,949
(w-y
(W’)
mm 1.3 kPa WwJ (W”‘) Permanent set 6 creep
- 5 I 110 ,6o6!o.uoo I
096
16
2594
i !
114
/fJ , OO/ I/. ouu !
mm ICO Set S Crew
91)
,a/
I
O”$
I
m
O,/Ull
u.u/-?
62:
1
I : I
2.906
,
I
I
/9/j
I I
I
/7
590
P.5
I I 13
833
-, k&d
I
I I
m
/Q/ I 003 /aY
oofw ,
Qg
d
n,
/383
&/J/7
34
-7700
/ I /
/9//
I
I
I
I
I
/ 49
,
I
1
I
I
I
SPANLENGTH(S)
m
I 1 j-18
1 I
I
1 49
1
I
I I
I
I
I
I
I I
I I
SPANLENGTH(S)
I
I
I
m I I
I I
15.5 32 40 .-
I L
SPANLENGTH(S)
,
I
I
,
m /
1
, I I
I I
I
-18 -1
I
I
15.5 32 j
I
I I
49
I/J
I I
j I
,
700
&&j
/.
115.5 *I
kPa Wind (W”‘) Set 6 Crew
NO Wind (WY
I!?.? 462
.3 L
I
I
999
_ !
NO Ice. NO Wind (W’)
NO Ice.
! 5,P45
I
4
I
1 1
-1.9 -1
Permanent
lo.nK7 I
I
mm,ca Permanent
0.0971
4693
SPANLENGTWS)H(S)
set 6 Creep
NO Wind
L
TENSION,N
1
/Q/
15.5
-18 -t NO Ice,
m5-
SW,N
99
I
0
(W’)
kPa Wl”d
0./7-5210.02, I
I
Ice
Permanent
7
1
m
3L
SPANLENGTH(S) 2’3.
32 49 Nmm
/o/
j
I
NO Wmd
999
/o/ ~U.OQU 393
SAG,mm
SIG FLCTOR
Y
I
’ 1
-18 -1 NO Ice.
499
I
ice , Wind cw”%-/g Set
?!6
SPANLENGTH(S)213.
1
Figure 3.4tandard
I
sag and tension
calculation
fornl (tnetric).
TRANSMISSION
12 DC-576
LINE DESIGN MANUAL
(S-76)
;;L;FL
CONDUCTOR ~77h’d -.. I Code
Name
Weight Breakutg
Diameter
Load
&&!6
Tensat
inch
Initial.-&OF
Final, Computed
&%,&!&?-lb
-1/oF
Loaded,
*F *OF by -
No Wind
X //300
lb
Area
2
% ti
lb
Temp.
18
% &$&lb
(AI
d
Coeff.
Modulus.
in2 of Linear
(E)
Final 0.000
o/&~
(W’)
No Ice.
NO Wind
(WY
per “F
SPAN LENGTH(S)
Ice. Wind(W”‘) 6 creep
InitialAE
FEET
0 30 No
Ice.
No Wind
(W’)
60 90
-Inch Pemlanent
SPAN LENGTH(S)
Ice. Ib/ft2 Wind(W”‘1 set h creep
FEET
0 30 NO Ice.
No Wind
(W’)
60 90 120
Figure 4.-Standard
sag and tension
calculation
FinaljD. lnltial
Exp.:
(W’)
No Wind
set
_25-
Date
Ice.
-Inch -Ib/ft2 Permanent
Factors:
/7alb
Limltatlons:
Final.
No
LOADING h/ecrv
-
Rated
No Ice.
.h?dR 24
SAGCALCULATIONS
form (U.S. customary).
AE
‘/ u
53x g,epLx 4
L
106
lb/in2
106
lb/in2
24 :i
CHAPTER
I-BASIC
DATA
13
Stress-strain curves are prepared from the data obtained from these tests. As the test specimen is slowly loaded, readings of elongation are made so that the initial curve may be plotted. As the specimen is unloaded, elongation readings are again taken so that the fin& curve may be plotted. A typical, stress-strain curve for a wire has a straight line segment, which in the deformation is proportional to the applied load. The unit stress (load divided by original area) is proportional to the unit strain (deformation divided by original gage length). The numerical value of this ratio (stress/strain), usually expressed in gigapascals (pounds per square inch), is the modulus of elasticity. For an ACSR conductor, there is no straight line segment on the initial curve, so a straight line average of the portion of the curve under use is used for determination of the modulus of elasticity. The final curve is always a straight line and has the same slope regardless of the maximum load applied, provided the yield strength is not exceeded. The slope of this line is the final modulus of the conductor. Other characteristics of the test specimen may be determined from the stress-strain test. The proportionul limitis the stress value at which the deformation ceases to be proportional to the applied load. The maximum stress which can be applied without causing permanent deformation upon release of the load is the elastic limit. The yield strength is the stress at which the deformation ceases to be proportional to the applied load by a specified percent of elongation (usually 0.2 percent). Ultimate tensile strength is the maximum tensile stress which a material is capable of sustaining. Tensile strength is calculated from the maximum load during a tension test which is carried to rupture with the original cross-sectional area of the specimen. All metals have lower ultimate strength values when subjected to a fluctuating stress. The amount of decrease will depend upon the range of the fluctuating stress and the number of repetitions. Alcoa (Aluminum Co. of America) states [7] that research and experience in transmission line design indicates that if the limits of variation in tensile stress are approximately 10 percent, the maximum value of the fluctuating stress necessary to produce fracture will be approximately 70 percent of the ultimate strength. This stress is referred to as the working limit. Creep is the plastic deformation that occurs in metal at stresses below its yield strength. Metal that is stressed below the yield point will normally return to its original shape and size when unloaded because of its elasticity. However, if the metal is held under stress for a long period of time, permanent deformation will occur. This deformation is in addition to the expected increase in length resulting from the stress-strain characteristics of the metal. Figure 5 shows a stress-strain curve that illustrates the origin of values used in conductor sag and tension calculations for transmission lines. An explanation of figure 5 is: l ADFG represents the initial loading curve plotted from test data taken during the loading of a specimen in a stress-strain test. l The average slope of curve AF has been extended and labeled “Average slope of initial from zero to full load.” The slope of this line is used for the initial modulus in calculations. The value in this example is 40 GPa (5.8 x lo6 lb/in2). l CGis the final loading curve plotted from test data during the unloading on the test specimen. The slope of this line is the final modulus. l The conductor represented by the curves is to have a maximum stress of 69-MPa (10 000 lb/in2) under full load conditions. l BFis drawn parallel to the final curve CG and between the points for full load and zero load. l AB is the permanent elongation and is called the permanent set l The lo-year creep line is drawn from previously computed values. The creep value DEis read horizontally between a point on the initial curve and a point on the creep curve at the same stress value.
TRANSMISSION LINE DESIGN MANUAL
14
-
30 000 200
175
2s 000
150 I
20000 /
N .-E
125
2
5
2 - IS 000
100
/ 68 e:
c” cn
-Full
10000
v; c I v)
75
SO
I
5 000
D
0
A/ i b
es
-Creep -
0.4
0.5
0 0.6
-c
c Permanent Set UNIT Fii S.-Stress-strain 104-D-1048.
STRAIN,
and creep curves illustrating
percent origin
elongation of values used in sag and tension calculations.
DE represents the creep value over a lo-year period. We assume that the average tension over a period of 10 years will he at 15.5 ’ C (60 o F) un d er no load conditions. limits conductor stress to 18 percent of the ultimate strength at these conditions. values used for our calculations reflect all of these conditions. Figure 6 shows stress-strain and creep curves for an ACSR, 26/7 (26 aluminum strands strands) conductor as furnished by the Aluminum Association. l
conductor The USBR The creep and 7 steel
8. The Parabola and the Catenary.-Two curves, the parabola and the catenary, are generally used in the calculations for conductor sags on transmission lines. The parabola, an approximate curve, is often used because it simplifies the calculations. When a wire or cable is assumed to conform to the curve of the parabola, the mass of the wire or cable is.assumed to he uniformly distributed along its horizontal projection (the horizontal span length). For the parabolic solution, it is safe to assume that the sag will vary as the square of the span length for spans that are at least double the length of the ruling span.
CHAPTER
I-BASIC
DATA
15
35 000 [I
225
30 000
I75 25 000
N .E
20 000
2 vi z (r E-I
15 000
IO 000
// H
5 000
25
U.E
UNIT
Figure 6.-Stress-strain 104-D-1049.
0.3
STRAIN,
and creep curves for an ACSR,
0.4
0.45
percent
2617 conductor
as furnished
by the Aluminum
Association.
The second curve to be considered is the catenary. Any perfectly flexible material of uniform mass will hang in the shape of a catenary when suspended between two supports. Although commercially available wires and cables are not truly flexible, they will, in very short spans, conform closer to a catenary since
than they
is assumed The
to any other
will
similar
catenary
and in long
is easily
understood
parabolic
of an imaginary Figures
7 and
equations
the
curve
long, 8 show
the
the
arc
the
the
of the short
or the
be appreciable
that
For
reasonably
catenary becomes
conductors
curve.
conductor
more
be considered the
mass
as truly of the
flexible
conductor
conductor. span
parabola.
in heavy even
may catenary, with
no unusually
However, loading
areas
pronounced
in an inclined
the
sag will
between
a
with-comparatively
if the spans span
large
difference
is actually
low
are inclined. a small
This portion
span.
the
Figures
following
can
realizing
a level,
the
difference
level
spans,
along
for
either
This by
for each. for
distributed
using
spans.
In longer of a catenary
obtained
when
tensions
needed
shape
to be uniformly
sag calculations
be very
curve.
sag in the
parabolic 9 and
example
and
10 show problems.
catenary the metric
curves,
respectively,
and
U.S. customary
and also the commonly sag and tension
used
calculations
TRANSMISSION
LINE DESIGN
MANUAL
Parabola
Directrix X2
Y=40 w= Force
per unit
length
L = p + $$ = Length
of cable
H = 2aw = w& = Horizontal '=
w(3p2+8s2) 6p
of cable and load
= Vertical
tension tension
T=.z
m
= Maximum
S,= $
= Sag at
any point
S= g
= Maximum
tension
sag
Figure 7.-Parabolic
curve and equations.
104-D-1050.
CHAPTER
I-BASIC
17
DATA
Catenary
y=
w = Force
4
) = a cash
(e++e+
per unit length
L = a (e’-e’)
=2a
v=y(e
x o -%*)=
of cable and load
sinh + = Length
H = aw= T -SW= Horizontal
$
of cable
tension
aw sinh + = Vertical
tens ‘ion
T = yw = aw cash $- = H cash $= Maximum S= y-a = a(cosh a=
S
8 -I) = Maximum
tension
sag
= Length of cable whose mass is equal to horizontal tension = Parameter of catenary Figure
8.-Catenary
curve and equations.
104-D-1051.
TRANSMISSION
18
DCm-576
MANUAL
(3-78)
M
;;;;LL
CONDUCTOR f/D3 Code
LINE DESIGN
2
mm
k)psn
"%
SAGCALCULATIONS
LOADIHG~ Linear
Name Rated
SreJklng
Strength
DLsme,er
aB
Tension
L~m,tat,ons
Force
Dead /3
mm
Factor.
Load
Force
mm Ice
O./m
hPa
N/m
915-7
/5-;
18.
Wand
Resultant Area
(rV’)
(w,‘)a
(W’“)
Cc&f.
ad-51
N/m
Total
b/j2
N/m
34.
Modulus.
0.000
of
Linear
NO Wind
O.OOQL/65 0.000~
Final
#d.?ztm
ln~tlal Final
0 /~perOc
56.
GPa I/do
GPa
AE34
75-T
-369
N
AE dL
939
318
N
(W’)
Figure 9.-Sag and tension
DC-576
(El
Exp..
lnttaal
NO Ice.
Set O.OOOJb Creep
(A)&..&--rnd
Temp.
Permanent
N/m
calculation
form
for example
problems
on parabolic
and catenary
curves (metric).
(3.78)
;;;f'
CONDUCTORI+' Code Name 2 Rated
kfm
TensIon
Load
/.
A
500
31
Final.
+ iz~“.
AF
0
%fO
2 OF 50 E
by -
LOADING
WeIghI Ice
&lb 33f
Z!&.?F
Factors
Dead
lb
Llmltatlons
Loaded, Fmal.
fl
Inch
In,t,al.-°F
Computed
d
SAGCALCULATIONS I LOADING ~-"J/ Welght
Breaking
Dmmeter
/
26
lb lb
Area
5.70
lb
Temo.
“1 7 % 6
(AI
1. 2,
Ib/ft
opt/s
Iblft
Creep
0.00dL
lb! It
Total
0.000
7
-0. (W”‘)
2.
a&?%
Coeff.
o.??o
4-09f7
o.000
UNSTRESSED LENGTH\
Figure lO.-Sag and tension calculation
2
o/D
form for example problems
(E)
Final/o*76 In,t,al$.
Exp:
per OF
5;
Set 0.0003
SAC FACTOR
on parabolic
? 6
3
5
8--
8 f’2
Ib/ft Modulus.
12 of Linear
Permanent
O’o ~-lb Date
jT\;“”
Wtnd Resultant:
c00
(W’)
(W”)
SAG, ft
and catenary
/Z6
x 106
lb/l9
* 106
lb/ln2
Final
AE
7
lb
lnltlal
AE
&$tt
lb
SW,lb
1 TENSIONsIb
curves (U.S. customary).
CHAPTER Example
Z.-Parabolic
Assume:
366-m
‘C
DATA
19
(metric)
ruling
span
403-mme,
ACSR,
44 482-N
maximum
NESC 15.5
curve
I-BASIC
heavy
26/7
conductor
tension (13 -mm
loading
sag at no load
=
14 556
ice,
0.19-kPa
wind
plus
constant
at minus
mm sagRS
Sag,
_
VW2
(Span,
I2
where: sag in ruling
span,
sagRS
=
Sag, RS Span,
= sag in any other =
ruling
span
= span
length
mm given m
of any
other
Sag,=
(sa&S
1200-ft 795 NESC
(Span1 j2, 104m2
SagI = K Gwn1)2, mm
100 200 300 400 500 600 700 800 900 1000
1 4 9 16 25 36 49 64 81 100
1,
(U.S.
1 087 4 346 9780 17 386 27 166 39 119 53 245 69 544 88 017 108 663
customary)
span
ACSR, maximum
heavy
60 o F sag at no load
= K (Span, I2
m
ruling
kcmil,
) (Span 1I2
m
1.0866 x 10w4m-’
curve
10 OOO-lb
span,
14 556
span
Assume:
given
L= = (366)2
K =(Rs)2
Z.-Parabolic
mm
WI2
sagRS
Example
span,
length,
loading =
47.69
26/7
conductor
tension (l/2ft
in ice,
4-lb/fts
wind
plus
constant
at 0 OF)
18 ’ C)
TRANSMISSION
20
LINE DESIGN MANUAL
SaRS -= (RSY
sa& (Span,
1’
where:
S%RS
=
sag in ruling
Sag,
=
sag in any
=
ruling
span
=
span
length
RS Span
1
span,
ft
other
given
span,
length,
ft
of any
other
given
47.69
sagRS
-
K=(RS)Z
105fi2
200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
Assume:
366-m
44 482-N
maximum
15.5
‘C
15.5
o C tension
sag at no load
figure
H =
aw =
a =
H/w
0.4 1.6
1.32 5.30 11.92 21.20 33.12 41.69 64.91 84.78 107.30 132.41 160.29 190.76 223.88 259.65 298.06
2 10.0 14.4 19.6 25.6 32.4 40.0 48.4 57.6 67.6 78.4 90.0
span
ACSR, heavy
ft
(metric)
403-mm2, NESC
From
ruling
10-5ft-1
S481= K (Spanl)“,
(Span1j2 I
ft
curve
ft
=3.3118x
=(1200)2
Spanl,
3.-Catenary
span,
(SagRs1 (Span 1I2 = K (Span, >2 WI2
Sag, =
Example
ft
26/7
conductor
tension (13- mm
loading =
at no load
14 556 =
ice,
0.19-kPa
wind
at minus
mm
18 638
N
8: T=
SW =
18 638, - (14.556)
18 405/15.9657
=
1152.7839
(15.9657) m
=
18 405
N
18 “C)
CHAPTER x =p/2
Example
= 1/2span,
50 100 150 200 250 300 350 400 450 500
0.043 313 0.086146 0.130 120 0.173 493 0.216 866 0.260240 0.303 613 0.346986 0.390 359 0.433133
curve
795
ruling
kcmil,
10 OOO-lb NESC
ACSR,
heavy
loading =
at no load
=
9.
Design
the Regional by the Denver
may and
office
4-lb/ft2
4190
curve curves .-A
=
(1.0940)
3782.29
at 0 “F)
=
4137.83
lb
ft
Sag=a(c;hz-
z.- 1 cosha
showing
0.000 349 531 0.001 398 367 0.003 147 243 0.005 597738 0.008 750 491 0.012 608 78 1 0.017 174 947 0.022452 180 0.028 444 171 0.035 155 107 0.042589680 0.050753087 0.059 651 036 0.069 289745 0.079 675 954
the
percentage
useful
proportion seven
the technical
further
of the regions. design
in chapter work
Design
of each
between
a clearance
design
l),
1.322 5.289 11.904 21.172 33.097 47.690 64.961 84.921 107.584 132.967 161.087 191.963 225.618 262.074 301.358
relationship
in determining
are discussed
of the Bureau’s to cover
wind
lb
- (47.69)
x a
Instructions
1 084 4 340 9113 17 393 21215 39257 53542 70096 88952 110 144
ft
be particularly
catenary
Directors
in ice,
0.026439 0.052 878 0.079 317 0.105 756 0.132 195 0.158 634 0.185 073 0.211 512 0.237 951 0.264 390 0.290829 0.317 268 0.343707 0.370 146 0.396585
11 is a catenary
Parabolic
0.000940156 0.003 764194 0.008 411558 0.015 087 698 0.023607738 0.034053 971 0.046445 57 1 0.06080607 1 0.077 162 490 0.095 546 05 1
conductor
(l/Z-
47.69
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
relationship
- 1),
mm
tension
x = p/2 = l/2 span, ft
Figure
Sag =a(cosh;
1
customary)
26/‘7
H = aw = T- SW = 4190 a = H/w = 4137.83/1.0940
This
21
span
maximum
60 OF sag at no load 60 OF tension
(U.S.
DATA
coshz-
a
1200-ft
Assume:
X
m
4.-Catenary
I-BASIC
at any
point
span
length,
in a span.
II.
on transmission
instructions
transmission
sag and
lines
are issued line
is delegated
to these
and include
directors
the following:
to
TRANSMISSION
I””
0,
lb
LINE DESIGN MANUAL
30
2'0
40
5’0
PERCENT Figure Il.-Catenary
a.
Design
curve showing
percentage
relationship
70
$0
SPAN
80
90
100
LENGTH
between
sag and span length.
104-D-1052.
data.
(1)
Length
of line
(2)
Voltage
of line
(3)
Number
(4)
Type
(5)
Ruling
(6)
Insulators:
(7)
Conductors
and
(8)
Maximum
tension
(9)
Final
of circuits of structures span number,
tension
size, overhead under
at 15.5
and
type
ground loaded
OC (60
wires:
number,
size,
and
type
conditions for conductors and “F) with no wind for conductors
overhead ground wit -es and overhead groul nd
wires (10)
For
steel
towers,
ground
wires
the
horizontal
and
vertical
spacing
between
conductors
and
overhe,
ad
CHAPTER (11)
For
(12)
Final
steel
towers,
sag at
overhead
the
15.5
conductor
OC (60
ground
(14)
wires The annual isoceraunic level This number is calculated
clearance
at 15.5
the
Design
c. d.
Minimum Drawings
loading
e.
Number
49
23
to tower
steel with
OC (120OF)
’ F) between
the
conductors
and the probable number either per 100 kilometers
for
coefficent
for
the
and
of power outages or per 100 miles
“per-lOO-miles”
conductors
vahle
overhead
ground
due to lighting. of transmission is 1.6 times
locations
of transpositions.
all pertinent data concerning the line Initial entries on the summary form
charts,
so that should
a compact, ready be made when the
steel
tower
are obtained, filled out.
notebook, records-if
along they
sheets for other lines, for easy reference. summary sheet is simple in layout, easy
normally
required,
with summary are kept. The has
room
for
any
and by the time The completed
reference is available. design work is assigned.
entries should be made as data the form should be completely
source.
the
than those given in a. of structures to be used. clearance
A Transmission Line Data Summary Transmission Line Data Summary Form.on figure 12, should be prepared for each transmission line designed. This form should
information
and
conditions.
f. Design data drawings including sag templates, structure limitation diagrams, and conductor height tables for wood-pole structures. 10. shown
no load
value.
clearances, other and characteristics and
o C (60
mmlerical
“per-IOO-kilometers” b.
and
DATA
wires
Midspan
length;
clearances
“F)
(13)
line
I-BASIC
additional
data
that
the transmission form should
might
form,
as
contain
Additional
line is put into service, be placed in a looseleaf
Nothing is better than good to fill out, contains all data
be useful,
and
is an excellent
24
TRANSMISSION
LINE DESIGN
TRANSMISSION LINE
Region: Project: Name of Line: Length: Elevation, min.-max.: NESC loading: Type of
km
MANUAL
DATA SUMMARY
Specifications Voltage: In service: Data by: kPa wind, lb/ft* wind, contractor:
mi
zone,
mm ice, in ice,
construction:
Insulators Size: -. Strength: Number per
mmx
in x
l-Ql( N (
in)
Conductor at 15.5
lb)
No.
+K(O.-), +K(O.-),
and overhead
ground
wire
to ground clearance "C (60 "F)
mm
ft
Overhead
ground
wire
_
-
Name : size:
Type: Stranding: Ultimate strength: Tension limitations 50% us at -"C( OF) initial 33-l/3% US at -"C(eoF) initial 25% US at -"C(OF) final 18% US at 15.5 "Cf 60 "F) final 15% US at 15.5 "C( 60 OF; final Diameter: Area : Temp. coeff. of linear expansion: Modulus of elasticity Final: Initial: NESC Force (weight) per unit length Bare: Iced: Wind: Resultant (with constant): Ellipse resultant: Ruling span: sacs
OC OF
string: Conductor
Conductor
at at
mm* --
kcmil
mm ml*
mm dia.
in dia.
lb
N
lb
lb lb lb lb
N N N
lb lb lb
N
lb in
in
in*
-p&C
__
perOF
2 pergc
----Tn*
per"F
GPa GPa
lb/in* lb/in2
GPa GPa
lb/in2 lb/in2
N/m N/m N/m N/m N/m m
lblft lb/ft lb/ft lb/ft lb/ft
lb/ft lb/ft lb/ft lb/ft lb[ft
ft
N/m N/m N/m N/Ill N/IO In
OF) final: OF) final:
nun Em mm mm mm
ft ft ft ft ft
mm mm mn mm mm
OF) final: OF) final:
N N N N N
lb lb lb lb lb
ft
-
Full load: Cold curve: Ellipse: 15.5 "C (60 49 'C (120 Tensions Full load: Cold curve: Ellipse: 15.5 “C (60 49 'C (120
___ -OC
(
OF)
Key map: Plan-profile drawings: sag template: Stringing sag tables Cond"&r; Overhead ground wire:
Structure
Figure
12.-Transmission
line data summary
Limitation
form.
Chart:
104-D-1053.
ft ft ft ft ft lb lb lb lb lb
<
CONDUCTOR 11.
General
conductor under line design. This
Information.-The
SAGS AND TENSIONS
determination
of sags
and
various conditions of temperature and loading determination enables design elements, such
to be established and permits the use of sag templates, criteria are in use as a basis for making sag and tension parabolic curve. If a uniform,
perfectly
flexible
and
inelastic
stringing calculations:
length
corresponding
tensions
is of basic importance as the most economical tables, and other (1) the catenary
of material,
such
for
aids. Two general curve, and (2) the
as a chain
points of support. The tension at any horizontal component which is uniform
point in the throughout
component which varies along along its length. The vertical
This means that the total tension of the tension at the low point
the
If it is assumed that points of support,
curve of the and parabola) increasingly as the span
the mass of the cable is uniformly instead of along the cable itself,
cable is that of the are almost identical greater length
ratios greater
as the sag increases. increases.
the
value
of this
less than 0.05, and should than 0.20, the catenary
encountered introduced stringing (100 error
where
in practice
will
in sag and the conductor.
tension
ft) of span length for spans greater
a portion
of a curve
distributed the resultant
parabola. The results of the two when the sag is small; however,
Within a limited range of values method may be used for calculations. to spans
cable will consist of two the length of the cable,
Since
of the ratio Generally,
ratio
longer
or cable,
be the method may present
0.05.
The
used for difficulty.
a sag-to-span
computations
have
not
components: (1) a and (2) a vertical
along a horizontal line mathematical equation
between for the
methods of calculation (catenary the difference in results becomes larger
sags, the
catenary
of less than be greater
difference
catenary method
method
ratios between Fortunately,
ratio
should
hangs
the mass minimum be at the
in the cable will also vary of the cable is zero.
of sag to span, either the the use of the parabolic
is less than
involve
spans
increases
or the parabolic should be limited
can
also
be used
0.05 and 0.20. For most transmission 0.20.
than
The the
error
tolerance
for
ratios lines
inherent
or
allowed
in
In general, the error allowed in stringing is 12 mm (0.04 ft) per 30.5 m for spans up to and inchtding 366 m (1200 ft), and 152 mm (0.5 ft) maximum than 366 m. The curve assumed by the cable in a steep inclined span is actually
for a very
large
level
span,
so calculations
for steep
inclined
spans,
even
though
the spans may be short, should be made using the catenary method. Computed sags should to 3 mm (if in feet, to two decimal places) regardless of the method used. Sag and tension data can be divided into three categories according to the physical
state
conductor,
of time
with
any
in transmission span length,
in still air between two fixed supports, it will take the form of a catenary. For the catenary, of the conductor is assumed to be uniformly distributed along the arc of the conductor. The tension in the cable will be at the lowest point of the arc, and the maximum tension will
the curve. component
II
reference
to its past
and
present
degree 25
of stressing,
and
the
length
be accurate of the the
TRANSMISSION conductor
has been
(2) final
loading
(1) a small this
under
stress.
condition,
and
The initial percentage
condition
preparing
These
LINE DESIGN
three
(3) final
categories
loading
MANUAL
are referred
condition
to as: (1) initial
with
loading condition applies to conductors which of the stress value selected as the maximum are
used
as stringing
sag templates,
which
data
are used
for
unstressed
to determine
have not operating
condition,
been stressed beyond stress. Sags based on
conductors,
uplift
to determine maximum stress conditions. applies to conductors (2) Th e f ina 11 oa d in g condition
loading
creep.
forces
and
as basic
on structures.
data
for
Tensions
are
used
selected
as the
maximum
for only
a short
time.
sag and
tension,
and
maximum stress (3) The final
operating
stress,
Sags and tensions stringing
data
for
conditions. 1oa d’ m g condition
but
based
where
on this
creep
the
have
stressed
has been
to the value
under
this
are used to determine
conductors.
applies
been
conductor
condition
prestressed
with
which
Tensions
to conductors
are used
which
stress
the full-load to determine
have
been
in place
for several years. Creep values are generally based on a lo-year period, since about 95 percent of the creep has been removed from the conductor over this length of time. Sags based on this loading condition are used for preparing sag templates that can be used for spotting structures on plan-profile Sag and conditions,
drawings.
Corresponding
tensions
are used
in broken
conductor
tension values for a given span length and conductor will vary according that is, the sag for the final loading condition with creep will be greater
calculations. to the loading than the sag for
the final loading condition, and the sag for the final loading condition will be greater than for the initial loading condition. The difference in the sag between final loading with creep final loading conditions is obviously due to creep. The value of this creep is dependent magnitude of the average in the sag between final permanent To compute
tension and the length of time and initial loading conditions
set is dependent upon the magnitude sags and tensions based on initial
for the conductor Likewise, the final
set must
of the loading
maximum conditions,
under study must be determined and modulus of elasticity must be determined
tensions based on either the To relate initial conditions, permanent
the tension has been is due to permanent
final loading condition final conditions, and
be determined.
To
determine
used in formulas involving the and used in order to compute
values,
the
The
loading
permanent curve
and
approximating elongation
the at zero
set may the
loading
conditions
unloading
initial stress
Whenever electrical subjected to the effects
be taken line.
loading between
as the difference In the curve,
the
case where the
initial
1 Numbers
as the in brackets
the
permanent
modulus
line
at zero stress
initial set
and
modulus
modulus
may the
may
and recommendations
for
conductor
tensions
requirements California
Rules for Overhead Line Construction refer to items in the Bibliography.
[l].t
and
be taken
as
loading curve between the is the slope of the unloading
be taken unloading
between
the initial
is represented as the
by a line
difference
are set forth
in
line.
conductors or overhead ground wires are strung above ground, of wind, temperature, and ice, all of which add load to the wires,
rules have been adopted as the basic standard code the Bureau of Reclamation serves, except California. is published
in elongation
modulus. sags and
condition with creep. creep, values of creep
initial
the slope of a straight line which most closely approximates the initial point of maximum stress and the point of zero stress. The final modulus line.
applied. The difference set. The value of the
stress attained by the conductor. the initial modulus of elasticity
or the final loading final conditions with these
the sag and the on the
in NESC.
by all of the 17 Western has established its own
they are Standard
These
NESC
States that code, which
CHAPTER The the
standard
loading
NESC[S]. length
NESC
loading
districts
of the
According of the
horizontal
load
conductor
(ice
determined
per
unit
covered
from
conditions Uniied
to NESC,
components
total
and
Henry, which
on the
general
loading
load
on a conductor
shall
load
per unit
(ice covered
length
due
a horizontal
to
specified),
length wind
to which
resultant
apply map
be the resultant where
in general
in section loading specified)
to
25 of per unit and
the
pressure
on the
projected
area
of the
has been
added
a constant
that
can
be
1.
Radial thickness of ice, mm (in) Horizontal wind pressure, kPa (lb/ft* ) Temperature, OC (OF) Constant K to be added to the resultant of all conductors, N/m (lb/ft) State
Medium,
as shown
vertical
Table 1.-NESC
The
are Light,
States
the
27
SAGS AND TENSIONS
of the where
table
II-CONDUCTOR
of California
specifies
conductor
loading
constants
(K)
Heavy
Loading Medium
Light
13 (0.5)
6 (0.25)
0 (0)
0.191 52 (4) - 18 (0)
0.191 52 (4) - 9.4 (+ 15)
0.430 92 (9) - 1 (+30)
4.3782 (0.30)
2.9 188 (0.20)
0.7297 (0.05)
heavy
loading
conditions
of 13-mm
(0.5-in)
radial
thickness
of
ice and 0.29 kPa (6 lb/ft2) of wind pressure on the projected area of cylindrical surfaces at minus 18 ‘C (0 “F) for all parts of the State where the elevation exceeds 914 m (3000 ft) above sea level. Unlike the NESC, the California code does not require the addition of conductor loading constants. California light loading conditions of no ice and 0.38-kPa (8-lb/ft2) wind pressure on the projected area of cylindrical where the elevation above snow
are likely
to occur
surfaces at minus 4 ’ C (25 OF) are specified sea level is 914 m or less. However, our experience at elevations
below
914
m in northern
California;
for
all areas has shown
therefore,
of the State that ice and some
Bureau
lines in this part of the State are designed for NESC medium loading conditions. This loading is more practical for the expected weather conditions and exceeds the requirements of the California code. In Montana and Wyoming, NESC medium loading is specified for most of the area covering these States. However, extremely low temperatures so we have revised, for Bureau use, these 1 in section Both the strung of the
2. NESC
and
California
been encountered areas to NESC
recommend
that
conductors
in these states during the winter heavy loading as shown on figure and
overhead
ground
wires
be
at tensions such that the final unloaded tension at 15.5 ’ C (60 ’ F) will not exceed 25 percent ultimate strength, and the initial unloaded tension at 15.5 “C will not exceed 35 percent of
the ultimate strength. The NESC ultimate strength under maximum percent For
codes
have loading
of the ultimate ACSR conductors,
permits tensions assumed loading.
strength under the Aluminum
maximum Company
under The
load that California
do not exceed 60 percent of the code limits maximum load to 50
assumed loading. of America recommends
that
the
tension
shall
not exceed 50 percent unloaded tension shall
of the ultimate strength under maximum loading conditions; and that the final not exceed 25 percent of the ultimate strength at minus 18 ’ C (0 OF) in NESC
and
loading
California
heavy
districts,
at minus
9.4
‘C
(15
’ F) in NESC
medium
loading
districts,
2%
TRANSMISSION
and at minus
1 ’ C (30
those recommended vibration. Several
years
’ F) in NESC by
the
light
codes
ago, we installed
and
steel
LINE DESIGN
loading result
districts.
with
some
of the
overhead
conductors,
25 percent of the ultimate strength at the following temperatures:
ground
so we now
of both
These
in considerably
tensions
at a final
breaks for
high-strength
clamps.
Vibration
in one
problems
unloaded
ground
from
of 25 percent
occurred
final
overhead
less than
conductor
tension
to vibration
a maximum
steel
to the
unloaded
due
suspension
design
are substantially
less damage
wires
of the ultimate strength at 15.5 ’ C (60 OF). N umerous more wires of the seven-wire strand at the supporting occurred
MANUAL
wires
or also
tension
of
and conductors
Temperature OC (OFI
District NESC heavy loading NESC medium loading NESC light loading
-40
(- 40)
-29
(- 20)
-18
(0)
When extra-high-strength steel is used for overhead ground wires, we design for a maximum final unloaded tension of 20 percent of the ultimate strength at the temperatures shown above for the different loading districts. Bureau design criteria for conductors and overhead ground wires should be in accordance with the
data shown on figure 1; note that there are four limiting conditions shown. Although the ice and wind loadings prescribed by the codes are generally applicable for determining the loading conditions to be used in the design of a transmission line, specific climatic and weather
conditions
should
be studied
for each
transmission
and South Dakota transmission lines, 38 mm (1.5 in) of ice on the conductors, was considered as it did not seem simultaneously. Certain limitations regarding in various local safety codes. applicable authorities. of spans, References
are given
inclined
level
to various
to some
be exceeded, except a general discussion for which sag and
methods
(symmetrical)
(asymmetrical)
or group
of lines.
For
example,
on our
North
allowable sags, tensions, and span lengths are set forth in NESC These codes or regulations should be reviewed to determine
limitations which should not In the following paragraphs, and special span combinations,
in such spans. A perfectly
line
the crossarms were designed to support a vertical load due to but no extra wind load for the excess ice above 13 mm (0.5 in) probable that heavy icing and high winds would occur
span degree.
simple treatment by either the parabolic for computing sags and tensions in level
which
by written permission from the proper is given concerning the various types tension data are likely to be required.
are in general
is infrequently However,
found
the level
and the
use for
computing
in practice
span problem
since lends
sags and almost
itself
tensions
all spans
are
to comparatively
or catenary relations. Numerous methods have been derived spans, the majority of which are-based on catenary relations
in the form of dimensionless ratios. Four of these methods Reference [6] offers the greatest facility in most problems
are described in references [4, 5, 6, 71. and is discussed further in the following
section.
be made
the
Before
method,
using and
then
any care
method, should
a careful
study
be given
to the
should application
of the
to determine method
As might be expected, the computation of sags and tensions for inclined their asymmetry. Most inclined spans are supported by suspension or pin-type
the within
limitations these
of
limits.
spans is complicated insulators at both
by ends,
CHAPTER or by suspension A few
or pin-type
inclined
spans
can be designed purposes,
without
correction.
catenary solving can
curves each
insulators
may the For
be used
span
extremely
to theoretical
sag condition for
at both
or correcting
ruling
the data
determination work from
requirements
the
spans,
hillside
of support
proper
at the
level
over
railroad,
special
clearances
to ground
treatment. discussed
waterway,
such
and
line,
be used
applies
conductor condition
and
the
and
sag curves
to obstructions. which 14.
to a broken under this
communication
structure
may
support
to provide
A method in section
end. span
as extending
as the upper
be made
For
usually
calculations,
other
of inclined
spans.
spans
elevation
should
at the
type
for symmetrical
tensions in spans adjacent of assuring compliance
highway,
insulators suspended
on symmetrical same
span,
conductor
the
computed
steep
points
of sags and standpoint
Usually,
based
spans dead-ended at both ends also require special is given as reference [S]. Inclined spans are further The design
by dead-end-type
ends.
sag template
as an individual
determining
SAGS AND TENSIONS
at one end and
be dead-ended
by modifying
spotting
II-CONDUCTOR
then which
Inclined to this
case
is important in with clearance
powerline
crossings;
and
from the standpoint of determining the unbalanced loads on the structures. The computation of sags and tensions under this condition is quite involved, due mainly to the many variables introduced. A method which applies directly to this problem is given as reference [8]. In addition to this published solution,
an unpublished
that offers as appendix
a margin A, and
method
of facility an example
was devised
by
Mr.
over other methods. problem using this
G. R. Wiszneauckas,
former
Bureau
This method has been included method is shown in section 16.
engineer,
in this
manual
In a series of suspension spans, where relatively short spans occur adjacent to a relatively long span, it is desirable to determine the changes in sags and tensions which would result from temperature and loading changes and produce dangerous loads values. The consequently,
nature most
this problem with in section 16. Problems substation
from unbalanced on the structures;
of this problem of the methods slight
relating
for
to spans
with
An
example
concentrated
approach
In some cases, such changes clearances may be reduced
is very similar handling the
modification.
or switchyard
loadings. in others,
spans
to that of the broken conductor problem
loads
broken conductor problem; problem can be applied to
on unbalanced
are relatively
or unbalances will below the required
few
conditions and
is presented
are confined
mainly
to
taps or tie-down arrangements
in which
problems are complicated by the elastic effects No published method is known which adequately
are used. Such of the tie-down in addition to the dead load applied. treats this problem; however, a method was devised
by
facility,
the
Bureau
Another dead-ended in references handled 12.
that
by one
of the
Sag and
Calculating Engineers’ published
handles
this
problem
with
methods
Tension
Tables [4] were Society in book
given
Calculations first made
of Western form by the
in reference
18.
[12].
Using Copperweld public by Mr. James
Pennsylvania Copperweld
in November Steel Co. That
then, have been in constant use by engineers designing sags and tensions by Martin’s Tables consist of filling interpolating, tables.
see section
problem similar to spans with concentrated loads appears in the use of extremely short spans with long insulator strings. This problem may be handled by use of the methods [S, 10, 111. Problems where the concentrated load consists of dead load only can be
and
computing
values.
There
Sag Calculating Charts.-Martin S. Martin in a paper he presented 1922. In 1931, first edition, and
the tables were first several editions since
overhead transmission lines. out a calculation form by
is a trial-and-error
method
required
‘s Sag to the
Calculations of reading tables,
in the
use of these
30
TRANSMISSION The
“Graphic
a series
Method
of correlated
conductor.
Graphical
superimposing The
for
Sag-Tension
graphs
‘to
methods
graph
Copperweld
upon
are very graph,
and
for overhead
Tables.
The
as with
Martin’s
lines.
general
procedure
Tables.
charts for
required occasion,
sag and but
values were
[6]
are based charts
various
developed
provide
and factors of which eliminates
using
is applied
the charts
and
to a wire,
as is done
stretches. If the tension of load on a suspended
tables
should
in the wire increases, wire, the elongation
a conductor
problems
the length (stretch)
in preparing
the calculation
using
a graphical
that
time
of the catenary
curves,
these
all wire
is the
between
to some two
same
unstressed force
of construction solution.
is elastic between
in Martin’s
charts
times the vertical and the trial-and-error
most types part of the
is strung
of sags and
as given
relationship
SF/ T (span length the interpolating
be aware
when
employing
of an overhead
conditions.
to simplify
tension
is a system
characteristics
considerable
on the functions
sag and
the
require for
by Alcoa,
tension
when using the tables. The range of the charts covers it may be necessary to revert to Martin’s Tables for
Designers tension
reading
solving
However,
length factors, elongation factors, conductor divided by the tension)
the
satisfactory
Charts
The
developed
Calculations”,
determine
Sag Calculating
tensions
LINE DESIGN MANUAL
of the methods but,
extent.
supports,
on
When the
wire
of the wire increases. With different amounts and the tension in the wire will change.
A temperature change in the wire also changes its length. If the temperature changes while the wire is unstressed (at zero tension) and the wire is free to change its length, the length changes but there is no change in tension. When the wire is suspended in tension and the temperature changes, the change in length the wire. All changes sags and tensions The conductor changeover the metric
is affected by both the temperature change and the elastic due to ice, wind, and temperature are taken into consideration
in conductors by sag and tension
this method calculation
period, we have both a metric form to which we have added
and item
Item
(1) (2)
(3) (4) (9 (6)
(7) (8)
(9)
Conductor size Conductor code name’ Rated breaking strength’ Diameter,’ mm (in) Radial thickness of ice, mm (in) Wind, kPa (Ib/ft2 ) Loading W’, N/m (lb/ft) W”, N/m (lb/ft)
(10)
Wind, N/m (lb/ft)
(11)
W’
(12)
Area A, mm2 (in2 > Temperature coefficient of linear expansion
(13)
“, N/m (lb/ft)l
of charts and tables. form is shown on figure a U.S. customary numbers to help
13.
characteristics when computing During
form for our use. explain the form:
Figure
the
of
metric 13 shows
Explanation Determined from economic studies
From NESC or State codes From NESC or State codes From NESC or State codes Vertical force (weight) of conductor’ Vertical force (weight) of conductor with ice’ (if applicable) Force of wind on conductor and ice’ (if applicable) Resultant force, including applicable constant if NESC loading’ Cross sectional area of conductor’ Change in length of conductor due to temperature change’
CHAPTER
II-CONDUCTOR
Item (14)
Final modulus E, GPa (lb/in2 )
(15)
Initial modulus E, GPa (lb/in2 )
(16)
Final AE, N (lb)
(17)
Initial AE, N (lb)
(18)
Span length, m (ft)
(19) (20) (21)
Thickness of ice, mm (in); and force of wind, kPa (lb/ft2 ) Temperature, OC (OF) Tension, N (lb), initial
(22)
SW, N (lb) (two decimal places)
(23) (24)
SW/T (four decimal places) SW/AE (seven decimal places)
(25)
Unstressed length (six decimal places) Permanent set and creep’ (six decimal places) Unstressed length at -18 OC (0 OF) (six decimal places)
(26)
(27)
(28) - (3 1)
Unstressed length (six decimal places)
SAGS AND TENSIONS
31
Explanation Slope of final (unloading) curve of stress-strain diagram’ Slope of initial loading curve of stress-strain diagram’ (average slope between maximum loading and point where entire conductor starts to assume loading) Product of conductor area (12) and final modulus ( 14) Product of conductor area (12) and initial modulus (15) Length of span for which computations are to be made For full-load condition For full-load condition Expected or desired tension at full-load conditions (Must not exceed 50 percent of ultimate strength of conductor. May be limited by 33-l /3 percent of ultimate strength of conductor for no-load initial conditions, or 25 percent of conductor ultimate strength for no-load final conditions. At temperatures indicated on fig. 1). Span length (18) times resultant force per unit length of conductor (11) SW (22) divided by full-load tension (21) SW (22) divided by initial AE (17) From Copperweld charts [ 61 at intersection of SW/T (23) and SW/AE (24) values
If value of unstressed length is for initial condition, then only a change for temperature, number of degrees change times temperature coefficient of linear expansion (13), need be made. However, if the value for unstressed length is to be for the final-condition, then it will also be necessary to add the permanent set and creep to the value of unstressed length (25) Change in value is equal to the degrees of temperature change times temperature coefficient of linear expansion (13)
TRANSMISSION
32
LINE DESIGN
MANUAL
Item (32) (33) (34) - (38)
Explanation
SW, N (lb) (two decimal places) SW/AE (seven decimal places) SW/T (four decimal places)
(39) - (44)
Sag factors (interpolate to five decimal places)
(45) - (50)
Sags, mm (ft) (two decimal places , if in feet) Tensions, N (lb)
(51) - (55)
’ Available from manufacturers’
Span length (18) times unloaded conductor force per unit length of conductor (8) SW (32) divided by final AE (16) From Copperweld charts [ 61 at intersections of unstressed length values (27) - (3 1) and SWlAE(33) From table at back of Copperweld charts book [ 61, sag factor for each value of SW/T (23) and (34) - (38) Span length (18) times sag factors (39) - (44) SW (22) and (32) divided by SW/T (23) and (34) - (38), respectively
catalogs or data in appendixes.
Figure 13 can be used for any combination of ice, wind, and temperature conditions to find the resulting sags and tensions in a conductor. The procedure is the same for all cases, but one must be sure of the basic data and to keep in mind whether initial or final conditions are being computed.
for
13. Preparation a specified loading
lengths, profile survey locating sag and conditions
catenary
356used
span
and
longer
of structures on plan-profile drawings. The data required to prepare a sag template tension values of the conductor at the ruling span length for the temperature and desired. These basic sag values can be computed and extended to corresponding longer in this
span lengths by chapter. Whatever
The tension values catenary parameters, relations.
by 0.635-mm for plotting
and also a curve
span
The the
template
is made
temperature
final sag values. loading conditions.
to the sag values of the ruling be known in order to expand on
a transparent
(lo- by 14- by 0.025- in ) size. plan-profile sheets, represents
at an assumed
minimum
curve
is plotted
or
are the loading values
either the parabolic or catenary relations, or by any of the method used should be governed by the limitations of that
corresponding which must
at 49 OC (120 “F) or 54 ‘C (130 “F), maximum sags. The minimum temperature 1 ‘C (30 “F) and minus 51 ‘C (-60 minimum
ruling and
and the resulting sag values plotted against the corresponding span lengths-a conductor curve results. When this curve is plotted to the same scale as a transmission line plan-profile drawing, it is commonly called a sag template and can be used to facilitate the spotting
for shorter and methods shown method. compute
If sag values for a conductor at a specified of Sag Template.are expanded to give corresponding values of sag at shorter
sheet
The template, the conductor
from
initial
Figure 14 shows’a sag template Changing any of these specified
of plastic
approximately
temperature template,
curve, if desired,
be drawn for any temperature on locality and climatic
sag values, prepared conditions
and for
254-
by
made to the same scales that were profile curve at 15.5 O C (60 O F),
temperature. A maximum may also be drawn on the curve may OF), depending
span are required only to the basic sag values by the
the other
curves
usually taken for checking
between conditions. are plotted
minus The from
a specific conductor under specific would change the shape of the curves,
CHAPTER DCm-578
II-CONDUCTOR
SAGS AND TENSIONS
(3-73)
!yT:ALL SAG CALCULATIONS (1)
CONDUCTOR Rated Breaking Tension
Lmear Force Factor:
(3)
Strength
Dfalmlero
N
L~m~tat~one.
_cs,
mm ice (W”)
(6)
kPa Wmd
Imtial.~,-?&%--N
Resulranr
Oc
25
h -N
Loaded.v.A% Flnal.15.5’
N
o.oal
Permanent Set 0.00 Creep 0.00
N/IT
Total 0.00
0
1TEMP../ oc UNSTRESSED LENGTH
Modulus. (E) FInal (14)
(13)
lmtlal
Exp.: Final AE
PdC
I
18)
(24)
j
!
49 mm Ice kPa Wind (W”‘)
(25)
SAG, mm
SW,N
]
/
I
(45)
(22)
TENSION, N
(51)
I
(29)
/
(36)
(30) 31
I
(37)
(521
33 SPANLENGTH(S)
50
(53) (54) 55)
32
m I
I
/
-13 -1 15.5 32 49
SPAN LENGTH(S)
mm Ice
m
No Ice. No Wind (W’)
No Ice. No Wind (W’)
m
SPAN LENGTH(S)
mm Ice kPa Wind (W”‘) Permanent Set IL Creep
No Ice. No Wind (W’)
N
(21)
(33)
(
h Creep
No Ice. No Wind (w’)
GPa N
m (39,
(23)
AE
Gpa
(15) (16) (17)
(26)
15.5 32
)
SAG FACTOR (
f
I
SPAN LENGTH(S)
-1i No Ice. No Wind (W’)
ifi
(26)
N/m
lnllial
Ice
Set
(II)
(W”‘)
N/m N/m
Date -
kPa Wind (W”‘) j(20) Permanent Set 6 Creep 1 1-13
Permanent
(IO)
Temp. Coeff. of Linear
.-%-
LOADING (19) -mm
(9)
Area (A)(12)m&
-N
Computed by
(8)
Dead Load Force (W’)
mm
Final.
(7)
LOADING
(2)
Code Name
I I 1 I
-13 -1 15.5 32 49
Figure
13.-Explanation
of standard
sag and tension
calculation
form.
I -
---
TRANSMISSION
34
LINE DESIGN MANUAL
SAG TEMPLATE 242mm2(477kcmil) ACSR 24/ 7 Ruling Span =213.4m (mft) Maximum Tension 532 472N (7300 lb)=42% ultimote strength NESC Heavy Loading=13-mm($-in)ice,O.lS-kPa(4-lb/ft*) wind + K ot-I8 Scales: Horlzontal 25.4mm -61m (I in = 200 ft) Vertical 25.4mm = 12.2m( I in =40 ft)
I
12.2m 1 (4011)
305
244
(1000)
(800)
.
\
I
\
le.3 (600)
they would the minimum
h
122 (400)
Figure
and and
I
0 meters
14.-Typical
I
61
122 .._-
construction.
requirements
this specific job. The 15.5 no-load” curve are plotted
I
104-D-1054.
’ C (60 OF) “final no-load” curve in the center of the template, and The 15.5 ’ C final no-load curve the plastic material between these two curves should be cut away. is used for plotting the conductor location on plan and profile drawings because this is the temperature which are identical to the 15.5 ‘C curve, used as a basis for NESC clearances. Clearance curves, are drawn below the 15.5 ‘C final no-load curve. The amount of clearance is determined from the following
no longer be good for temperature “initial
sag template
I
OC(O OF)
of NESC:
Assume line voltage Plus 5 percent overvoltage
115
kV
5.75
120.75 kV Maximum line voltage 120.75 69.7 kV Line to ground = n Assume 2 13.4-m (700-ft) ruling span. Clearance from NESC, 1977 edition, Rule 232:
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
232.A. Basic clearance Table 232-l) Basic clearance for 50-kV, 53.3-m span, in heavy loading area where equipment ating height is less than 4.3 m (14 ft) . . . . 232.B. Additional clearances 232.B. 1. Voltages exceeding 50 kV 232.B.l .a. Plus 10.2 mm (0.4 in) for each kilovolt 10.2 (69.7 - 50) = 201 mm %
(69.7
- 50)
(175-ft) oper. . . . . .
Clearance 6706 mm (22.0
ft)
above 50 kV
ft . . . . . . . . . . . . . . . . . . .
= 0.66
35
201 mm
(0.66
ft)
18mm
(0.06
ft)
232.B.l .b. Additional clearance calculated in 232.B. 1.a. shall be increased 3 percent for each 304.8 m (1000 ft) over 1005.8-m (3300-ft) elevation. Assume an elevation of 1920.2 m (6300 ft): 1920;ii ioo5a8 (0.03) (201) = 18 mm 630;o;;300
(0.03)
(0.66)
= 0.06
ft . . . . . . . . . . . . .
232.B.2. Sag increase 232.B.2.c. Span is longer than 53.3 m (175 ft). Assume line operates below 49 OC (120 OF). Calculate clearances in 232.B.2.c.( 1) and (3), use smaller clearance of the two. 232.B.2.c.( 1) Clearance specified in table 232-l shall be increased 0.03 m (0.1 ft) for each 3.05 m (10 ft) over 53.3 m (175 ft). 213j4i553e3
(0.03)
= 1.57
m
7o01; 175 (0.1) = 5.25 ft 232.B.2.c.(3) Limits Assume difference in final sag at 15.5 OC (60 and49 OC(120OF),nowind= 1.2m(4ft) Total clearance required by NESC . . . . . . 6706+201+18+1219=8144mm 22 + 0.66 + 0.06 + 4 = 26.72 ft Plus, for width of profile line on drawing and in plotting . . . . . . . . . . . . . . . . . . Total ground clearance on sag template . . .
For lines in California, a 54 ’ C (130 ’ F) final and for locating the structures instead of the 15.5 be in accordance The sag template calculation sheets,
with
reference
1219 mm 8144 mm
(4.0 ft) (26.72 ft)
small errors . . . . . . . . . . . . . . . .
8754
610 mm mm
(2.0 ft) (28.72 ft)
no-load ’ C (60
curve should be used for the sag template ’ F) final no-load curve. Clearances should
[l].
shown on figure 14 was made figures 15 and 16:
15.5 ‘C (60 “F), final, Minus 40 ‘C (-40 OF)
OF), no wind, . . . . . . . . . . . . . . .
no-load initial,
sag for 213.4-m no-load sag for
from
the
(700-ft) 213.4-m
data
ruling ruling
indicated
on the
span span
= =
4874 2243
sag and
mm mm
tension
(15.99 (7.36
ft) ft)
36
TRANSMISSION
DCm-576
LINE DESIGN MANUAL
(3-73)
;llNT;;'
SAGCALCULATIONS
LOADlUG Linear
Force Dead
13
Factor
Load
Force
8.
(W’)
a=kPa
W,“da.
Area
(A,~ammi!
Temp.
Coeff.
0.000
No Wind
Set 0.004
,“:
27 I 3450
Nlm MOduIus.
01 Linear
(E)
Final
Exp.:
p.
d03
GPa
In,tml_5-j,mGPa
0 ~J.&$.fLyl/wrQC
Final
AE
/?
gm
lnttlal
AE
15
2.31
N 252
N
15.-Sag
and tension
calculation
form for example
problem
on sag template
(metric).
(3-78)
krm;/
CONDUCTOR g,?? Code
Permanent
(W’)
Figure
DC-570
N/m
Rdd
Resultant (W”‘)
NO Ice.
f6ff?
mm Ice (N”)
$-/!fL
v7
hdb?
LOADING -kJ+--
F/!&k
Name Rated Diameter
Weight Load =;7
Breakmg /7.
Tenston
280
lb
Final.
Final. Computed
Ice lb
‘AL d
%
673.4
-zT
% e$!&?&
lb
Area
OF
50
% 9Lofl
lb
Temp.
-f&L+
18
% &.2&m
lb
LOADING
0.000
Date ! “o”“‘t
lmd
UNSTRESSED LENGTH
(Al
0 /o
B-
D
No Wand
Inch
D. (W”‘)
87L
.I,
7
Ltnear
o.oo~r/48-~
)b/ft
Total
O.OOC&?&2.-
Modulus.
(E)
Final/O,53 lnrtral
Exp.:
per OF
v
Set O.OOCX-&2creep
lb/0
in2 of
Permanent
Ib/ft
SAG FACTOR
;
SAG,R
Final
AE
lnltial
AE
(
x 10s
8./7,?/ 1/
x
SW,Ib
I
16.-Sag and tension
calculation
:E
j
TENSION, lb
%+-FEET
SPAN LENGTI
form for example
problem
on sag template
lb/ln2
106 )b/in2
1/
&
(W’)
Ice.
Figure
lblft
p-f.7
1.
a.
Cc&f.
SPAti LENGTk
NO Ice.
(W’) .e
(W”)
Resultant:
lb
zz&?F
by ___
Weight
+ JIk,,.
Llmttatmns.
In,lial,-&F
Factors
Dead
Inch
Loaded.
SAGCAL,CULATIONS
(U.S. customary).
CHAPTER Using
the
relationship
from
II-CONDUCTOR
section
SAGS AND TENSIONS
37
8,
sag,
sagRS -= UW2
C$an,
j2
where, SagRs = sag in ruling span, mm (in)
Sag, = sag in any other given span, mm (in) = ruling span length, m (ft) span i = span length of any other given span, m (ft)
RS
4.874 m
sagRS
For 15.5 OC final: (RS)Z = sagRS 60 OF final: (RS)~ =
For - 40
= 1 0707 x 10S4m-’
15.99 ft = 3.2633 x 10-5ft-’ (700 ft)2
sagRS
=
-40 OF initial:
(RS)~
Assume values for span lengths sags as shown in table 2.
7.36 ft = 1.502x (700 ft)2 (x),
square
these
Span length
(Span length) 2
horizontally,
m
ft
m2
60.96 121.92 243.84 365.76 487.68 609.60
200 400 800 1200 1600 2000
3 716.12 14 864.49 59 457.95 133 780.38 237 831.78 371612.16
same and
scales 25.4
as those mm
=
multiply
by the
15.5 ‘C (60 OF) Sag
0.4 x 1.6 x 6.4 x 14.4 x :i:::::i5
used
105 lo5 lo5 10:
on the
m or
m
mm
0.398 1.592 6.366 14.324 25.464 39.788
398 1592 6 366 14 324 25 464 39788
plan-profile
1 in =
template for the span lengths shown in table sag template to permit its use on an entire extremely steep span where a special catenary
Kvalues
to obtain
the
-40 OC (-40 OF) Sag
K,X2 ft2
12.2
and
=K,
for sag template
x2
x
10-5ft-1
(x2),
Table 2.-Calculations
the
=K,
2.243 m = (213.36 m)2 = 4.9272 x 10-5m-1 =K,
VW2
Using
=K 1
’
sas,S
initial:
OC
(213.36 m)2
K22 m
mm
ft
0.183 0.732 2.930 6.592 11.718 18.310
183 732 2 930 6 592 11 718 18310
0.60 2.40 9.61 21.63 38.45 60.08
ft 1.31 5.22 20.89 46.99 83.54 130.53
sheets
40 ft vertically),
(25.4
mm plot
= the
61 m or 1 in = sag values
on
2. The curves should be expanded far enough transmission line, with the possible exception curve should be used.
200 the
ft sag
on the of an
38
TRANSMISSION Draw
must the but
a vertical
be kept
line
at the center
perfectly
vertical
of the
when
the
LINE DESIGN MANUAL template
(zero
template
span
is being
Clearance (conductor to earth) curves should be located 15.5 OC (60 o F) final sag curve. The clearance curves will
be offset
vertically
,411 curves should maximum conductor be noted
on the
14. inclined inclined
spans spans
it by
the
values
at the will
of clearance
for a reference
for
laying
specified
Spans.-In to some may may
practice,
degree.
get rather be classified
end; and (2) inclined spans falling in the first category
require located
This
distances
to the
final
line line.
below
sag curve
required.
The conductor horizontal and
size and type, vertical scales
the ruling span, used should also
nearly
every
span
of
a transmission
layout be used
to ahnost
is inclined
supported by at the other
purposes
sags and span. Some
vertical,
inclined computed
spans for
or spotting purposes, the ruling span sag template based on without correction. Inclined spans dead-ended at both ends
layout or spotting A series of spans
for stringing
The method used for calculating somewhat on the steepness of the level
spans insulators
which are dead-ended at both ends. Problems concerning usually can be handled by modifying or correcting data
special treatment, even for on extremely steep inclines.
insulator offset calculations (sec. 30(b), ch. V).
line
As might be suspected, the computations for sags and tensions for complex, depending upon the degree of their asymmetry. In general, into two categories for design purposes: (1) inclined spans supported
spans. For structure spans usually may
spans, from extremes.
line.
a transmission
NESC
be identical
by suspension or pin-type insulators at both ends of the span, and inclined suspension or pin-type insulators at one end of the span and by dead-end type
symmetrical symmetrical
out
template.
Inclined
(asymmetrical)
from
be identified on the sag template. tension, NESC loading, and the
length)
used
while
purposes, if they are fairly long spans and are located on extremely steep inclines may require
in order tensions
to get each for
successive
a dead-ended,
span
properly
inclined
span
sagged depends
methods of calculation are good for all dead-ended other methods apply to particular areas between these
For a dead-ended span of normal length and a relatively span with the same horizontal distance between supports on figure 17, the sag D(for this case) is measured vertically
small incline, the calculations for a level may be used. Using the notation shown and is the vertical distance between the
straight
is tangent
line
joining
the
supports
Figure
and
a parallel
17.-Sag on inclined
line
which
span-equivalent
to the
span method.
conductor’s
curvature.
CHAPTER If the
span
is long,
or if there
II-CONDUCTOR
is a relatively
SAGS AND TENSIONS
large
difference
in elevation
39
of the
end
supports,
some
correction should be made in the calculations. Calculations based on the catenary are preferred over those based on the parabola because the conductor conforms to a catenary curve when suspended between
supports-the
of a cateriary as the
The
by using equivalent
level
span. is then
spans Another
sag value.
Thus,
span,
of the
an qrrirulfw/ span the
calculated
as can
the
greater
horizontal
level
span.
span
in the usual
This
be used
as the slope
equivalent
span
equals
manner.
shown
difference
between error
between
method,
alt bough
plus
field the
and =
may
an average
2SI-S.
between The
where w is the conductor linear force factor per unit length.
Figure
Tl + T2 2T, - wH 2 = 2
18.~Sag on inclined
span-average
tension
this
method.
gives
can
be
results
limitations. the slope
sag
span
and
the
D for the equivalent
less than
in the span
18:
portion
11 to be the same
However,
field
be used with tension
comparable
an approximation,
wilhin
T, - T, = wH
Tav=
the
in assuming supports.
difference
(SLS)
method
IIWS
on figure
is some
distance in the
S’ + This
up to 20 percent. gives good results,
11ie notation
the
the sag, there
same
ordinarily
is taken
with an incline method, which Using
the
In computing
span
are as accurate
span for
a parabola.
sag for a level
minimized which
steeper
and
and
I percent
error
has a corrected
TRANSMISSION
40
T,,.
Use ;2lcoa,
and
or other
A method
Zare
and
included
sags
calculation.
Since
for
calculated
various sag by
sags and tensions
was developed
staff. For [S]. A b rte’ f version
a sample
tensions
the
for calculating
of any incline,
as table
and
Correct
of Reclamation
see reference
procedure,
methods.
intended
to spans
Bureau
formulas,
L t to calculate
acceptable
originally
is applicable of the
length
LINE DESIGN MANUAL
by Mr.
a full
discussion
of this the
method
method
conditions the
in steeply
using
Copperweld,
relationship
SL ,/L.
D =
inclined
spans,
but
which
D. 0. Ehrenburg
while
he was a member
of his method,
including
derivations
follows is based
showing
nonmenclature,
on a parameter
2, the
of
formulas, functions
of
3.
Nomenclature and units Metric
U.S.
customary
T, = Te = w = h = V = w’ = S = S, = a = b = c = a’ = b’ = A = E = a = d = 2 =
tension at upper support effective (average) tension of conductor linear force factor of conductor per unit length wind load per unit length of conductor ice load per unit length of conductor (w + v)~ + h2 = resultant force per unit length of conductor actual length of conductor unstressed length of conductor horizontal spacing of supports vertical spacing of supports straight line distance between supports spacing of supports in plane of w’, at right angles to vector w’ spacing of supports in plane of w’, in direction of vector w’ area of conductor cross section modulus of elasticity of conductor coefficient of linear expansion sag of conductor parameter
Necessary given data: Loading conditions (ice, Size, type, and stranding Linear Linear
force force
factor factor
per per
wind, and temperature) of conductor unit unit
length length
of bare of iced
conductor conductor
Force on conductor due to wind Resultant force on conductor Cross-sectional area Modulus of elasticity Temperature Maximum Horizontal Vertical
of conductor of conductor
coefficient of linear tension in conductor spacing spacing
of supports of supports
expansion
for
conductor
N N N/m N/m N/m N/m
(lb) (lb) Wft) Wft) Wft)
m m m m m m m mm2 GPa
w> (ft) (ft) (ft) (ft) WI (ft)
mm
WI
(lb/W
(in2 ) (lb/in2 )
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Table 3.-Functions Z
f0
0.010 ,020 .030 .040 .oso
0.000 016 ,000 066 .ooo 150 .OOO266 .OOO416
67 6 0 7 7
.060 .070 .080
.OOO600 1 ,000 8169 .OOl 067 .OOl 351 ,001 668
.llO .120 .130 .140 .150
.002 ,002 ,002 .003 .003
.160 .170 ,180 .190 .200
41
of Z
coth Z
l/Z
23
100.003 50.007 33.343 25.013 20.017
100.000 50 .ooo 33.333 3 25.000 0 20.000 0
0.000 001 ,000 008 .OOO027 ,000 064 .OOO125
0.000 000 .OOO000 .OOO000 .OOO002 .OOO006
01 16 81 56 25
24
16.687 14.309 12.527 11.141 10.0333
16.666 14.285 12.500 11.111 10.000
7 7 0 1 0
,000 216 .ooo 343 .OOO512 .ooo 729 .OOl 000
.OOO012 .OOO024 .OOO040 .OOO065 .ooo 100
96 01 96 61 0
018 402 819 270 754
9.1275 8.3733 7.7356 7.1895 6.7166
9.090 8.333 7.692 7.142 6.666
9 3 3 9 7
.OOl 331 .OOl 728 ,002 197 .002 744 .003 375
.OOO146 .OOO207 ,000 285 .OOO 384 ,000 506
4 4 6 2 3
.004 .004 .005 ,006 .006
272 824 409 028 680
6.3032 5.9389 5.6154 5.3263 5.0665
6.250 5.882 5.555 5.263 5 .ooo
0 4 6 2 0
.004 .004 .005 .006 .008
096 913 832 859 000
,000 655 4 .OOO835 2 ,001 050 ,001 303 .OOl 600
.205 .210 .215 ,220 .225
,007 .007 .007 .008 .008
019 366 722 086 459
4.9462 4.8317 4.7226 4.6186 4.5192
4.878 4.761 4.651 4.545 4.444
05 90 16 45 44
,008 .009 .009 ,010 .Oll
615 261 938 648 39
.OOl 766 .OOl 945 ,002 137 .002 343 .002 563
.230 .235 .240 ,245
.008 .009 .009 .OlO .OlO
840 230 628 034 449
4.4242 4.3334 4.2464 4.1630 4.0830
4.347 4.255 4.166 4.081 4.000
83 32 67 63 00
,012 ,012 .013 ,014 .015
17 98 82 71 63
.002 .003 ilO3 .003 .003
798 050 318 603 906
.255
.OlO .Oll ,011 .012 .012
873 305 745 194 652
4.0062 3.9324 3.8615 3.7933 3.7276
3.921 3.846 3.773 3.703 3.636
57 15 58 70 36
.016 ,017 ,018 .019 .020
58 58 61 68 80
.004 ,004 .004 ,005 ,005
228 570 932 314 719
.280 .285 ,290 .295
.013 .013 .014 .014 .015
118 592 076 567 068
3.6643 3.6033 3.5444 3.4876 3.4327
3.571 3.508 3.448 3.389 3.333
43 77 28 83 33
.021 .023 .024 .025 .027
95 15 39 67 00
.006 .006 .007 .007 .008
147 598 073 573 100
.305 .310 ,315 .320 .325
,015 .016 .016 .017 .017
576 094 620 154 697
3.3797 3.3285 3.2789 3.2309 3.1845
3.278 3.225 3.174 3.125 3.076
69 81 60 00 92
.028 .029 .031 .032 .034
37 79 26 77 33
.008 .009 ,009 .OlO .Oll
654 235 846 49 16
.018 .018 .019 .019 .020
249 809 378 956 542
3.1395 3.0959 3.0536 3.0126 2.9729
3.030 2.985 2.941 2.898 2.857
30 07 18 55 14
.035 .037 ,039 ,041 .042
94 60 30 06 88
.Oll .012 .013 .014 .015
86 59 36 17 01
.265 ,270 .275
TRANSMISSION
42
LINE DESIGN MANUAL
Table 3 .-Functions z
All
plan-profile
coth Z
l/Z
23
24
0.355 .360 .365 ,370 .375
0.021 .021 ,022 ,022 .023
137 740 352 973 602
2.9343 2.8968 2.8603 2.8249 2.7905
2.816 2.777 2.739 2.702 2.666
90 78 73 70 67
0.043 .046 ,048 ,050 ,052
74 66 63 65 73
0.015 .016 .017 .018 .019
88 80 75 74 78
,380 ,385 ,390 .395 .400
,024 .024 .025 .026 .026
240 887 543 207 880
2.7570 2.7245 2.6928 2.6620 2.6319
2.631 2.597 2.564 2.531 2.500
58 40 10 65 00
.054 .057 ,059 .061 .064
87 07 32 63 00
.020 .021 .023 .024 .025
85 97 13 34 60
.405 .410 .415 .420 .425
.027 .028 ,028 .029 .030
562 252 95 1 659 376
2.6027 2.5742 2.5464 2.5193 2.4929
2.469 2.439 2.409 2.380 2.352
14 02 64 95 94
.066 ,068 .071 .074 .076
43 92 47 09 77
.026 .028 .029 .031 ,032
90 26 66 12 63
.430 ,435 .440 ,445 .450
.031 ,031 .032 .033 .034
102 856 579 331 092
2.4672 2.4421 2.4175 2.3936 2.3702
2.325 2.298 2.272 2.247 2.222
58 85 73 19 22
.079 .082 .085 .088 .091
51 32 18 12 13
.034 19 .035 81 .037 48 .039 21 .04101
,455 ,460 ,465 .470 ,475
.034 .035 .036 .037 .038
861 640 427 223 028
2.3474 2.3251 2.3033 2.2821 2.2613
2.197 2.173 2.150 2.127 2.105
80 91 54 66 26
.094 .097 ,100 .103 .107
20 34 5 8 2
.042 .044 .046 ,048 ,050
86 77 75 80 91
.480 ,485 ,490 .495 .500
.038 .039 .040 .041 .042
842 665 497 338 188
2.2409 2.2210 2.2016 2.1826 2.1640
2.083 2.061 2.040 2.020 2.000
33 86 82 20 00
.llO ,114 .117 .121 .125
6 1 6 3 0
,053 .055 .057 .060 .062
08 33 65 04 50
The loading conditions, other conductor data
manufacturers’
f(z)
of Z-Continued
catalogs.
conductor required The
horizontal
size, and maximum may be obtained and
drawings.
Procedure steps: 1. Determine c from c2 = a2 + b2 2. Determine b’ from 21’= b(w + v)/W’ 3. Determine a’ from a’ = dn
vertical
tension are determined by previous studies. from tables shown in appendix C or from
spacing
of supports
can be determined
from
the
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
4. Determine coth Z from coth Z = 1 +O.l67t$y
(-$)
where : A = T,‘(max) - 0.5 w’b’ 0.5 w’c For short spans,
0.5 w’c
zJ= A
T,‘(max) - 0.5 w’b’
5. From table 3, determine Z from coth Z found in step 4 6. Determine S, from S, = (S-c) + c where
s-c=$f(Z)+Z
24
Find f(Z) from table 3 or from f(Z) = 0.1 67(Z2 + Z4 /20) 7. Determine values for “No-load Chart” a. Assume values for Z (usually two values smaller and three or four values larger than the basic Z value found in step 5) b. Find S-c (from step 6) for each value of Z assumed in step 7.a. c. Determine So (from step 6) for each assumed value of Z d. Determine values for T, and T, by using the assumed values of Z in the formulas: T, = 0.5 w S, coth Z + 0.5 wb, and T, = 0.5 w S,, i 0
+ 0.5 w s,
e. Determine values for d from d = 0.25 cZ + ““;,;“’
Z3 for assumed values of Z
f. Find the slope of the temperature lines from slope equals AE/S, 8. Determine values for “Full-load Chart” a. Find S-c for each value of Z assumed in step 7.a., where smc = (9
f(z)
+ Cd2
@‘I2
z4
72c3 b. Determine S,, for each assumed value of Z, where S, = (S-c) + c c. Determine horizontal spacing of the temperature lines from (Sol) (5.9, for increments of 5..5 OC from minus 7 to 48 OC, or (Sol) (lo), for increments of 10 OF from 20 to 120 OF.
43
TRANSMISSION
44
LINE DESIGN
MANUAL
9. Prepare graph: a. Plot the tensions for the assumed values of 2 against the slack S-c. This will give four curves: T,’ and T,’ for full load, and T, and T, for no load b. Plot sag d against slack S-c on the same graph c. Find the maximum average tension at full-load conditions by drawing a vertical line from the point of maximum tension on the full-load curve T,’ down to the full-load curve T, d. Starting at the maximum average tension point found in step 9.c., draw temperature lines down to the no-load T, curve. The slope of these lines was determined in step 7.e., and their horizontal spacing was found in step 8.b. e. Determine the sag at every 5.5 OC from minus 7 to 48 OC or at every 10 OF from 20 to 120 OF by drawing vertical lines from the points where the temperature lines intersect the no-load T, curve down to the sag curve f. Label all parts of graph Figure
19 shows
\
the
inclined
span
used
for
the
following
example
calculations:
support
a=
m
ft) ft) c = 583.69 m (1915 ft) 545.59
(1790
b= 207.26 m (680
h
WI
w+v
INSULATOR STRING. SWING DUE TO WIND FORCE
Figure
19.-Sag
on inclined
span-parameter
Zmethod.
104-D-10.55.
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Example
Metric
Loading = 6-mm ice, 0.38-kPa wind, at minus 9.4 OC Conductor = 1092 mm’ , ACSR 84/l 9 Bluebird diameter = 45 mm area = 1181 mm* E = 5 1.46 GPa (initial) a = 0.000 020 7 per OC w = 36.6453 N/m h = (45 + 12) (0.38) = 2 1.66 N/m v=9.1314N/m w’ z&36.6453 + 9.1314)2 + (21.66)2 = 50.64 N/m a = 545.59 m b = 207.26 m c = 583.69 m = 18736m
= 207.26 a’ = dc’2_02
= d(583.69)2
- (1 87.36)2 = 552.80 m
A= T,‘(max) - 0.5 w’b’ = 88 964 - 0.5 (50.64) (187.36) = 5 699 0.5 w’c
’
0.5(50.64) (583.69)
A2 = 32.479
coth 2 = 1 + O.l,,;$r
($)=
1 + 0.167 (5G)2(3+9) 5.699
= 5h729
Z= 0.17822 f(Z) = 0.005 305 (0.005 305) +
(545.59j2 (207.2612 (o 178 2214 . 72(583 69)3
= 2.7054 + 0.0009 = 2.7063 S, = (S-c) + c = 2.7063 + 583.69 = 586.40
For “No-Load Table” a = 545.59
0.5 w = 18.3226
c/4 = 145.92
b = 207.26 c = 583.69 w = 36.6453
0.5 wb = 3797.55 a2 lc = 509.98
3a2 - 2b2 = 9 6023 * 144c
a2b2 172c3 = 0.8931
b2 /3c2 = 0.0420
45
46
TRANSMISSION
2 s-c
0.16 2.179 585.87 10 735 71462 67 166 23.39
SO
0.5 ws, T, Ti? d
0.17 2.461 586.15 10 740 67 581 63 254 24.85
LINE DESIGN
0.1782 2.706 586.40 10 744 64 747 60 402 26.06
MANUAL
0.18 2.759 586.45 10 74.5 64 135 59 776 26.32
0.19 3.075 586.77 10 751 61061 56 670 27.79
0.20 3.408 587.10 10 757 58 298 53 875 29.26
0.21 3.758 587.45 10 764 55 806 51 352 30.73
AE/S, = 103 640 “Full-Load Table”
For
a’ = 552.80 b’ = 187.36
0.5 w’ = 25.32 0.5 w’b’ = 4743.96 (u’)~ /c = 523.54 (a’)? (b’)* /72c3 = 0.7492
c = 583.69 w’ = 50.64 Z s-c
1
SO
0.5 ws, T,’ Te’
0.16 2.237 585.93 14 836 98 258 92 806
0.17 2.526 586.22 14 843 92 895 87 399
AS = &x(5.5) = 586.47(0.000 Results of these from nlinus 9.5 U.S.
0.1782 2.778 586.47 14 849 88 981 83 459
0.18 2.833 586.52 14 851 88 138 82 598
metric calculations to 48 o C.
are shown
on figure
20 along
Loading = l/4-in ice, 8-lb/ft2 wind, at 15 OF Conductor = 2 156 kcmil, ACSR 84/ 19 Bluebird diameter = 1.762 in area = 1.83 10 in2 E = 7 463 320 lb/in2 (initial) a = 0.000 011 5 per OF w = 2.511 lb/ft h = 1.762 + 0.5 (8) (1) = 1.5080 lb/ft 12 v = 0.6257 lb/ft w’ = x/(2.51 1 + 0.6257)2 + (1 .5080)2 = 3.480 lb/ft u= 179oft b = 680 ft c= 1915 ft
a’ =,/m
3(~‘)~ - Zb’12 = 1o o7 144c (b’)2 /3c2 = 0.0343 0.19 3.157 586.85 14 859 83 887 78 303
0.203.498 587.19 14 868 80 073 14 442
0.21 3.858 587.55 14 877 76 62.5 70 950
020 7)(5.5) = 0.066 77
Grstoniarv
b’=b(y)
c/4 = 145.92
=680($$)=612.918ft =&19;5)2
- (612.918)2 = 1814.265 ft
with
initial
sags for temperatures
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Temp. Sag (“Cl (m) -9.5 24.8 -7.0
25.0
90 000
In {
80 000
Ec zi 5 z
70 000
k
60 000
3
SLACK (S-c), Figure 20.-Results 104-D-1056.
of example
problem
on
an inclined
meters span using parameter Zmethod
(metric).
48
TRANSMISSION
A=
T, ‘(max) - 0.5 w’b’
LINE DESIGN MANUAL
= 20 000 - 0.5(3.480) (612.918) = 5.682 0.5(3.480) (1915)
0.5 w’c
A2 = 32.286 ’
coth 2 = 1 +0.167 A3 O( Z= 0.178 75 f(Z) = 0.005 336
=
2
i2
>
1 +0.167
(‘8;;;2565)2 5.682
(0.005 336) +
(179o)2
(j&)
= 5’6558
(680)2
72(1915)3
(0.178
7514
= 8.9280 + 0.002 99 = 8.93 10 so = (S-c) + c = 8.9310 + 1915 = 1923.93 For “No-Load Table”
Z s-c
a= 1790
0.5 w = 1.2555
c/4 = 478.75
b = 680 c = 1915
0.5 wb = 853.74 a2/c= 1673.16
3~’ - 2b2 = 31 5. 144c .
w = 2.511
a2 b2 /72c3 = 2.93
b2 /3c2 = 0.04203
I
so 0.5 w&J Tl
Te d
0.16 7.15 1 922.15 2 413.26 16 135 15 099 16.73
0.17 8.10 1923.10 2 414.45 15 193 14 220 81.54
0.1788 8.93 1923.93 2 415.49 14511 14 093 85.781
0.18 9.05 1 924.05 2 415.64 14 419 13 439 86.36
0.19 10.09 1 925.09 2 416.95 13 727 12 740 91.18
0.20 11.18 1926.18 2 418.32 13 106 12 112 96.00
0.21 12.33 1 927.33 2 419.76 12 545 11544 100.83
AE/S, = 7 100 For “Full-Load Table” a’ = 1814.26 b’ = 612.92 c= 1915 w’ = 3.480 Z S-C so 0.5 w’s0 7.1’ Te’
AS= &(lO)
0.16 7.34 1 922.34 3 344.87 22 150 20 924
0.5 w’ = 1.740 0.5 w’b’ = 1066.48 (a’)2/c = 1718.82 (u’)~ (b’>2 /72c3 = 2.45 0.17 8.29 1 923.29 3 346.52 20 941 19 705
0.1788 9.17 1 924.17 3 348.06 20 003 18 758
1 3 19 18
= 1924.17(0.000 011 5) (10) = 0.2213
0.18 9.30 924.30 348.28 868 622
c/4 = 478.75 3(a’>2
-
2(b’12
=
33
o8
144c (b’)3 /3c2 = 0.034 15 0.19 10.36 1 925.36 3 350.13 18 910 17 654
0.20 11.48 1 926.48 3 352.08 18 050 16 783
0.21 12.66 1 927.66 3 354.13 17 273 15 996
CHAPTER Kes~~lts 15 to
120
of these
calculations
II-CONDUCTOR
are shown
on figure
SAGS AND TENSIONS 21 along
with
initial
49
sags for temperatures
from
OF.
22
20
000 I
\\ !
T
TL \ 000 I
10 000
Temp. (OF)
Sag (ft)
70 80 90 loo 110 120
81.2 81.75 82.75 83.7 84.6 85.5 86.4 87.3 88.25 89.2 90. I 91.0
t--
T
16 000 I--
:: El 0 0.
c
I
\Tr !!E
14 000
000
000
000 8
I
0
SLACK Figure 21.-Results
of example problem
on an inclined
I
IO
9
(s-c).
II
._
IZ
.-
I3
feet
span using parameter
Zmethod
(U.S. customary).
104-D-1057.
50
TRANSMISSION 15.
Galloping
Conductors.-
LINE DESIGN MANUAL
A galloping
conductor
is a phenomenon
usually
caused
blowing on an iced conductor. relatively light wind of about 48 to 56 km/h (30 to 35 mi/h) may be in the form of either rime or glaze. A few cases of galloping conductors without the of ice have
been
In 1930,
Mr.
noted,
but
A. E. Davison
the In
by the
reaction
lifting force. 1932, Mr.
instructor
at Harvard
temperature will melt
are extremely
of the Hydroelectric
of wind
J. P. Den
formation which, of aerodynamic
cases
and
Hartog,
Power
Commission
School,
conductor, An airfoil
of about 0 ‘C (32 a portion of the radial
and a periodic
noted
Engineering
with the stability.
glaze,
OF) ice,
research presented
sun will
a theory cross may
has published is the
result
several of the
with
Westinghouse
that
sag of the conductor
galloping
increase)
than
the
articles
conductor
on the
which Electric
lift controls and
CO.
was the result
of a glaze
and a light and around
wind is blowing. the conductor,
type
The sun and then
shade at the bottom of the conductor where takes shape and the possibility of galloping
at 0 OC (32 OF), with
resultant
presented
aerodynamic
13 mm (l/2
conductors, This method
in) of ices and a wind
of 48.3 km/h (30 mi/h) or a wind pressure of 0.096 kPa (2 lb/ft2). This approximates condition under which most cases of galloping have occurred. The path of conductor approximates a loop of elliptical shape. The major axis of the ellipse is slightly larger uses a 6 percent
presence
capable of causing a certain be formed at a freezing-thawing
conductors becomes very real. Based on numerous observations and on several motion pictures of galloping developed an empirical method for determining the conductor oscillation path. on the stabilized
Canada
of the conductor
section easily
is shining run down
the water will be blown back by the light wind into the it will again freeze. As this process continues, the airfoil
of Ontario,
twisting
engineer
has an airfoil cross section when the the water
a ice
rare.
and work on galloping conductors, Mr. Davison suggested that galloping
the results of his pioneer subject since that time. produced
these
by The
sag under
the
loading
Davison is based velocity
the loading oscillation (the Bureau
condition
described
above, and is inclined from the vertical in a direction by an angle equal to the angle of sideswing. In level a small distance above the normal level of the points
opposite the direction of the conductor sideswing spans, the highest point of the full ellipse is only of attachment of the conductor to the insulator
string.
overhead
not
As long
overlap,
as the
ellipses
galloping
will
in which
the
for all conductors not
and
ground
wires
of a transmission
the conductors to come in contact with each other overhead ground wires. Contact would re’sult in outages and possible damage to the Observations of lines with long spans and heavy conductors indicate that the conductors
in two
loops
cause
magnitude
of oscillation,
or size of ellipse,
is approximately
line
do
or with the conductors. may dance half
size; that
is, the major axis of the ellipse is approximately one-half of the total conductor sag in the span. Application of this method to several existing lines, in regions subject to sleet conditions, has shown that those lines with sufficient ground wires to prevent overlap
spacing of the
between ellipses,
conductors and between had no outages under the
conductors and sleet conditions.
overhead The lines
that showed an overlap of the ellipses had a record of many outages under sleet conditions. There have also been observations where iced conductors have galloped in a manner similar to a skip rope being turned, with the midpoint rising as far above the points of support as it hangs below those points when at rest. This a designer cannot There ellipses.
* For
NFX:
sort of galloping is rare, fortunately, economically be expected to meet.
is no definite However, our
heavy
loading
because
clearance
limits
are indicated
which
length of span where galloping will change from full-sag ellipses to half-sag experience indicates that for our line locations and conditions, we should use
area.
CHAPTER full-sag
ellipses
to gallop
in spans
in two
be used.
and
ground
overhead Experience
the ends
a weak
To
spot and
determine
the
wires
to prevent
ground conductors structure
and with
that
spacing
required
ground
wires, and
1. For loading conditions a temperature of minus 1 ‘C for the given span length. a. Figures 22 and conductor, and figures steel, 7-wire overhead
the
wear of time.
all hardware
conductors
a particular
hardware,
24 and ground
25 show wire.
b. From the calculations on conditions conducive to galloping,
the
and
between
For
a 289.5-m
(950-ft)
s p an, based
on the
wires,
proceed
span
ordinarily in relatively and
length
overhead with
span
for
given a given
as follows: (2-lb/ft2) wind pressure, and overhead ground wire
based on a 213.4-m for a 242 mm2 (477 for a lo-mm
a 213.4-m
(700-ft) kcmil) (3/8-in)
(700-ft)
ruling
and sags
ruling ACSR
span. 24/7
high-strength span,
and
for
sag WI
5255 4386
213.4-m
conductors
check
If galloping
failure
permissible
for
carefully
vibrations,
cause
maximum
mm Conductor Overhead ground wire
can
the
sag calculations
these figures, the sags are:
very
and
span
of
conductors
occurred.
wind
and
of 13 mm (l/2 in) of ice,3 0.096-kPa (30 OF), d e t ermine the conductor
Assume a 289.5-m (950-ft) 23 show the sag calculations
and
condition
or to determine
are likely
to 53 percent
between
to have
spot
loading ground
conductors equal
of contact
is known
in the
period
the axis
reduced.
galloping weakened
overhead
spans, major
the probability
on the between
for
longer
to examine
or excessive
contact,
In with
is greatly
where
in a short
conductors
overlap,
practice
of a line
concentrate
possibly
in length.
of galloping,
in a conductor
overhead given
do not
51
SAGS AND TENSIONS
size ellipses,
it is good part
a failure,
weather
ellipses
as a result
in any
ft)
so one-half
If these wires,
clamps
in producing
moderate
loops,
has shown
of the
has created slow
up to 183 m (600
or more
the sag, should
II-CONDUCTOR
(17.24) (14.39)
ruling
span,
the
sags are:
sag Conductor Overhead ground wire 2. Determine loading conditions
0, the given
angle in l.,
a. Conductor B = tan-l
of sideswing, and
using
heavy loading
area.
the force
(ft>
9675 8075
(31.75) (26.50)
conductors triangles
4.4898 N/m 21.186 N/m Or
b. Overhead ground wire 13= tan- l 3 For NEST
for the
mm
3.3079 N/m 11.777 N/m Or
and shown
overhead on figures
= 1 lo 58,
ground
wires
for
the
22, 23, 24,
and
25.
52
TRANSMISSION
DCm-576
LINE DESIGN MANUAL
(S-78)
Ltnear
Force Dead
Area Temp. 0.000
NO Ice.
No Wind
Figure
Factory
Load
Fwce
(W’) Creep
0.000
Jag
Total
O.CO,!
003
(A).arn& C&f.
01 Llnear
Exp.:
0 /9peperOC
(W’)
22.-Conductor
sag and tension
calculation
form
for example
problem
on galloping
conductors
(metric).
CHAPTER
II-CONDUCTOR
;;;tL
SAGS AND TENSIONS
53
SAGCALCULATIONS
LOADING
.d-
Vv
Weight Factors: Dead Weight (W’) + hn. 5i
ICY (w”) lb Wind Resultant:
0. L 14%
lb/f1
D, L/53
tb,tt lb/l1
e/. (W”‘)
‘F
LOADING
UNSTRESSED LENGTH
Inch Ice.
Creep o.ooa*-Total O.ooa
I.lb/ft Modulus. (E) Final/D,fl Initial&@/-x FinaIM { ~~~ Initial% 3 &q
Area (A) &&.%k in2 Temp. Coolf. of Linear Exp.: 0.004 o/k
Permanent set 0.00
per OF SACFlCTOR 1
i! 6 I SPANLENGTH(S) AFEET
SAG,H
1 SW,lb
x 106 lb/in2 106 lb/i&? -lb /I/ lb
1 TENSION,lb
NO Ice. No Wind (W’)
Llb/ft2
SPANLENGTH(S)
-FEET
calculation
for example
Wind(W”’
No Ice. No Wind (W’)
Figure 23.-Conductor customary).
3.
Construct
at an angle The major to one-half method,
sag and tension
half-sag
of 28 from
ellipses the
plane
as shown
form
on figure
of the conductor
26.
when
The the
problem
major 0.096-kPa
axis of the ellipse is equal to one-half the sag plus 6 percent, of the major axis. The easiest way to construct the ellipses which
is explained
in numerous
drafting
or related
texts.
on galloping
conductors
axis
ellipse
is inclined
wind
is blowing.
of the
(24b/fta)
(U.S.
and the minor axis is equal is by the use of the trammel
TRANSMISSION
54 DCm-578
LINE DESIGN -
(3-78)
;;;pL'
llkili
CONDUCTOR,f&mm Code
MANUAL
,/d’!‘c %ei:
?-W/b
SAG CALCULATIONS
LOADIME &a+----
Name
Linear
Rated
Breaking
Strength
olamerer~22&!5L Tension
18
&o
N
mm
kPa
l”~tl~l.-~%,-&-%~N
.-a%
%a!.2
0/o
N
50 -%2o-zoN
F,nal.~%.
/g
O’o g
by
Dare
AL/?
Temp.
Co&f.
o.cm
6.
L/L
N/C?7
17, 88 L5
Ice.
NO Wmd
ground
FIMI
w
GPa
Inttlalfig*5
0 //pePc
Fanal
SAG FACTOR
?
wire sag and tension
9
AE
GPa
Lf? 924
AE k
SAG,mm
:
77
E
SW,N
:
TENSION, N
m
calculation
form for example
problem
on galloping
conductors
(3-78)
!;,fL
/t
CONDUCTOR3 f Code
00
Q
O.C%.&
(W’)
Figure 24.-Overhead (metric). DC-576
(E)
Exp..
SPAN LENGTH(S) 2 1.3. 36
NO
0.00
N/m
lnltial LENGTH1
o.ooo*
Total
Modulus. of Linear
SW E
ser creep
-
/TEMP. ; oc “UftSTRESSEO
LOADING
N
(A)Amm2
Permanent
N/m
(W”‘)
Area
N/m
(W”)//.
W Ind
Resultant 25
(W’I m,&?8j
ForC2
mm Ice
od$&i?
Fmal.&C.
Computed
Factor.
Load
A
Llmltatlons
Loaded
Force Dead
i/i!?
.?tee(.
7--w/ re
LOADlNG -LM Welghl
Name Rated
SAGCALCULATIONS
Breaking
Diameter
Load
m
Factors:
Dead
/nib Inch
Wetght
+ L”.
Ice lb
A
(W’) m,73
Resultant: Area
(A)
o.ooo [TEMP.. oF /UNSTRESSED LENGTH
LOADING
No
Ice.
NO Wind
Gc7fl,iis
-lb/@ Permanent
Inch
/)
5.D79
226
ou
creep
0.006--
Ib/ft
Total
O.OO+
Ib/ft
In2
of Linear
Permanen~OO~
Ib/ft
Modulus.
per ?=
SAG FACTOR
Y
B
(E)
Exp.:
1
Final~x
106
lb/in2
lnttlaf~ox
106
lb/in2
Final
AE d!
fb
lntttal
AE
tb
SAG.11
/
1 TENSION, lb
SW,lb
(W’) 120
//3
(W’“)
Coeff.
453
0.
Wind
TemD.
Iblft
5.967
(W”)
lo.999
764 b.am
Qq? 51 0. J/L?
lo&z.
967
~9-7
In.o/L
WindW”“i3o
Figure 25.-Overhead (U.S. customary).
51
m
97
/ 2 ,229 I 14f. I I
/437
1.3 1
I
f/.24
JqQS
V.
/+f.JP
1
/4/.
I
1
S
~6
SPANLENGTH(S).-FEET
Ice.
Set & creep
l,g,dnn
o.
994
373
IO, 000
llp7
51
0.
/630
1
I
ground
wire sag and tension
calculation
form
for example
problem
I
5%
,
on galloping
conductors
FAal
CHAPTER II-CONDUCTOR Type HS Structure 289.5-m (950ft) Span Based on 213.4-m (70%ft) ruling span 3658-mm (12-ft) Pole spacing NESCHeavy Loading Conductor ful I- load tension = 33 362 N (7500
Conductor:
242
mm*
Sag Half sag +6%
Major axis Minor axis
lb)
OGWful I- load tension =2l 418 N (4815 lb) Half-sag ellipses
SAGS AND TENSIONS
OGW:
8= ll”58’ IO-mm (i-in)
2 9f sag +6%
Major axis Minor axis
(477 mm 9675 4835 290 5128 2564
55
kcmil\fPjCSR.
24/7
(3.35) (15.88) ( 0.95) (16.83) ( 8.42)
H.S. Steel Cf_t) mm 8075 4038 242 4250 2125
(26.50) (13.25) ( 0.79) (14.04) ( 7.02)
8 = 15’ 42’ 4023 (13.2
Figure 26.-Half-sag
ellipses for example
problem
on galloping
mm ft)
_
conductors.
104-D-1058.
TRANSMISSION
56 16.
Broken
conductor
Conductors.-The
is important
condition
with
crossings;
structures.
The
the
of the
nature Using
given
this
work
requirements
and
also
computation
over
from
of sags and
from
the
the railroad,
waterway,
of determining
tensions
under
in spans
of assuring
highway,
standpoint
of sags and
tensions
standpoint
this
to a broken under
communication
the
condition
adjacent
compliance unbalanced
is somewhat
this
line, loads
and
on the
complex
due
to
variables.
a technique in
determination
in design
clearance
powerline
LINE DESIGN MANUAL
by G. R. Wiszneauckas
section
for
a 345-kV
shown
in appendix
transmission
line
span
A, a broken over
conductor
Interstate
Highway
problem
is
No.
25
(Sta. 789 + 95 and 790 + 83) and the Colorado and Southern Railroad crossing (Sta. 795 + 48), both located in Colorado. Figure 27 shows the profile portion of the plan and profile drawing for this example
problem.
Please
note
that
this
figure
is predominately
in U.S.
customary
references to this figure, such as stationing, are also in those units. The conductor as 644 mm2 (1272 kcmil), ACSR, 45/7 stranding, with a full-load (NESC heavy) (13 800 lb). Assuming a broken conductor in the span on the at Sta. 797+30, the ruling span for the three remaining spans to be 320.95 m (1053 ft). At 49 OC (120 “F) f’ma 1 conditions,
AE d HO HI LJ Ll
P s s
basic
nomenclature
used
of cross-sectional
Product
Horizontal displacement of insulator string Initial horizontal tension in conductor Horizontal tension in conductor after a change
= =
Length Initial
= =
Final span Horizontal
= =
of insulator span length length force
caused
Force Force
(weight) (weight)
W 8 4
= =
Total Angle
vertical load, of deflection
=
Change
The
resulting
values
indicated
-
2.110
+
problem
are
and
modulus
of elasticity
of the
of 4 in span
conductor
length
by
Wwhen
the
insulator
string
is deflected
by an angle
8
string acting
W = w l/2 of insulator
on insulator
string
+ w2 string
length
by the curves show the suspension insulator string on the structure string on the structure at Sta. 787 +00 2 110 mm (83 in), and the insulator (37.5 in). This will result in a new span length of 312.789 m (1026.21 ft) 6.92 + 3.13 = 1026.21 ft]. The 24 310-N 0.955 = 312.789 m, or 1030 -
at Sta. 797 + 30 will deflect will deflect about 955 mm [313.944
example
sag in conductor span length of conductor
of insulator of conductor
in span
in this A.
string
=
w2
area
has been assumed tension of 61 385 N
is:
= = =
= =
Wl
section
=
General symbol for General symbol for Unit force (weight)
W
in this
therefore,
northwest side of the steel structure to a dead-end structure is calculated the tension for this ruling span is
24 310 N (5465 lb), with a corresponding sag of 11 211 mm (36.78 ft). The calculations, tables, nomenclature, and broken conductor curves all in accordance with the broken conductor thesis ‘shown in appendix The
units;
CHAPTER (5465~lb) the
expanded been the
tension
conductor
to make
shown
figs.
28 and
in the
the
as a dashed
adjacent
29) is used
adjacent
sag curve curve
for
span. plotting
on figure
to compute
The
I.-Broken
Highway
the
calculated
on the
corresponding
sag is 15 736
plan-profile.
27 to indicate
the
The
expected
centerline
(Sta.
789 +95
and
result
790+83)
795 + 48)
Ruling span =
where
S =
span
length.
Metric
s, m
S3, m3
304.373 341.376 3 13.944
28 198 004 39 783 130 30 942 582
959.693 m
98 923 716 m3
Rulingspan=dz=321.
058m
U.S. Customary
s, ft
s3 ) ft3
998.6 1120 1030
995 805 877 1404928 000 1092727000
3 148.6 ft
3 493 460 877 ft3
Ruling span =dw=
sag in this mm
sag in the
Conductor Calculations
centerline (Sta. Span Calculations:
59
SAGS AND TENSIONS
span.
Example
Railroad Ruling
(from broken
II-CONDUCTOR
1053.34 ft
(51.64
ft)
crossing
of a conductor
span which span break
with is has in
TRANSMISSION DCm-576
LINE DESIGN MANUAL
(3-78)
f;;LL
SAGCALCULATIONS
LOADMG Linear
VY
Force
maa -Lz oa
Factor,
Load
Face
kPa
//.
Wtnd
(W”‘)
(A).zm&
Temp.
Co&f.
TEMP..1 oc UNSTRESSED LENGTH
LOADING Lmm
O./q/q2 Permanent
Wind
Set
(W”‘)
h Creep
set
Permanent
creep
N/m
T?P9
43
of Ltnear
N/m
Total
Modulus.
(I3
Fmal lnltlal
01~perOC
SAG FACTOR
Final
AE
lnltial
AE
SAG,mm
~
44 3)
1 SW,N
Ice.
No Wind
-mm
:/
800
,
7,/L,
/ 0
0,
g
nno
No
Ice.
(W’)
‘5.5 32
I/. j
49
1
454
002
JR/
Ice.
kPa Permanenf
No
Ice.
/L5
/
0. ah87
D.03.3
q/E
GPa f
?zGPa
c//9
009
N
924
827
N
1 TENSI0N.N
//
7 17
g97
I
I
,
SPAN LENGTH(S) 350.59
15.5 19
(W’)
Ice kPa Wind (W”‘) Set 6 Creep
No Win4
&!dtk 46,
SPAN LENGTH(S)-m
i-/p j
/ /
I 1
300
!o.
000 o&j
j/,
no/
3
I/,
-18 No
/
O.OO/
0.1506
I
1z -mm 0,/q/53 Permanent
3
1
~0.000
mm Ice
No Wind
csf/
’
Ice
/3
46 4
0.000
SPAN LENGTH(S)-m l-/g
I No
0.004
N/II7
’
Exp.:
v
K = r/.37$2
f/ESC
N/m
I/of?0
’
ii
Ice kPa
92.77 L75z,
cw.,ao*
37.
ResulIanl
#. /977
X~=#524/
mm Ice (W”)
Area
o.ow
J
018
m
I
I
I
I
1
I
SPANLENGTH(S)-..&!o,?5 o,oD~ 1/J) ;21 0 239-q i 15,
I
I
I
I
I
1 I !
1 eon
/gin
I
I
21
(W’)
Wind
(W”‘)
Set 6 Creep
No Wind
(W’)
I i
1
I-18 -1
I
I
/
I I
I
I
I I
I
I-
;
15.5
I
I
73L
!6 SN#LI
I
problem
(metric).
32
I
0.3933
49
Figure 28.-Sag
and tension calculation
w
form for broken
31
conductor
/5
/L
&Jo
CHAPTER
DC-573
II-CONDUCTOR
SAGS AND TENSIONS
(3-78)
;;;tL CONDUCTOR &&22 Code
kr.&gR ‘-r-A
i
Name Rated
Breakrng
Load
Diameter/*-qf/‘i Tenston
Final
Computed
k
No
-Inch __ Permanent
100
lb
-
~
lb
Area
lb
Temo.
% ___
lb 0.000
Date UNSTRESSED LENGTH
(A)
*&=a,31
fi lb/l1
a
SB/L
A:
78/T
.1,
00
(W”)
Wind (W”‘)
/, of Linear
o//
NESC
/977
Permanent
:,“:::
73
Set 0.000
o.ooo~ZLJ-
Total
O.Oo/
Modulus.
(E)
Final
?,.-?s
I
SAG FACTOR
z;
/
SAG, f!
1
SW, lb
1
FEET
/ 05;‘i!
(W’)
SPAN LENGTH(S)
Figure
FEET
I I
29.4ag
1
I
I
and
tension
calculation
I I
form
x 106
lb/In2
Exp.:
per OF
SPAN LENGTH(S)
Ice.
dA+s
creep
(W’)
Ib/ft2 Wlnd(W”’ Set 6 Creeo
/( = a.30
Ib/ft
1n2
Coeff.
i!
Ice.
No Wind
Vu J (W*)~/..
Resultanr:
‘yo ____
To”p”j
No Wind
lb
&
___
Weight Ice
lb
OF 50
&OF
ha
Factors:
Dead +&on.
*OF..XI-4c
by
Inch
Ice.
.?1/
‘F&4
LOADING
Ice.
Weight
Llmlratlons:
Inltval.-
No
LOADING
Y$‘$
Inch
Loaded, Final,
SAG CALCULATIONS
for
broken
conductor
problem
I
(U.S.
customary).
TENSION,
lb
TRANSMISSION
62 Horizontal
Tension
Calculate
the
Then Ho = and w is the
linear
T-
LINE DESIGN MANUAL
Calculations: 49 ’ C (120
o F) sag and
SW , where Ho is the force factor.
tension
horizontal
on sag calculation
T is
tension,
Metric
and
Tabulate component
P
full
line
(figs.
28 and
tension,
s is the
29). sag,
U.S. Customary H,, = 5465 - (36.78) (1.434) = 5412 lb
HO = 24 310 - (11.211) (20.9277) = 24 075 N H
the
forms
Curves: the
data
of tension
for
Hand P
the
acting
in the
curves
(tables
conductor.
The
p=-
4, 5, 6, and
Pforce
7). The
H
force
is the
4 W,d i cos 0
and is the horizontal force which resists the movement of an insulator string of length vertical to any angle 8 while a vertical load ?VTis acting. Plot the Hand Pcurves (figs. 30 and 31) from the data in tables 4, 5, 6, and 7.
Table 4.-P curve computations for example problem No. 1 -broken conductor (metric)
i= 2286 mm
$.=7095N d, mm
d/i =
500 1000 1250 1500 1650 1800 1950 2050 2150
0.2187 .4314 .5468 .6562 .7218 .I874 .8530 .8968 .9405
cos e
d/i cos 0
p, N
0.9758 .8992 .8313 .I546 .6921 .6164 .5219 .4425 .3398
0.2241 .4864 .6531 .8696 1.0429 1.2174 1.6344 2.0267 2.7678
1 589.99 3 451.01 4633.74 6 169.81 7 399.38 9 063.15 11 596.07 14 379.44 19 637.54
Sill6
’ WT = vertical force at attachment point, which is one-half the insulator force plus force of conductor.
4 WT has been used in this section
for clarity;
horizontal
is
it is shown as Win appendix
A.
i from
the
CHAPTER
II-CONDUCTOR
63
SAGS AND TENSIONS
Table 5.-P curve computations for example problem No. l-broken conductor (U.S. customary)
‘WT=15951b
d, in
d/i = sin e
20 40 50 60 65 70 75 80 85
0.2222 .4444 .5555 .6667 .7222 .7778 .8333 .8889 .9444
i=7.5ft=90in cos
dli cos e
e
0.9750 .8958 .8315 .7453 .6917 .6285 .5528 .4581 .3288
p, lb
0.2279 .4961 .6681 .8945 1.0441 1.2375 1.5074 1.9404 2.8723
363.50 791.28 1065.62 1426.73 1665.34 1973.81 2404.30 3094.94 4581.32
1 W, = vertical weight at attachment point, which is one-half the insulator weight plus weight of conductor.
Table 6.-H curve computations for example problem No. I -broken
H,, = 24 075 N 1
2
3 WLO
HosinhK
N 12 13 14 16 18 20 22 24
000 000 000 000 000 000 000 075
L,, = 321 m
3369.803 431 3369.803 431 3369.803 431 3369.803 431 3369.803 431 3369.803 431 3369.803 431 3369.803 431
'
4
-- HO-H,
(2) (3)
AE
0.999 .999 .999 .999 .999 .999 .999 1.000
w = 20.9277 N/m
728 751 773 818 863 908 953 000
3368.886 844 3368.964 350 3369.038 486 3369.190 127 3369.341 768 3369.493 409 3369.645 050 3369.803 431
Numbers in parenthesis are column numbers.
5
6
(4) sinh-‘(5)
H, 0.280 .259 .240 .210 .187 .168 .153 .139
741 151 646 574 186 475 166 971
0.277 .256 .238 .209 .186 .167 .152 .139
178 335 382 048 110 688 573 518
conductor (metric)
AE = 44 419 008 N 7
8
9
IHl w
(6) (7)
L o‘I (8) 1 m
1146.8054 1242.3725 1337.9397 1529.0739 1720.2081 1911.3424 2102.4766 2300.7784
317.869 227 318.463 555 318.940 742 319.649 841 320.147 930 320.509 184 320.781 162 321 .OOO001
3.130 2.536 2.059 1.350 0.852 .490 .218 .ooo
77 45 26 16 07 82 84 00
TRANSMISSION
64
LINE DESIGN
MANUAL
7.-H curve computations for example problem No. l-broken
Table
H,, =54121b 1
Lo =1053
2
3
HL lb
Ho sinh wA
2700 2900 3200 3500 4000 4500 5000 5412
757.452311 151.452311 757.452311 757.452311 757.452311 757.452311 757.452311 757.452311
4
ft
conductor (U.S. Customary)
w = 1.4340 Ib/ft 5
6
AE = 9 985 800 I
8
10 G9=
HO-HI 1- 7
(2) (3)
gf
0.999 728 .999148 .999178 .999 809 .999 859 .999909 .999959 1 .ooo 000
751.246284 751.261433 151.284 157 757.307 638 751.345 510 757.383383 151.421256 151.452311
0.280462 .261125 .236651 .216 314 ,189 336 .168 307 .151484 .139958
ZH1
sinh-1 (5)
0.276910 .258245 .234496 .214120 .188223 ,167 522 A50911 .139 505
(6)(7)
w
=fO
3765.5904 4044.6304 4463.0404 4881.4505 5578.8006 6276.1506 6973.5007 7548.1172
1042.1573 1044.5056 1046.5651 1048.1451 1050.0586 1051.3933 1052.3780 1053.0001
Loft
(81,
o= Lo in
(81,
122.88 101.88 77.16 58.20 35.28 19.32 1.44 0.00
10.24 8.49 6.43 4.85 2.94 1.61 0.62 0.00
Numbers in parenthesis are column numbers.
Read
the
insulator
deflections
from
2110
mm
955 mm Then,
the
313.944 Read
the
(Sta. 797+30). corresponding
new
span
length
for
m (1030
ft) - 2.110
horizontal
tension
line
tension,
T =
SIC =
16640
+
crossing
ft)
30 and
over obstructions in sag and tension
30 and
31:
span
+
is equal
0.955
31)
to:
m (3.13
in the
ft)
=
312.789
m (1026.21
ft).
conductor at the first suspension point and figures 28 and 29 to compute the lb), of tension
in the
conductor
may
now
if desired:
(1.5.736)(20.9277)
difference in sag due to this in a slightly larger sag than
clearances corrections
on figures
Use this value of tension, 16 640 N (3740 49 ‘C (120 “F) sag. Th e h orizontal component to the
The results
curves
(83 in) at Sta. 797+30 (37.5 in) at Sta. 787+00
m (6.92 (figs.
be corrected H +
the
completed
=
16969
N, or 3740
+
(51.64)(1.434)
=
3814 lh.
correction is small, and the use of the corrected horizontal would actually exist; therefore, by ignoring the correction,
will be slightly greater are seldom made.
than
those
computed.
For
these
tension actual
reasons,
the
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
65
Sag curve for broken conductor: Metric K = Sag/Span2
15 736 = L = 1.6062 x 10-4m-’ (3 13)=
(Span)‘,
span, m
m2 x lo4
48 96 144 192 240 288 366
0.2304 0.9216 2.0736 3.6864 5.7600 8.2944 11.2896
Sag = (K) (Spanj2, m 0.370 1.480 3.331 5.921 9.252 13.322 18.133
3000
2500
z 2 aa emaa .-EE.- .= 2000 .‘= EE
0
5000
10000
HORIZONTAL Figure 30.-Curves
for broken
conductor
15000
FORCE, problem
20000
newtons (metric).
104-D-1060.
25000
TRANSMISSION
66 U.S.
LINE DESIGN
MANUAL
Custontnry
K = Sag/Span’
=
51.64 = 4.9056 x lo- 5ft- ’ (1026)= Span, ft
(Span)=, ft= x lo5
200 400 600 800 1000 1200 1400 1600 1800 2000
0.4 1.6 3.6 6.4 10.0 14.4 19.6 25.6 32.4 40.0
d=83 in
sag = (K) (Span)=, ft 1.96 1.85 17.66 31.40 49.06 70.64 96.15 125.58 158.94 196.22
d,
!
ti Curve
60'
0
1000
2000
HORIZONTAL Figure 31.-Curves
for broken
conductor
3000
4000
sooo
FORCE, pounds problem
(U.S. customary).
104-D-1061.
6000
CHAPTER The
sag template
figure
for
the
II-CONDUCTOR
Span
with
reduced
67
SAGS AND TENSIONS tension
due
to the
broken
conductor
is shown
on
32.
SAG TEMPLATE FOR EXAMPLE PROBLEM NO. I U.S. Highway No. 25 Sta. 789+ 95 and 790+83 Sta. 795 +48 Rai I road Ruling Span = 313 m (1026 ft) Reduced tension at 49 “C (120 OF), no ice, no wind= I6 640 N (3740 lb) 24.0
14.4
E c
9.6
:
t47
4.6 0
168
144
120
96
72
46
24
0
24
SPAN,
600
200
400
The
broken
conductor
to the highway of 9754 clearance to the railroad requirements.
Example Any
2.-Unbalanced
number
template
0
curve
plotted
tension
on figure
96
120
144
168
200
400
600
ft due to broken
27 indicates
conductor.
there
would
104-D-1062.
be conductor
clearances
mm (32 ft) at Sta. 789+95 and 7925 mm (26 ft) at Sta. 790+83. would be 14 326 mm (47 ft). These clearances all meet NESC and
The State
Condition
of real or imaginary
shown in appendix involved solution
for reduced
72
m
SPAN, Figure 32.-Sag
48
problems
may
be studied
by use of the broken
A. A hypothetical situation has been assumed using the basic broken conductor concept:
to illustrate
conductor the
thesis
use of a more
68
TRANSMISSION A transmission and
a series
situation.
All
excepted
span
(4-lb/ft2)
line spans,
except
plus
before
a bundle
(1150-ft)
is loaded
wind,
equilibrium
with
of 350.5-m
have
NESC
constant
and
after
of two
18 OC
kcmil),
for this
no wind
loading
unbalanced
(1272
assumed
no ice and heavy
at minus the
MANUAL
644 mm2
sp ans has been
one,
under
LINE DESIGN
load
conditions (0 “F).
45/7
conductors,
of an unbalanced
at minus
18 ‘C
of 13-mm
Figure
condition
ACSR, study
(0 OF).
(l/2-in)
33 shows
load The
ice, 0.19-kPa
the
conditions
for
exists.
INITIAL CONDITIONS (Before unbalance due to ice) L
L --c
_
d, ~
L,
L2
d, Lo
_
_
Conditions
d2 LO
for
L4
L3 d3
_
Lo
L5
3
d4 Lo
_-~-
_
L6
3
LO
Lo
d, Lo
_
equilibrium:
H, = H,+ P,;
H, =H2+P2;
H,=H,+P,;
H3=H4+P4;
H,=
0, =d,-d,; L, = Lo-O,; L, = Lo-2d,
02=d2-d3; L,=L,-0,;
%=d3-d,-, L,=L,-0,;
0,=d,-d,; L,=L,-0,;
0,=d,-d,; L,=L,-0,;
H,+P,;
H,-
H,+P,
; etc.
0,=d,-d,; L,=L,-0,;
etc. etc.
FINAL CONDITIONS (After unbolonce due to ice) Figure 33.-Conditions
and
for equilibrium
before and after
unbalanced
Conductor data and data for plotting the Pand Hcurves the graphical solution is shown on figures 34 and 35. The 1.
procedure Lay out
for the graphical the graph axes
in span length $ and insulator horizontal force. Allow room and 2.
fourth Plot
3.
Plot
quadrants. the PL 1 curve
PL 2
curve
4. Plot the PL1 simplify calculations,
+L2
computed.
the
this
solution is: using millimeters
(inches)
condition.
are shown
for
the
deflection a! Use newtons (pounds) on the graph for the development
by
plotting
d versus
PI P2
by plotting d versus curve by plotting dversus is taken
as the
average
104-D-1063.
in tables
ordinate
values
table
using
table 10 or 11. + P2)/2 using table force
15,
of change
for the abscissa of curves in both
using
(PI P
8 through
values of the first
10 or 11.
in the
series
10 or 11. To of spans
being
CHAPTER
II-CONDUCTOR
69
SAGS AND TENSIONS
Table 8. -Line data computations for example problem No. 2unbalanced condition (metric) Two 644 mm’, ACSR, 4517 (duplex conductors) Maximum conductor tension = 61 385 N, initial Twenty 177 928-N insulator units per suspension string -18 ‘C, no load Insulator string vertical force (w,)
1 156.5 N
0.5 WI
578.3N
Conductor vertical force, 350.5-m span (w,) w,=o.5
20.9277 N/m (no load) x 2 cond. 43.889 N/m (full load) x 2 cond.
wr +w2
Insulator string length (i) Tension (7) final
1 156.5 N 578.3 N
14 670.3 N 30 766.2 N 15 248.6 N
31 344.5 N
3 734 mm
3734mm
30 514 N
Conductor vertical force (w)
-18 OC, 13-mm ice, 0.19-kPa wind
20.927 7 N/m
57 403 N 43.889 N/m
Sag (s), 350.5-m span
10 621 mm
11 865 mm
Horizontal
30 292 N
56 882 N
44 419 008 N
44 419 008 N
tension (Ho = T - SW)
Area times final modulus (4E)
Table 9.-Line data computations for example problem No. 2unbalanced condition (U. S. customary) Two 1272 kcmil, ACSR, 4517 (duplex conductors) Maximum conductor tension = 13 800 lb, initial Twenty 40 000-lb insulator units per suspension string 0 OF, no load
0 OF, l/2-in ice, 4-lb/ft2 wind
Insulator string weight (wr)
260 lb
260 lb
0.5 w1
130 lb
130 lb
Conductor
weight, 1150-ft span
b3) wT=o.5wr+w2 Insulator string length (i) Tension (7’) final Conductor
weight (w)
Sag (s), 1150-ft span Horizontal
tension (Ho = T - SW)
Area times final modulus (.4E)
1.4340 lb/ft (no load) x 2 cond. 3.0073 lb/ft (full load) x 2 cond.
3 298.2 lb
6 916.6 lb
3 428.2 lb
7 046.8 lb
147 in
147 in
6 860 lb
12 904 lb
1.434 lb/ft 34.85 ft
3.007 3 lb/ft 38.93 ft
6 810 lb
12 787 lb
9 985 800 lb
9 985 800 lb
70
TRANSMISSION
LINE DESIGN
MANUAL
Table 1O.-P curve computations for example problem No. 2unbalanced condition (metric) p=- WTd i case WT = 15 248.6 N (no load), 31 344.5 N (full load) d, mm
d/i = sin 6
500 1000 1500 2000 2500 3000 3250 3375 3500 3600 3650 3700 3734
0.133 90 .26181 ,401 71 .535 62 .66952 .80343 .870 38 .903 86 .937 33 .964 11 .97750 ,990 89 1 .ooo 00
cos e 0.990 99 .96341 .915 17 .84446 .I4279 .59540 .492 38 .427 83 .34844 .265 50 .21094 .134 61 .ooo 00
i = 3734 mm
d/i cos e
No load
Full load
PI
P2
2
0.135 12 .217 96 .43866 .634 28 .90136 1.349 40 1.767 70 2.112 66 2.690 08 3.631 30 4.63402 7.357 91
2 060.39 4 238.50 6 688.95 9 671.88 13 744.48 20 576.46 26 954.95 32 215.11 41 019.95 55 372.24 70 662.32 112 197.83
4 235.21 8 712.52 13 749.58 19 881.19 28 252.68 42 296.27 55 407.67 66 220.27 84 319.21 113 821.28 145 251.04 230630.01
3 147.84 6415.52 10 219.29 14 716.51 20 998.62 31436.43 41 181.40 49 217.79 62699.72 84 596.94 107956.91 171414.29
p,
+p2
Table 11 .-P curve computations for example problem No. 2unbalanced condition (U. S. customary) p= -WTd
i cos 0
WT = 3428.2 lb (no load), 7046.8 lb (full load) d, in
20 40 60 80 100 120 130 135 140 142 144 146 147
d/i = sin e
cos e
0.136 05 .272 11 .40816 .54422 .68027 .81633 .88435 .91837 .952 38 .965 99 .97959 .99320 1 .ooo 00
0.990 70 .96227 .91291 .83894 .73296 .57759 .46682 .39572 .30491 .25858 .20101 .116 42 .ooo 00
i= 147 in
dli cos 8
No load PI
Full load
0.137 33 .28278 .447 10 .64870 .928 11 1.413 34 1.894 41 2.32076 3.123 48 3.735 75 4.873 34 8.531 18
470.79 969.43 1 532.75 2 223.87 3 181.75 4 845.21 6494.42 7 956.03 10 707.91 12 806.90 16 706.78 29 246.59
967.74 1 992.69 3 150.62 4 571.26 6540.21 9 959.52 13 349.53 16 353.93 22010.54 26 325.08 34 341.45 60 117.52
p2
PI
+p2
2 719.27 1481.06 2 341.69 3 397.57 4 860.98 7 402.37 9921.97 12 154.98 16359.23 19565.99 25 524.12 44 682.06
Table 12.-H curve computation for example problem No. 2-unbalanced full-load condition (metric)
H,=56882N 1
Hl, N
L,=350.5
2
3
Ho sinh “2
HO
I--
4 -H,
AE
WO
m
AE = 44 419 008 N
w = 43.889 N/m 5
6
(4)
(2) (3)
H,
sinh-’
7 (5)
2Hl W
8
9
(6) (7)
G= Lo - (8, m
13500 15 750 18 000 22500 27000
7715.007 734 7 715.007 734 7715.007734 7 715.007'734 7715.007734
0.999 023 .999074 ,999 125 .999226 .999 327
7701.470171 7707.863 637 1708.257 102 7 709.036 318 7 709.815 534
0.570 924 .489 388 .428231 .342624 .285 549
0.543 733 .471700 .416123 .336252 .281804
615.1883 717.7197 820.2511 1025.3139 1230.3766
334.50 338.55 341.33 344.76 346.73
16.00 11.95 9.17 5.74 3.77
31500 36000 40500 45 000 50000
7 715.007734 7715.007 734 7 715.001734 7 715.007 734 7715.007 734
.999 429 .999530 .999 631 .999733 .999845
7710.602465 7711.381680 7 712.160 896 7 712.947 827 7 713.811 908
.244781 .214 205 .190424 .171399 .154276
.242400 .212600 .189 292 .170 571 .153 670
1435.4394 1640.5022 1845.5649 2050.6277 2278.4752
347.95 348.77 349.35 349.78 350.13
2.55 1.73 1.15 0.72 0.37
56882 60000 65 000 70000 75 000
7715.007734 7 715.007734 7715.007734 7715.007 734 7715.007734
1 .ooo 000 1 .ooo 070 1 .OOO183 1.000 295 1.000 408
7715.007734 7715.547 785 7 716.419 580 7717.283661 7 718.155457
.135 .128 .118 .110 .102
632 592 714 247 909
.135 220 .128 240 .118 431 .110025 .I02728
2592.0846 2734.1703 2962.0178 3189.8653 3417.7129
350.5017 350.63 350.81 350.96 351.09
0.0085 -0.13 -0.31 -0.46 -0.59
80000 85 000 90 000 95 000 100 000
7 715.007 734 7715.007 734 7715.007734 7115.007734 7715.007 734
1 .OOO5 20 1.000 633 1 .OOO746 1.000 858 1.000 971
7 719.019 538 7 719.891 334 7720.763130 7721.627 211 7 722.499007
.096488 .090822 .085 786 .081280 .077 225
.096 339 .090 698 .085 681 ,081 191 .077148
3645.5604 3873.4079 4101.2554 4329.1030 4556.9505
351.21 351.31 351.40 351.48 351.56
-0.71 -0.81 -0.90 -0.98 -1.06
105 000 110 000 113764 115 000 120000
7715.007734 7 715.001734 7715.007734 7715.001734 7715.001734
1.001 1.001 1.001 1.001 1.001
1723.363087 7724.234883 7724.890659 7 725.098964 7 725.970760
.073556 .070220 .067902 .067 175 .064 383
.073490 .070162 .067850 .067 125 .064 339
4784.7980 5012.6455 5184.1692 5240.4931 5468.3406
351.63 351.70 351.75 351.77 351.83
-1.13 -1.20 -1.25 -1.27 -1.33
Numbers in parenthesis are column numbers.
083 196 281 308 421
P
; 2 I z i? : 2 n g c, v, $ 0 -I 1 2 5
Table 13.-H curve computations for example problem No. 2-unbalanced
H,, = 12 787 lb 1
Hl, lL.
3 WLO
H,sinh-
HO
l-WO
4
5
AE
6
(4)
-H1
sinh-’
(2) (3)
(5)
1 1 1 1 1
734.472 734.472 734.472 734.472 734.472
747 747 747 747 747
0.999 .999 .999 .999 .999
020 070 120 220 320
1 732.772 1732.859 1 732.946 1733.119 1733.293
964 687 411 858 306
0.577 .495 .433 .346 .288
591 103 237 624 882
7 000 8 000 9 000 10 000 11000
1 1 1 1 1
734.472 734.472 734.472 734.472 734.472
747 747 747 747 747
.999 .999 .999 .999 ,999
420 521 621 721 821
1733.466 1733.641 1733.815 1 733.988 1734.162
753 935 382 829 276
,247 .216 .192 .173 .157
638 705 646 399 651
.245 174 .215 044 .191474 .172 542 .157 005
12 12 14 15 16
000 787 000 000 000
1 734.472 1 734.472 1734.472 1 734.472 1 734.472
747 747 747 747 747
.999 1 .ooo 1.000 1 .ooo 1.000
921 000 121 222 322
1734.335 724 1 734.472 747 1734.682 618 1734.857 800 1735.031 247
.144 .135 .123 ,115 .108
528 643 906 657 439
.144 ,135 .123 .115 JO8
17 000 18 000 19 000 20 000 21000
1 734.472 1 734.472 1 734.472 1 734.472 1734.472
747 747 747 747 747
1.000 422 1 .OOO522 1 .OOO622 1.000 722 1 .OOO822
1 735.204 1735.378 1735.551 1735.725 1735.898
694 142 589 036 480
.102 .096 .091 .086 .082
071 410 345 786 662
22 23 24 25 25
1 734.472 1734.472 1 734.472 1 734.472 1 734.472
747 747 747 747 747
1.000 1.001 1.001 1.001 1.001
1 736.073 1 736.247 1736.420 1 736.594 1 736.694
665 113 560 007 607
.078 .075 .072 ,069 .067
912 489 351 464 909
923 023 123 223 281
Numbers in parenthesis are column numbers.
7
8
2Hl y
(6) (7)
-
0.549 .476 .420 .340 .285
5 15 828 715 033 008
10
9
9= Lo ft
H1
3 000 3 500 4 000 5 000 6 000
000 000 000 000 574
AE=9985 800 lb
w = 3.0073 Ib/ft
Lo= 115oft
2
full-load condition f US. customary)
@h
o= Lo- W, in
1995.145 2 2 327.669 3 2 660.193 5 3 325.241 9 3 990.290 3
1096.36 1109.90 1119.18 1130.69 1137.26
53.64 40.10 30.82 19.31 12.74
643.68 481.20 369.84 231.72 152.88
4 5 5 6 7
8.63 5.88 3.94 2.51 1.42
103.56 70.56 47.28 30.12 17.04
655.338 320.387 985.435 650.483 315.532
7 1 4 8 2
1141.37 1144.12 1146.06 1147.49 1148.58
030 230 591 401 228
7 980.580 8 503.973 9 310.677 9 975.725 10 640.774
6 7 4 7 1
1149.44 1149.9924 1150.72 1151.21 1151.63
0.56 0.01 -0.72 -1.21 -1.63
6.72 0.09 -8.64 -14.52 -19.56
.lOl .096 .091 .086 .082
895 261 218 677 568
11 305.822 11970.870 12 635.919 13 300.967 13 966.016
5 9 3 6 0
1152.01 1152.33 1152.62 1152.89 1153.15
-2.01 -2.33 -2.62 -2.89 -3.15
-24.12 -27.96 -31.44 -34.68 -37.80
.078 .075 .072 ,069 .067
830 417 288 408 857
14 15 15 16 17
4 8 2 6 3
1153.37 1153.59 1153.80 1153.99 1154.11
-3.37 -3.59 -3.80 -3.99 -4.11
-40.44 -43.08 -45.60 -47.88 -49.32
631.064 296.112 961.161 626.209 007.947
-----
Table 14.-H curve computations for example problem No. 2-unbalanced
$=LoHo=30292N 1
Hl, N
2H1 W
sinh -1
L, = 350.5 m
2
3 WLO
HO
Ho sinh 2~
l-0
13 500 15 750 18 000 21 000 25 000
3 616.546418 3 616.546478 3616.546418 3 676.546478 3676.546478.
0.999 622
30292 31500 36000 40500 45 000
AE = 44 419 008 N
w = 20.9211 N/m
4
5
(2) (3)
-(4)
-H1
AE
no-load condition (metric)
6
sinh-’
I
W
Hl
0.268 979 .231287 .202803 .174 155 .146 519
9
(6) (7)
Lo m
@=
-2Hl
(5)
8
.999881
3 675.156143 3 615.344 241 3 675.528 015 3675.778080 3 676.108 969
0.272 234 .233 355 .204 196 .175037 .147044
3 676.546478 3676.546478 3676.546418 3676.546478 3 676.546478
1 .ooo 000 1 .OOO027 1.000 129 1.000 230 1.000 331
3616.546418 3676.645 745 3671.020752 3671.392084 3677.763415
.121370 .116 719 .102 139 .090 800 .081728
.I21 074 .116 456 .101962 .090 676 .081 637
2 894.919 3 010.364 3 440.416 3 870.468 4 300.520
2 3 3 3 4
49500 54000 58500 60584 63000
3676.546478 3 616.546478 3676.546478 3 616.546418 3 676.546 418
1.000.432 1.000 534 1.000 635 1 .OOO682 1.000 736
3 678.134 746 3678.509754 3 678.881085 3679.053883 3679.252416
.074 306 .068 121 .062887 .060 726 .058 401
.074 ,068 ,062 .060 .058
238 068 846 689 368
4 5 5 5 6
730.572 160.624 590.616 789.838 020.728
4 4 5 3 5
351.19 351.27 351.35 351.38 351.42
67 500 12 000 76 500 81000 85 500
3 616.546 3 676.546 3 676.546 3 676.546 3 676.546
478 478 478 478 478
1.000 1.000 1.001 1.001 1.001
838 939 040 142 243
3 619.621424 3 619.998 755 3 680.310 086 3 680.745 094 3 681.116 425
.054 .051 .048 .045 .043
513 111 109 441 054
.054 486 .05 1 089 .048 090 .045 425 .043 041
6 6 7 7 8
450.780 880.832 310.884 740.936 170.988
5 6 6 7 7
351.48 351.53 351.58 351.63 351.69
-1.03 -1.08 -1.13 -1.19
90 000
3 676.546 3 676.546 3 676.546 3 676.546 3 616.546 3 616.546
478 478 418 478 478 418
1.001 1.001 1.001 1.001 1.001 1.001
344 446 547 648 749 851
3 3 3 3 3 3
.040 .038 .037 .035 .034 .032
905 962 194 581 102 741
.040 .038 .037 .035 .034 .032
8 601.040 9 031.092 9 461.144 9 891.196 10 321.248 10 751.300
7 8 8 8 9 9
351.73 351.78 351.81 351.86 351.90 35 1.94
-1.23 -1.28 -1.31 -1.36 -1.40 -1.44
94 99 103 108 112
500 000 500 000 500
.999673 .999123
.999 791
Numbers in parenthesis are column numbers.
681.487 681.862 682.234 682.605 682.976 683.351
756 764 095 427 758 766
894 952 185 573 095 735
1290.156 1 1505.182 1 1720.208 1 2 006.909 5 2 389.178 0
341.02 348.13 348.86 349.51 350.06
350.4994
(0
3.48 2.37 1.64
0.99 0.44
0.00
350.57
-0.07
350.79 350.96
-0.29
351.08
-0.46 -0.58
-0.69 -0.71 -0.85 -0.88
-0.92 -0.98
Table 1S.-H curve computations for example problem No. 2-unbalanced
2
1
Hl, lb
4
3 WLO
HO
Hosinh-c
l-0
-ff,
AE
(2) (3)
AE = 9 985 800 lb
w = 1.434 Ib/ft
Lo = 1150 ft
H,, = 6810 lb
no-load condition (U.S. customary)
5 (4)
sinh-’
(5)
T
826.248 383 826.303762 826.331866 826.414522 826.491178
0.275 416 .236087 .206583 .165 283 .137750
0.272048 .233947 .205 141 .164540 .137 318
4184.1004 4881.4505 5 578.8005 6973.5007 8368.2008
6 810 I 000 8000 9000 10 000
826.564130 826.564130 826.564130 826.564130 826.564130
1 .ooo 1.000 1.000 1.000 1.000
826.564130 826.579835 826.662491 826.145 148 826.821804
.121315 .118083 .103333 .091 861 .082683
A21079 .117 810 .103150 .091732 .082589
11000 12000 13000 13620 14000
826.564130 826.564130 826.564130 826.564130 826.564130
1.000 420 1.000 520 1 .OOO620 1.000 682 1 .OOO720
826.911287 826.993943 827.076600 827.121847 827.159256
.075 174 .068916 .063621 .060729 .059083
15 000 16000 17000 18000 19000
826.564130 826.564130 826.564 130 826.564130 826.564130
1.000 820 1 .OOO920 1.001 020 1.001 121 1.001 221
827.241913 827.324569 827.401225 827.490708 827.573 365
20000 21000 22000 23000 24000
826.564130 826.564130 826.564130 826.564130 826.564130
1.001 1.001 1.001 1.001 1.001
827.656021 827.738618 827.821334 827.903990 827.986647
321 421 521 621 721
Numbers in parenthesis are column numbers.
9
G= Lo - (‘3h ft
0.999 618 .999 685 .999 719 .999819 .999919 000 019 119 219 319
(6) (7)
H,
826.564130 826.564130 826.564130 826.564 130 826.564130
3000 3500 4000 5 000 6000
8
I
6
10
f#J= Lo - GO, in
1138.28 1142.00 1144.44 1147.42 1149.10
11.72 8.00 5.56 2.58 0.90
140.64 96.00 66.72 30.96 10.80
9497.9080 9762.9010 11 157.601 1 12 552.301 3 13947.0014
1149.9972 1150.17 1150.91 1151.45 1151.87
0.00 -0.17 -0.91 -1.45 -1.87
0.00 -2.04 -10.92 -17.40 -22.44
.075 103 .068 862 .063578 .060692 .059049
15 341.7015 16736.4017 18 131.1018 18995.8159 19525.8020
1152.21 1152.50 1152.74 1152.89 1152.98
-2.21 -2.50 -2.74 -2.89 -2.98
-26.52 -30.00 -32.88 -34.68 -35.76
,055 149 .051708 .048671 .045 972 .043556
.055 121 .051685 .048 652 .045 956 .043542
20920.5021 22 315.2022 23709.9024 25 104.602 5 26499.3027
1153.16 1153.36 1153.53 1153.71 1153.83
-3.16 -3.36 -3.53 -3.71 -3.83
-37.92 -40.32 -42.36 -44.52 -45.96
.041383 .039416 .037 628 .035 996 .034499
.041 371 .039406 .037619 .035 988 .034492
27894.002 29288.7029 30683.403 32078.1032 33472.8033
1154.00 1154.15 1154.28 1154.43 1154.54
-4.00 -4.15 -4.28 -4.43 -4.54
-48.00 -49.80 -51.36 -53.16 -54.48
8 1
CHAPTER
UJUJ’(P) NOl133133(3
NVdS NI 39NWH3
SAGS AND TENSIONS
ONV U’W’(@) H19N31
II-CONDUCTOR
~OlVltlSNI
75
-6(
6000
Figure 35.-Graphical
IOOcm
solution
12000
14 000
16 000
HORIZONTAL
FORCE, pounds
of unbalanced
condition
18 ooo
(U.S. customary).
20 000
104-D-1065.
22000
24000
26000
28000
CHAPTER 5.
Plot
unloaded 6. curve
2d versus
the
end of the is necessary
II-CONDUCTOR P curve
using
SAGS AND TENSIONS table
10 or 11. Since
span with iced conductors, swing to read the change in horizontal
77
the
insulator
a like amount toward tension at the insulator
strings
each other, between
at each
this curve loaded and
spans. Plot
H, 1 ( no load)
the
is not needed
7.
Plot
the
curve
also
is not
for this
HLz (full
curve
load)
needed
usiug
solution, for
but
curve
this
table
14 or 15 and
normally using
solution,
is plotted
table but
HI
plotting
in the first
12 or 13 and normally
in the
$ . This
for reference.
HI
plotting
is plotted
versus
quadrant
versus
first
4 . This
quadrant
for
reference. 8.
Plot
fourth 9.
2 HI ,1 curve
the
(for
duplex
10.
Plot
the
point
by point, 2 HL 2 curve.
Ht the
conductors).
2HL2 - PL1 +
=
abscissa
Plot
quadrant, 2 HL, = duplex conductors).
quadrants. In the fourth Plot the 2 HL2 curve (for
values
of the
L2 curve. PL 1 +
Plot This
12. values 13.
of the H2 curve Plot the Ha =
from
the
ordinate
values
d2 + PL1 + L2 curve.
15.
P10ttheHq.=dg+PLt+L2
is done
L2 curve
of the basic Add graphically,
curve.
Add
graphically,
17. Plot the Hs = dh + f’~~ + Lo, d5 = ~HL* d6 =2HL1 - H6 curves in a similar manner. d curves
converge
accuracy for this problem; may continue until two
quite
rapidly,
so that
the
in the
first
the
Draw a reflection intersection of the
deflection
at that
Insulator spans
Effect
for
of the H 1 = 2 HL 2 - pL 1 + reflected curve with the d6 curve
The horizontal adjacent no-load
to switchyards
is about
Sag
and
and
by
from
quadrant.
subtracting
the
graphically,
abscissa
values
point by point, the abscissa basic 2 HL 1 = d curve. point by point, the ordinate 2 HL1 curve. point by point,
point
gives
the abscissa the
by point,
ordinate
the abscissa
the ordinate
- Hg, H6 = d5 +
d6 curve
of the
values
f’~~ +
a satisfactory
Lo, and
degree
as indicated on a final value.
figure
16 of the
of
L 2 curve in the fourth is taken as an acceptable
broken
quadrant. answer
tension in the conductor at the structure between the full-load span is indicated as about 74 800 N (16 800 lb). The insulator
structure
on
first
if more accuracy is desired, the plotting of Hand d curves d curves are essentially the same curve. If desired, an
however, successive
approximation of the d, curve may be computed conductor thesis in appendix A, and then plotted
as approach
in both
Of the pL t + L 2 curve to the abscissa values of the d3 curve. Plot d4= 2HL - Ha curve. Subtract graphically, point by point, Ha curve from :he ordinate values of the basic 2 HL 1 curve.
va1ues 16. of the
17.
curve
of the P L t + ~2 curve to the abscissa values of the dz curve. Subtract graphically, point by point, Plot the d3 = 2HL,- H3 curve. of the H3 curve from the ordinate values of the basic 2 HL, curve.
values 14. values
problem. and the
only
Plot the Hz = d+ PL1 + ~~ curve. Add graphically, of the PL 1 + L2 curve to the abscissa vahtes of the Subtract graphically, Plot the d2 = 2HL1 -Hz curve.
11. values
The
this
d .
1090
Tension
and substations,
on the sag and tension in the conductors. This reduced tensions. Based on the same maximum in accordance with applicable electrical safety
mm
in
(42.8
Short the
The to the span string
in).
Spans
insulator
.-In strings
short, may
dead-ended have
spans,
considerable
such effect
is especially true when the conductors are strung at tension at full-load conditions (ice and wind loading codes), the tension at no-load conditions (no ice and
TRANSMISSION no wind)
may
the insulators. without
The
taking
A method point
actually
be as much
total
the
into
of calculating
is outside
the span,
as twice
sag of conductors
insulators the
that and
calculated
insulators
will
effect
in reference
equations
for transmission The
insulators.
For
shows
the
two
lines.
catenaries
equilibrium,
nomenclature
the used
Nomenclature
The
conductor
are
tangent
horizontal
also be different inclined
spans,
method
has been
is satisfactory the insulator
assumes tensions the
for determining
one catenary,
point
where
in the
procedure
insulator
two
effect
this
conductor
2M
= = =
sag at center of insulator catenary, below end of insulator sag at center of insulator catenary, below support point, conductor sag, below end of insulator string, mm (ft)
inclined
length
04
= = =
total sag, insulators plus conductor, mm (ft) SV = arc length of one-half the conductor span, unstressed arc length of L, m (ft)
SP
= =
length of insulator string, arc length from insulator
A
=
cross-sectional
E
=
modulus
e
= = =
temperature parameter parameter
area
of elasticity
of span,
are not inclined on the catenary
be equal.
m (ft)
m (ft) catenary
of conductor, of conductor,
coefficient of conductor of the catenary described of the catenary described
center mm2 GPa
to end
mm
(ft)
m (ft)
of insulator
(in2) (lb/ft2)
by the by the
conductor insulator
string
in short spans.
string, mm (ft)
string
string,
low
to determine
is attached
must
on sag and tension
=
a2
conductor
method.
Dr 02 0s
a1
the
developed
and the insulator the
catenaries
for
where
description: =
considering
the sag calculated
for spans which effect is based
C
L Lu RS
without than
Another
at the
in describing
Figure 36.-Nomenclature 104-D-1066.
methods
in steeply [5].
the insulator effect for approximately level spans and by more than 20 percent. This method of calculating catenary.
by normal
account.
insulator
is given
LINE DESIGN MANUAL
m (ft)
another to
the
Figure
36
CHAPTER H
=
T
=
tension
W
=
linear
force
factor
(weight
Wt
=
linear
force
factor
of conductor,
X
=
M -
Xs
=
projected
Steps
horizontal
in the
component
II-CONDUCTOR
in conductor,
Xs
=
one-half
length
procedure
the
in conductor,
N (lb)
N (lb)
the
per
unit
length)
N/m
length
of insulator
of insulator
of conductor string,
string,
N/m
(lb/ft)
(lb/ft) span,
m (ft)
m (ft)
are:
Step I.-Calculate using
of tension
79
SAGS AND TENSIONS
Lu,
following
the
unstressed
arc
length
of
L,
for the
required
loading
condition
by
equations:
a, = H/W, , for conductor catenary
(1)
a, = H/W, for insulator catenary
(2)
a2 x,
x
=7>
for this equation assume X = (M - KS) (1 .OOOS)
Assumption of an appropriate a more accurate value of X. The calculations repeated to obtain calculations
increase
the
accuracy
value for X at this point greatly simplifies the calculation of calculated value of Xcould be substituted in equation (3) and a still more accurate value; however, subsequent repetitive very
little.
SP = a, sinh 3
(4)
a2
RSP=RS+SP
(5)
X2 = a, sinh-’ y
(6)
x, =x2 - x,
(7)
X=M- x,
(8)
L = a, sinh x a1
(9)
(10) >
80
TRANSMISSION Step Z.-With LA,
a range
determine
the
of tensions
temperatures
LINE DESIGN
(assume
H
which
the
for
=
MANUAL
5”) and
corresponding
conductor
would
unstressed
have
these
arc
arc
lengths
lengths:
Let: to Lu 0
= =
temperature unstressed
t1,
=
temperatures
=
unstressed
tz,
.
.
*
t,
LlC,, I,112, . . . Lu,
at known comluctor at new conductor
conditions arc length
at known
conditions
conditions arc
lengths
at new
conditions
Lu, = Lu, + Lu,e (tl - t,)
(11)
Lu, =Luo +Lu,e(t,-
to)
(11)
Lu, = Lu, + Lu,e (tn- to)
(11)
Step 3.-Plot tension against temperature corresponding to each unstressed arc length loading condition. From this plot, determine the tension at the desired temperatures. (1) through (8). tension, calculate values for X, X I, and X 2 using equations Step
&The
total
sag of the
D, =a, (cash:
D, =a, (co+
line,
insulators
plus
conductor,
is then
for each For each
determined:
- I>
(12)
l)
(13)
(14)
Dc, =D,
+D,
-D,
mm2
(951. kcmil),
(15)
Example Assume:
483
(4000 Ih) under NE:SC plus constant at’minus tension
insulator
strings.
ACSR,
G/7
conductor
with
heavy loading of 13-1~111~ (I/2-in) 18 ‘C (0 ’ F). U. SC a 45.72-m
maximum
tension
of
ice, 0.19-kI’a (I-lh/ft*) (1 SO-ft) span with
17 793 wind, 1 S-unit
N
CHAPTER Insulator
II-CONDUCTOR
string data
SAGS AND TENSIONS
Length
15 insulator units Anchor shackle Ball-eye fitting Compression dead end
81
Mass
m
(in)
kg
2.1908 0.0813 .0711 .5842 ___
86.25 3.2 2.8 23.0 ~
74.84 0.45 .68 10.07
165 1.0 1.5 22.2
2.9274 m
115.25 in
86.04 kg
189.7 lb
(lb)
w = 86.04 = 29.3912 kg/m = 288.2292 N/m 2.9274
w = (189*7) (12) = 19 75 lb/ft 115.25 ’
Metric Figure
DCm-579
37 shows
the
metric
sag and
tension
calculations.
(3-78)
;;c
SAGCALCULATIONS
LOAOIMG
k/e2 vu
Lmear
Factor,
Force Dead
_L3_
Load
Force
mm Ice
(W”)
O@!,&?.kPa
1-5 -qfl
Lgf
N/m
BD2
N/m
Creep
0.00oloo.
N/m
Total
O.OOn
Wind/d:
Resultant Area
(A)&m&
Temp.
Cc&f.
0.000
(W’)
(W”‘)~Jd,
Permanent
N/m Modulus.
of
Linear
+mm ?
2
Permanent
kPa Set
! TYJ..I
Ice Wtnd (W”‘) 6 Creep
UHSTRESSED LwCTH
/
Final
1
Ice.
NO Wmd
(W’)
I
AE
23
GPa
.-7/f
*/7?
SW,N
m
543.
TENSION, N
/5!16B8.@/?
I
I
773
I
I
I
!
I
I
15.5
I 1
49
1
I
and tension
calculation
form for insulator
I
effect
T - W, (sag) = 17 793 - 36.93 1 (0.5432) = 17 772.94 N
a1 = E = l7 772*94 = 481 . 2472 m w1 36.931
N N
I
32
GPa
AE je
SAG, mm
1 1 -11
Figure 37.Sag
H=
klj.rllL
m
0.0949~~.0~/
!
-1 No
SAC FACTOR
‘;
SPAN LENGTH(S)e&$=3. L/g
FInal
Irntialr/5.c?0
OGkk.pePC
3
(E)
Exp:
lnitlal
LOADING
Set O.OOOA
problem
(mtric).
ln~t:
TRANSMISSION
82
H 17 772.94=61 a2 =i? = 288.2292
x, =
LINE DESIGN MANUAL
6625 m *
- RS) (1.0005) = 61.6625(22.86
a,04
a1
SP = a, sinhX1
= 61.6625
- 2.9274)(1.0005)=2 481.2472
5553 m
= 2.5560 m
sinh ii56f:#5
a2
RSP -RS+SP=2.9274+2.5560= X2 =a,
X,
=X2
X=M-
sinh-1
RSP= a2
- X,
=5.4762-
6 1.6625 sinh- 1 ~~~~,5
X, =22.86-
L =a1 sinhX
5.4834 m
2.5553
=2.9209
2.9209=
19.9391
= 48 1.2472 sinh 4fi9i4!f32
= 5.4762 m
m
m
= 19.9448
m
4 W, (a, j2 .2/&y
Luo=L-
(
xa, + sinh % cash f
36.93 1 (48 1.2472)’ = 19 9448 _ = 19.9342
Temperature
2(33
318 479)
m
= - 18 OC = t,
T = 13 345 N
Assume
H 13 345 a, = - = -=850.6502 15.688 WI H a2 =w
13 345 =288.2292
m
= 46.3000
m
> 19.9391 + sinh 481.2472
19.9391
'Osh 481.2472 >
CHAPTER
x1 =
a, (M - RS) (l.0005) a1
SP= a, sinh$
II-CONDUCTOR
SAGS AND TENSIONS
= 46.3000 (22.86 - 2.9274) (1.0005) = 1 0855 m 850.6502
= 46.3000 sinh 41$~~~o = 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.0130 m 4.0130 X2 = a, sinh- ’ -RSP = 46.3000 sinh- 1 46.3000 = 4.0080 m a2
x, =x2 - x, X=M- x,
= 4.0080 - 1.0855 = 2.9225 m
= 22.86 - 2.9225 = 19.9375 m
L =a, sinhE=
Lu,=L-
850.6502 sinh 8Fi9QJ;b52= 19.9393 m
w12AE (“l I2
_X + sinh _Xco& -x a1
= 19.9393 -
a1
15.688 (850.6502)2 2(33318479)
a1
19.9375 19.9375 850.6502 ‘Osh 850.6502
= 19.9313 m
t, =
Lu,Lu,e - Lu, +t,
19.9342 19.9313-(0.000 19.9342 020 7) +(‘18)=-25030c = ’
Assume T= 12 010 Nm H(no load) H 12 010 a, = - = = 765.5533 m Wl 15.688
H 12 010 = 41.6682 m a2 = i? = 288.2292 x1 =
a2 (M - RS) (1.0005) = 41.6682 (22.86 - 2.9274) (1 .OOOS) = 1 0855 m 765.5533 a1
83
84
TRANSMISSION
SP = a, sinh?=
LINE DESIGN
MANUAL
41.6682 sinh b;T:852 = 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.0130 m RSP 4.0130 X, =a, sinh-’ ~ = 41.6682 sinh- ’ 41 .6682 = 4.0068 m a2
X, = X2 - Xl = 4.0068 - 1.0855 = 2.9213 m
X = M - X, = 22.86 - 2.9213 = 19.9387 m X L =a, sinh - = 765.5533 sinh 7F59535y3= 19.9410 m a1
W, Lu2
=L
-
(a,
1’
2*E
x + sinh x cash _x a1 a1 >
al
15.688 (765.5533)’ 2 (33 318 479)
= 19.9410-
19.9387 +sinh 19.9387 cash 19.9387 765.5533 765.5533 765.5533 >
= 19.9338 m
t, =
Lu, - Lu, +t,
Lu,e
Similar
=
19-9338 - 19*9342 + (- 18) = _ 18.97 OC 19.9342 (0.000 020 7)
calculations
temperatures
were
made
for
five
additional
assumed
Assumed T = H (no load), N
The
resulting determine line.
and
the
resulting
Temperature, OC
10 675 9 341 8 007 6 672 6 227
figure, of the
tensions,
were:
temperatures the
tensions
t, t, t, t, t,
are plotted for the
against
desired
the
= - 11.94 = -2.23 = 11.58 = 33.13 = 43.31
assumed
temperatures
and
tensions proceed
on figure in finding
38. Using the
total
this sag
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
0 rn z W I-
-23
-13
-5
0
+5
T EM PERATURE, Figure 38.-Tension-temperature
At-18OC.T= H
curve for insulator
11 800N 11 800
a, = - =-z752.1673 15.688 wt
m
H 11 800 a, =~=~~~,~~9~=40.9396
m
+I5
+25
+35
“c effect
problem
(metric).
104-D-1067.
+45
TRANSMISSION
86
x 1
LINE DESIGN MANUAL
= a, (M - RS) (1.0005) = 40.9396 (22.86 - 2.9274) (1.0005) = 1 0855 m 752.1673 a1
Xl
SP = a, sinh a, = ‘40.9396 sinh 40;0983~6= 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.013 m RSP
X, = a, sinh- ’ -
4.013 = 40.9396 sinh- 1 40.9396 = 4.0066 m
a2
X, = X2 - X, = 4.0066 - 1.0855 = 2.9211 m
X = M - X, = 22.86 - 2.9211 = 19.9389 m D, =a2 (.osh:-
1) =40.9396(cosh4s6-
1) =O.O144m=
14mm
D, =a, (coshz-
1) =40.9396(cosh~~~f~6-
1) =O.l962m=
196mm
D, =o,(coshc-
l) =752.1673(cosh7!~~q368~~3-
l) =0.2643m=264mm
D, = D, + D, - D, = 264 + 196 - 14 = 446 mm
At-
1 OC, T=9220N
H
9220
a, = - = = 587.7104 m w, 15.688
H a2 = k=
9220 = 31.9884m 288.2292
x1 = a, (M - RS) (1.0005) = 3 1.9884 (22.86 - 2.9274) (1.0005) = 1 0855 m a1 587.7104
SP = a, sinh 2
= 3 1.9884 bnh 31{yii4
= 1.0857 m
CHAPTER
RSP=RS+SP=2.9274+ RSP
X, = a2 sinh- ’ -
a2
II-CONDUCTOR
87
SAGS AND TENSIONS
1.0857=4.0131rn
= 3 1.9884 sinh- ’ 34.y1814 = 4.0026 m
X, = X, - X, = 4.0026 - 1.0855 = 2.9176 m
X = M - X, = 22.86 - 2.9176 = 19.9424 m D, =a,(cosh:-
1) =31.9884
D, =a2 (coshz-
1) = 31.9884(cosh~~~~~4-
D, =a1 (cash:-
D, =D,
+D,
(cosh31~~~~~4- 1) =O.O184m=
1) =0.2507m=251
l) =587.7104(cosh:89;~7412~4-1)
-D,
=338+251
- 18=571
18mm
mm
=0.3384m=338mm
mm
At 15.5 OC, T = 7740 N
H = ~7740 = 493.3707 m
a’ = w,
15.688
H
7740 = 26.8536 m a2 = w = 288.2292 =
x 1
a2
(M - RS) (1.0005) = 26.8536 (22.86 - 2.9274) (1 .OOOS)= 1 0855 m 493.3707 al
Xl
SP=a? sinh -
a2
= 26.8536 sinh :ey5y6
= 1.0858 m
RSP=RS+SP= 2.9274+ 1.0858=4.0132m RSP
X, = a, sinh- ’ -
a2
= 26.8536 sinh- l 2:08:3;?6 = 3.9984 m
88
TRANSMISSION X,
=X2
X=M
- Xl
= 3.9984
LINE DESIGN MANUAL
- 1.0855 = 2.9129 m
- X, = 22.86 - 2.9129 = 19.9471 m
D,=a,(cosh$-
1) =26.8536(~osh:6p88;;5~-
1) =O.O219m=22mm
D, =a,(cosh$-
l) =26.8536(co~h~~~~~~~-
l) =0.2982m=298mm
D, =a, (,osh~-
1) =493.3707(cosh499;83477d7-
D, =D, +D, -D,
At32
l) =0.4033m=403mm
= 403 + 298 - 22 = 679 mm
OC. T=6760N
H
6760 = ~ = 430.9026 m a1 = w, 15.688
H a’ =w=
x1 =
a2
6760 = 23.4536 m 288.2292 (M - RS) (1.0005) = 23.4536 (22.86 - 2.9274) (1 .OOOS)= 1 0855 m
430.9026
a1
SP = a, sinh 2 = 23.4536 sinh
1.0855 = 1.0859 m 23.4536
RSP = RS + SP = 2.9274 + 1.0859 = 4.0133 m
X2 =a, sinh-’ !?!f
= 23.4536 sinh- ’ ~~~,j3~6 = 3.9940 m
a2
X, = X2 - Xl = 3.9940 - 1.0855 = 2.9085 m
X=M-
X, =22.86-
2.9085 = 19.9515 m
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
D, =a, (yxh$--
l) = 23.4536 (cash $jp)&T;6 - $ = 0.0251 m = 25 mm
D, =a2 (c~sh$-
1) = 23.4536 (cash :;:23p6‘
1) =0.3409m =341 mm
D, =a, (cosha$-
1) =430.9026(cosh~~!~~256-
l) =0.4620m=462mm
D, =D,
+D,
- D, =462+341-
25=778mm
At43 OC, T=6260N
H a1 =w 1
6260 = -= 15.688
399.0311 m
H
6260 = 21.7188 m az = ii = 288.2292
x, =
a,@f - RS) (1.0005) = 21.7188 (22.86 - 2.9274) (1.0005) = 1 0855 m 399.03 11 a1
SP=a, sinh;
Xl
1.0855 = 21.7188 sinh 21.7188 = 1.0860 m
RSP=RS+SP=2.9274+
1.0860=4.0134m
X, = a, sinh-’ RSP = 2 1.7 188 sinh- l ~~~~~8 = 3.9909 m a2
X, = X2 - X, = 3.9909 - 1.0855 = 2.9054 m
X =M - X, = 22.86 - 2.9054 = 19.9546 m
D, =a, bosh:-
1) =21.7188
(cosh211f!!f~8-
1) =0.0271 m=27mm
90
TRANSMISSION
D, =a, (&$
1) =21.7188
LINE DESIGN
(cosh;;y;;;8-
MANUAL
1) =0.3677rn=368rnm
D3=al(cosh~-I) =399.0311 (coih;g-f,.,~l -I) =0.4990m=499rnm D,
=D,
+D,
=499+368-27=840mm
-D,
U. S. Customary Figure
DC-576
39 shows
the
U.S.
customary
sag and
tension
computations.
(6-76)
&,tL
SAG CALCULATIONS
LOADINGWeight Factws: Dead Welpht
(W’)
1, n 750 St.1
0. Initial.- &m°Fd.2d Fenal. -&?.e.?FX Loaded. OF Final. &OF
-5e -
Computed by -
4
3/7q
lb
SC,‘&!?&% @&!-lb
Resultant:
lb
0.000 o//
Ib/ft2 Wind(W”‘)/
[
90 .*n
I
Figure 39.-Sag
H = T - W,
H
a2 =r=H
t
8
I
0
60
1
and tension
T>/
7
Permanent Set 0.009
IbItt
Creep Total
Ib/ft
2.330
T
calculation
form
Modulus. (E) Final-x initial/,.56x
1 SAGFACTOR 1 SAG,ft FEET
I 0.09d9
lLuf&LLn//
I
I
I
I
3gg5*53g3 = 202 *3058 19.75
f-t
ft
78
I / I I I
effect
(sag) = 4000 - 2.5306 (1.78) = 3995.5393 lb 3gg5-53g3 = 1578 8901 2.5306 *
106 lb/i,? 106 lb/in2
Final AE .m lnttial AE s
150
for insulator
151
o.oo--O.ooa
Ib/ft
per “F
SPAE;LENGTH(S)
tnch Ice.
w
(W’“)
Ib/ft
Area (A) ti in2 Temp. Coeff. of Linear Exp.:
oF * UNSTRESSED 1TEMP. LENGTH
No Ice. No Wind (W’)
a,=-=
lb
Date
LOADING .km
Kfe
Ad.2
o/n
problem
tb lb
1 SW,Ib
1 TENSION,Ib
I.? 7959
I
I I
(U.S. customary).
I
JImlo
n;d
CHAPTER
x 1
II-CONDUCTOR
SAGS AND TENSIONS
= a, (M - RS) (1.0005) = 202.3013 (75 - 9.6) (1 .OOOS)= 8 3838 ft 1578.8901 4
Xl= 202.3058 SP=a2 sinhz
8.3838 sinh 202.3058 = 8.3862 ft
RSP = RS + SP = 9.6 + 8.3862 = 17.9862 ft
X2 = a, sinh- ’ E
= 202.3058 sinh- ’ :a’;~~5!8
= 17.9626 ft
a2
X, =X2 - Xl = 17.9626 - 8.3838 = 9.5788 ft
= 75 - 9.5788 = 65.4212 ft
X=M-X,
X sinh -=
L=a,
1578.8901 sinh l;;;p;;;1
= 65.4399 ft
4
Lu,=L-
w,
b,
2AE
= 65.4399 -
I2
--X+sinh&c& a1 i 4
a1 )
2.5306 ( 1578.8901)2 2 (7 490 285)
65.4212 65.4212 65.4212 1578.8901 + sinh 1578.8901 ‘Osh 1578.8901
= 65.4050 ft Temperature = 0 OF = t, Assume T = 3000 lb w H (no load) H = == 1 1.075 al=w H 3000 = -= a, = w 19.75 x 1
=
2790.6977 ft
151.8987 ft
a, (M - RSI (1 .OOOS) _ 15 1.8987 (75 - 9.60) (1 .OOOS)
SP=a2 sinh:=
Ql
2790.6977 151.8987 sinh 1;.l5;;;7 .
= 3.5618 ft
= 3.5615 ft
91
‘12
TRANSMISSION
RSP=RStSP=9.6+3.5618=
LINE DESIGN
MANUAL
13.1618ft
x2
RSP = a, sinh-’ = 151.8987 sinh-’
x,
=x2
~~~~91g87= 13.1454 ft
a2
- x,
= 13.1454 - 3.5615 = 9.5839 ft
X =M - X, = 75 - 9.5839 = 65.4161 ft
L = a, sinh:
65.4161 = 2790.6977 sinh 2790.6977 = 65.4221 ft
wl(al)2 LU, =L - 2AE
= 65.4221
x ( c+sinh-f
1
cosht
1.075 (2790.6977)2 2 (7 490 285)
-
1
65.4161 65.4161 65.4161 2790.6977 + sinh 2790.6977 ‘Osh 2790.6977
= 65.3959 ft
Lu, = Lu, + Lu,e(t,
t, =
- to)
Lu, - Lu, 65.3959 - 65.4050 + o = _ 12.10 OF Lu, e + to = 65.4050 (0.000 011 5)
Assume T = 2700 lb = H (no load) H 2700 a, = - = 1075=2511.6279ft WI * H 2700 a, = p = 19.75 = 136.7089 ft x 1
=a,@4 - RS) (1.0005) _ 136.7089 (75 - 9.6) (1.0005) = 3.5615 ft 2511.6279 a1
SP = a, sinh:
RSP=RS+SP=
= 136.7089 sinh
3.5615 = 3.5619 ft 136.7089
9.6 + 3.5619 = 13.1619 ft
CHAPTER X2 =a,
sinh-’
@E=
II-CONDUCTOR
93
SAGS AND TENSIONS
136.7089 sinh- l 1:; y;899 =
13.1417
ft
a2
X,
=X2
- X,
= 13.1417
- 3.5615
= 9.5802
ft
X = M - X, = 75 - 9.5802 = 65.4198 ft
L
=
a,
sinh
Lu, =L-
5
= 25 11.6279
sinh
65.4198
25 11.6279
F!&&?
= 65.4273 ft
cash -x a1
1.075 (25 11 .6279)2 2 (7 490 285)
= 65.4273 -
65.4198 65.4198 65.4198 2511.6279 + sinh 25 11.6279 ‘Osh 25 11.6279
= 65.4037 ft
t, =
Lu, - Lu, Lu,e
Similar temperatures
+t,
=
65.4037 - 65.4050 65.4050 (0.000 011 5) = -1*73 OF
calculations were:
Assumed
were
made
T-- H (no load), lb 2400 2100 1800 1500 1400
At
The figure,
resulting determine
of the
line.
0 OF,
temperatures the tensions
w,
1.075
five
additional
assumed
tensions,
= = = = =
the
resulting
11.30 28.72 53.58 92.53 110.88
are plotted against the assumed tensions for the desired temperatures and proceed
1 ft
and
Temperature, OF t, t, t, t, t,
T = 2645 lb
H 2645 = 2460.465 a, = - = -
for
on figure 40. Using in finding the total
this sag
94
TRANSMISSION
LINE DESIGN MANUAL
2600
2400.
g
2200
; 0v) z E
2000
1800.
1600
-20
0
+20
l 40
T EM PERATURE, Figure 40.-Tension-temperature
curve for insulator
+80 -
+60
effect
+I00
OF problem
(U.S. customary).
104-D-1068.
+I20
CHAPTER a2
=-=
x
H w
2645 -= 19.75
II-CONDUCTOR
SAGS AND TENSIONS
133.9241 ft
- RS) (1.0005) 133.9241 (75 = 9.60) (1.0005) = 3.5615 ft a1 2460.465 1
=a,(M 1
SP=a2 sinh$
= 133.9241 sinh 3.5615 = 3.5619 ft 133.9241
RSP=RS+SP=9.6+3.5619=
X2 = a, sinh- 1 Q
13.1619ft
= 133.9241 sinh- 1 l:‘; kyll
= 13.1408 ft
a2
X, =X2 - X, = 13.1408 - 3.5615 = 9.5793 ft
X = M - X, = 75 - 9.5793 = 65.4207 ft
D,=a,(cosh:-
D, =D,
l) =133.9241(khll~~~~~)481-
+D,
1)=0.6452ft
- D, = 0.8698 + 0.6452 - 0.0474 = 1.4676 ft
At 30 OF, T = 2075 lb H 2075 a, = - = = 1930.2326 ft w, 1.075 H _ 2075 a2 = w- = 105.0633 ft 19.75 x
=a,(M-
1
RS) Ql
(1.0005) = 105.0433 (75 - 9.60) (1.0005) = 3 5615 ft 1930.2326
95
TRANSMISSION
SP = a, sinh 2 = 105.0633 sinh RSP=RS+SP=9.60+3.5622 RSP
X, = a, sinh-’ -
LINE DESIGN MANUAL
3.5615 = 3.5622 ft 105.0633
= 13.1622 ft
= 105.0633 sinh”
1~~~6~3 = 13.1280 ft
a2
X, =X2 - Xl = 13.1280 - 3.5615 = 9.5665 ft
X=M-
X, =75- 9.5665 =65.4335 ft
D, =a,(cosh$
1) =105.0633(cosh1;;;;;3-
l)=O.O604ft
D, =a, (ah:
- 1) = 105.0633 (cash ll;;;;;;3
- 1) = 0.8213 ft
D, =a1 (co&:
- 1) = 1930.2326(cash
D, =D,
1;;;;;;6-
1) = 1.1092 ft
+D, - D, = 1.1092 + 0.8213 - 0.0604 = 1.8701 ft
At 60 OF, T = 1733 lb --
H 1733 a, = - =x= Wl .
1612.0930 ft
a, = /f=F5=87.7468 x 1- _ a,
ft
04 - RS) (1 .OOOS) 87.7468 = (75 9.60) (1 .OOOS) = 3.5615 ft a1 1612.0930
SP = a, sinh:
= 87.7468 sinh
RSP=RS+SP=9.60+3.5625
3.5615 = 3.5625 ft 87.7468
= 13.1625 ft
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
13.1625 X, = a, sinh-’ RSP = 87.7468 sinh-’ 87.7468 = 13.1136 ft a2
X, =X2 - X, = 13.1136 - 3.5615 = 9.5521 ft
X = M - X, = 75 - 9.5521 = 65.4479 ft
D, =a,
(cosh$-
l) =87.7468(cosh$~~~~8
D, =a2(ysh2-
$ =87.7468(cosh~~:~~~~-
D, =aI(cosht-
- l) =O.O723ft
I) =0.9817ft
l) =1612.0930(xsh1~~~~~~O-
$ =1.3287ft
D, = D, +D, -- D, = 1.3287 + 0.9817 - 0.0723 = 2.2381 ft
At90°F,T=15131b
H
a, = - = g$ WI *
= 1407.4419 ft
H
1513 = = 76.6076 ft a2 =w 19.75 x
1
=
Q-2
(M - RS) (l-0005) a1
= 76.6076 (75 - 9.60) (1 .OOOS) = 3 56 15 ft 1407.4419
SP = a, sinh x, = 76.6076 sinh 7iyo1756 = 3.5628 ft a2
RSP=RS+SP=9.60+3.5628 RSP
X2 =a2 sinh-’ -
= 13.1628ft
= 76.6076 sinh- l :i’i$i
a2
X, =X2 - X, = 13.0989 - 3.5615’= 9.5374 ft
= 13.0989 ft
98
TRANSMISSION
X=M-
X, =75-
9.5374=65.4626
LINE DESIGN MANUAL
ft
D, =a, kosh$
1) =76.6076(cosh;;~;;6-
1) =O.O828ft
D, =a+sh$-
1) =76.6076(cosh;~:~;;~-
l)
D, =a1 (cosh$
D, =D,
1) = 1407.4419 kosh lg4;;;g
+D,-
= 1.1306ft
- 1) =1.5227 ft
D, = 1.5227 + 1.1306 - 0.0828 = 2.5705 ft
At 110 OF:, T = 1405 lb
H a, = - = E Wl . H a2 = w
x
= 1306.9767 ft
1405 == 71.1392 ft 19.75
=a2(M-
= 71.1392 (75 - 9.60) (1.0005) = 3 5615 ft
Ra(1.0005)
1
1306.9767
a1
SP =a2 sinhs
= 71.1392 sinh ;i5fi12
= 3.5630 ft
a2
RSP=RS+SP=9.60+3.5630= X2 =a, sinh- l g
13.163Oft
= 71.1392 sinh-’
~~‘:~~~ = 13.0890 ft
a2
X, =X2 - Xl = 13.0890 - 3.5615 = 9.5275 ft
X=M-
X, =75-
D, =a,(cosh~-
9.5275 =65.4725 ft
1) = 71i1392 (cash ~~~1631~2 - 1) = 0.0892 ft
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
99
D, =a,(cosh$ 1) =71.1392(cosh;;~;~;;-1) = 1.2075ft 65.4725
-
1306.9767
D,
18.
=D,
- D 1 = 1.6403
+D,
Spans
With
Concentrated
infrequent
and
arrangements in addition figure 3.1 .
are used. to the dead
are confined Such force
to the
span
1. 2. string
Assume
a desired
Calculate that will
relating or switchyard
problems applied.
are complicated A method which
ft
ft
to spans spans
with concentrated in which
loads
taps
are
or tie-down
by the elastic effects of the tap or tie-down adequately treats this problem is shown on
to this problem than the method shown on figure 41 would be to sag normal sag for a given temperature and then add a calculated length for
the
force
may be determined F. F. Priest: spring
tension
of the
by the
at some
tie-down,
following
given
see figure
procedure
42. The
which
required
was developed
temperature.
the angle that will be formed by a vertical result from the horizontal tension in the
to the tie-down after installation 3. By multiplying the length reflected length of the insulator The difference in the originally
= 1.6403
= 2.7586
to substation
to compensate
additional length of conductor by a former Bureau engineer,
- 0.0892
Loads.-Problems
mainly
Probably a better approach the conductors to the calculated of conductor
+ 1.2075
1
(0 = tan-’ H/P). of the insulator string string is obtained (i,
line and the position of the insulator conductor and the vertical force due by the sine of this = isin 0).
angle,
the horizontal
between the length of the insulator string as it will lay in the near horizontal sagged span and its calculated horizontal reflected length after the tie-down
indicates the additional amount of conductor same characteristics as the originally sagged
required to give the final span without the tie-down.
tied-down
span
position is made, about
the
Example Conductor: Span length Force Spring Length
Calculate might short the
242 mm2 (477 kcmil), = 45.7 m (150 ft)
of hardware on tie-down tension at 15.5 ‘C (60 of insulator
sags and
string
tensions
be applicable during span, such as in the insulator
effect
=
ASCR
24/7
= 444.8 N (100 lb) OF) = 889.6 N (200 1829
for the
mm
conductor,
lb)
(6 ft)
without
tie-down,
for a range
of temperatures
that
installation. If the insulator force will be appreciable in a comparatively example used here, the original sags should be determined by considering
(see sec.
16).
LOO
TRANSMISSION
LINE DESIGN
MANUAL
P
LeveI' Span
Inclined
Span
s = 2PL + wL2
8H CONCENTRATED LOAD AT
CENTER OF SPAN
H H-TeH
t
P
Level Span
Inclined S=
Span
L, L, (2P + WL) 2LH
LOAD AT ANY POINT ON
SPAN
=Horizontal span length between conductor support points, m (ft) = Horizontal tension in conductor, N (lb) = Sag, from line of supports at concentrated load, m (ft) =Concentrated load, N (lb) = Linear force factor (weight) of conductor, N/m (Ib/ft) ;,L*= Horizontal distance from concentrated load to points of support, m (ft)
L H S P
Figure 41.Spans
with
concentrated
loads. 104-D-1069.
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
i = Length of insulator string, mm (ft) length of insulator string, in - Horizontal reflected ni = i-iH, mm (ft) H - Horizontal tension in conductor, N (lb) P - Vertical force added by tie-down (hardware tension) , N (lb) Figure 42.-Graphical method for determining concentrated load problem. 104-D-1070.
Assume the following
length
‘C
(OF)
-18 -1 15.5
(0) (30) (60)
mm 625 780 917 1039 1149
For 15.5 OC:
mm
required
by previous
for
calculations:
Tension,
SW, w
N
(2.05) (2.56) (3.01) (3.41) (3.77)
3750 3015 2571 2268 2050
(lb)
(843) (678)
(578)
(510) (461)
For 60 OF: 2571/1334.4
e = tan-’
578/300
= tan- l 1.926 70
= tan- ’ 1.926 70
= 62.57O
= 62.57O
ih = 1829
(ft)
+ spring
of conductor
sag and tension values have been obtained Temperature,
e = tan-’
additional
101
Sin
8 = 1829 (0.887 57)
= 1623.37 mm Ai = 1829 - 1623.37 = 205.63 mm
_
ih = 6 sin 8 = 6 (0.887 57) = 5.33 ft
Ai = 6 - 5.33 = 0.67 ft = 8 in
TRANSMISSION
102 The
Ai vahle
is the additional
Considering 8 constant can be made:
for setting
Temperature, OC (OFI -18 -1 15.5 32 49
(0) (30)
(60) (90)
(120)
amount
of conductor
the spring
Horizontal N 3750 3015 2571 2269 2050
LINE DESIGN MANUAL
tension
to be added at other
to the span after
temperatures,
the
the initial following
tension, (lb)
Hardware force, N (lb)
Spring tension, N (lb)
(843) (678) (578)
444.8 444.8 444.8 444.8 444.8
1501 1120 890 733 620
(510) (461)
(100) (100) (100) (100) (100)
(337.5) (251.9) (200) (164.7) (139.3)
sagging. tabulation
<
INSULATION, 19. Insulation which
will
Coordination.-Insulation
withstand
are three
LIGHTNING PROTECTION, CLEARANCEPATTERNS
the
different
voltage
voltage
requirements (1)
for the Lightning
(2) (3)
Switching
coordination
stresses
stresses
to which
to consider
design of high-voltage voltages, voltages,
60~HZ voltages,
and called power
the
AND
is the selection
system
when transmission
of an insulation
or equipment
determining
III
insulation
structure
will
be subjected.
and
electrical
There clearance
lines:
frequency
operating
voltages.
The probability of flashover must be controlled so that any system disturbance is minor. Lightning impulse voltages generally have the highest values and the highest rates of voltage rise. The time range for these voltages to crest is about 0.5 to 6 microseconds. Although it is impractical to provide
a sufficiently
high
impulse
conductor is struck by an average This is done by locating overhead current structures
to earth through for this purpose.
insulation
strength ground
Ievel
the steel towers or through This diversion of the current
string and air gap insulation values, and by obtaining In a region of average storm intensity of 30 storm on the average of 100 direct must be used on transmission The
lightning
current
the tower footing ground wire will
l l
Isoceraunic Stroke-current
level
clearances
Number
l
Span length Midspan clearance Number of insulator
If the tower,
height footing
(number magnitude
l
l
the
of tower
Tower Tower
l
to follow
a path
and
along
conductor
permissible strokes
and
voltage
developed may divert
wires provided by coordinating low footing a transmission
when
a
be controlled. the lightning on
wood pole the insulator
resistance. line will
be struck
mi) of line per year. Overhead ground wires lightning strokes and shield the conductors. the shield
wire,
down
the tower,
and through
top of the tower and the connected overhead of the current resistance in the tower footing. and
lightning protection design is based primarily the lightning performance of a transmission
l
l
a sufficiently days per year,
strokes per 161 km (100 lines to take these direct
is expected
the
lightning flashovers direct strokes and
the ground is accomplished
resistance to the ground. The entire attain a high voltage, mainly because
An evaluation acceptable affecting
to withstand
lightning stroke, wires to intercept
overhead
ground
on theory line are:
of lightning storm and wave shape
days
wire
configurations
and experience.
to be expected
each
The
for an
major
factors
year)
resistance location
of overhead
ground
between units
conductors
current
to midspan
stroke to midspan
may
cause
tower
wires and
(shield
overhead
is more
than
flashovers. 103
angles ground
twice
the
to conductors) wires permissible
stroke
current
to
TRANSMISSION For
transmission
flashover
rate.
or by
the
lines
lightning considerations
lightning
must
not
and
will
impulse could
levels,
an increase
in insulation
strength.
by the
insulation
is determined
may
be dictated
345
kV,
control
primarily
by either
switching
the
probability
insulation
strength length
impulses,
tower
does surge
surfaces
so switching
not
any
result
design;
that
have
however,
made
considerations
will
against
is a function
The number of surges very low. on simulated
towers
(extra-high
voltage)
increase
in switching
surge
does
result
field
effect This
dictate
in
of insulators
is due to the electric
proximity
the
factor
protection surge
At EHV
number
lightning
considerations prime
expected. switching
been
shape.
in the
This
is called
the
due to a switching
tower
the
surge
become
in a proportional
increase
strength.
and
surge
on tests
almost
a lo-percent
in switching
of the
is based
by
switching
surges
of flashover
to duplicate
example,
increase
to lightning
The
be made
For
proximity
Above
probably
insulation
adjustments
in a lo-percent
line
characteristics and the magnitude of the surges be selected to keep the probability of flashover from
where withstand
kV,
rate.
be overlooked.
of the line insulation insulators used may surge
to 345
the line insulation
flashover
flashover
Switching
up
At 345 kV,
LINE DESIGN MANUAL
distortion
effect
the insulation
not
caused
does
values
not
apply
at the
EHV
levels. Wave
shapes
grouped
for
for
lightning
testing
and
impulses
to provide
and basic
switching data
surges
for
are infinite
use in insulation.
in number,
Wave
shape
but
have
been
is defined
by
two
impulse
and
the
parameters: (1)
The
time
instant
that
the
(2)
The
time
the
impulse
crest
to crest BIL
have
have Two
a time
resulted
tail
the
beginning
of the
value. as the
of the
time
impulse,
interval
at which
trapped
charge
The
between the
system
Restriking
at the occurs
builds
Resistors overvoltages insulation.
when
up at a faster
in momentary voltages
time
reestablishment
on the are for
of a typical with
50 to 2000
UHV
transmission
impulse
testing
the
voltage
beginning
is one-half
have
BIL.
surge
of of the
of line
and
in transmission the
other
there
towers
switching line
is high-speed but
opening.
Transformers
connected
to ground
high-speed voltage
reclosing varies
with
period, breaker
and
the
may
will
reclosing
characteristics,
tests
voltages.
coordination.
reclosing
there
BIL
an increasing These
surge
insulation
to energization,
The
surges,
between
has been
and equipment.
is similar
surge
shape.
of switching
lies somewhere
developed,
insulation
wave
of 0.5 to 6 microseconds,
Coordination
of transmission
voltage;
SO-microsecond
microseconds,
are of concern
no initial
the
by
lightning
operation
in the
switching
on a 1.2-
coordination
with
switching the previous
energy
for
is based
from
and
operations
of a line
from
energization.
data
flashovers.
coordinated
ranging surge
affecting
the range
is usually
switching
latter
level)
is within
As EHV
of switching
The line
insulation
stress
in better
types energizing
breaker
between
is defined
parameter
to crest
to crest
of outdoor
tripout.
of the
which on the
principal
withstand.
is the on the
interval
its peak
value,
instant,
impulse time
impulse
60-Hz
amount
the
is the
reaches
to half
is the
(basic
so lightning and
voltage
and
1.2-microsecond which
which
value.
Time The
to crest,
One
following be energy
normally becomes
line length,
a line trapped
dissipate the
the
same
as
and the state
of switching. lines rate
are being than of the
deenergized
the dielectric arc
across
and strength
the
interrupting
the
recovery
voltage
of the interrupting contacts
across medium.
and
can
the
circuit
This
results
produce
extreme
system. incorporated EHV lines
in the closing stroke of a breaker to help reduce switching which, in turn, helps reduce the switching surge requirements
for
surge line
CHAPTER Some
causes
III-INSULATION,
of switching
l
Normal
l
High-speed
line
l
Switching
capacitor
l
Load
l
Out-of-phase
l
Reinsertion
l
Circuit
l
Current
Power in the
line
surge
energizing
PROTECTION,
overvoltages
and
CLEARANCE
PATTERNS
105
are:
deenergizing
reclosing banks,
shunt
reactors,
and
cable
circuits
rejection switching of series breaker
capacitors
restriking
chopping
frequency
system
overvoltages
alters
l
Voltages
l
Load Open
l
LIGHTNING
are caused
or removes
on the
the
unfaulted
rejection end of a long
Ferroresonance Although the clearance
by
condition, phases
energized
an abnormal such
during
line
condition
which
exists
until
a change
as:
a phase-to-ground
(Ferranti
fault
effect)
l
necessary
for power
frequency
voltage
is much
less than
for switching
or lightning, the clearance envelope is very sensitive to the insulator swing angle created Data on extreme winds during storms and their frequency of occurrence are necessary power frequency electrical insulation clearances. and and
surges
by the wind. to determine
In transmission line design, there are two basic insulations to be considered, the insulator string air. The insulator swing angle depends on the diameter-to-force (weight) ratio of the conductor, the ratio Consideration
(2) switching
of wind must surge,
span to low-point be given to each
and (3) p ower
span. of the
frequency.
three
of flashover following a circuit breaker operation. of tripouts per 161 km (100 mi) of line per year. of the mean recurrence interval. Bureau insulators
types
Switching
wood-pole designs are based on with the minimum air gap between
by a 0.19-kPa
wind
pressure
at 15.5
coordination the conductor
wires
separation ground
and
at midspan wires.
Insulation included
the
conductors must
See section withstand
will
be greater 20 for
must
not
than
minimum
be coordinated
impulse,
on the probability
value of the a wind pressure
the impulse insulation angle of the suspension
and the air-gap insulator strings
sufficient
occur
before
at the structure midspan across
so that flashover because
flashover occurs
angle of 30’) the overhead
between
the
at the
structure.
of the impedance
overhead The
of the overhead
clearances. the
insulator
string
and
the
air
gap.
Factors
0
Crest
l
Maximum
l
Strength of air to switching surges in relation to the impulse strength of the insulators, the ratio of critical impulse to switching surge withstand Percent allowance made between withstand voltage and critical flashover of air, or ratio withstand
of an insulator
string
l
l
withstand
or for a sideswing at midspan between
in an evaluation Maximum system factor
of the insulation operating voltage
(1) lightning
is based
of the impulse insulation and the structure with
o C on the conductors, the clearance
whichever is greater. For complete coordination, ground wires and the conductor must be made ground
stress:
performance
Lightning performance is measured by the number Power frequency performance is measured in terms
of 0.19 kPa (4 lb/ft*) at 15.5 ‘C (60 ’ F). On steel structures, clearance to the structure are coordinated for the sideswing caused
of voltage
surge
are:
of wave switching
to critical
surge
overvoltage
flashover
or of
TRANSMISSION
106 l
Contaminated
l
Nonstandard
a
Maximum
this
The
values the
on unfaulted
phases
factor
switching
that
voltage
can
vary,
of the
wave
is fi
surge
varies
of switching. is, taking
with
hut breaker
variation
in the
the surge
magnitude
values
line surges
length,
for all switching
or two
switching
situations
produce
highest
values.
and
that
barometric pressure. The Bureau surges. Some designers like
switching
two
extra
units
are
and, on 345-kV steel unit and for hot-line
because in addition transmission lines not only frustrating, original
be included
in the
If a transmission
one
for
construction, maintenance.
examples elevation
these
satisfactory
to use
insulation
strengths test data surfaces,
as the ratio of the impulse strength for value as a ratio between withstand upon value.
gap length, wave shape, and A factor of 1.1 is used for
examining
the
air
is dependent
fault
voltage
insulation
upon
the
on unfaulted
strength
for
power
one extra insulator unit is added to allow two extra units are added: for 230-kV steel
a possible
defective
unit
and
one
for
hot-line
one extra unit is added as a combination safety unit These extra units have proven to be very valuable
calculations
to reduce
shown
initial
in section
Lightning wrote
in the
basically
costs
as insulation coordination is not economical when
further
of insulation selection limit is governed by
for three different the switching surge
voltages. impulse
limits shown in the tables should be used for design discussed for hot-line maintenance and possible defective
line is to operate
designers,
Westinghouse,
and weighting
design.
The lower of the two elevation extra insulator units previously
discussed
of the
by statistical
to the hot-line maintenance safety they afford, they have helped to restrict Bureau to minimal “unexplained” flashovers and outages. Such flashovers and outages are but they are costly to an electrical entity and must be taken into consideration
Tables 16, 17, and 18 show tables show that the permissible
factors such Such design
1.175
factor for nonstandard sea level. 1.2 for the maximum
atmosphere, are used when
added,
The
for
to use a 3-sigma
wood-pole transmission line construction, defective unit. For 115-kV steel structures,
construction, maintenance; for a defective
uses
surge
the state
distributions determined from upon the proximity of grounded
flashover, but since sigma is a variable depending we have set 17.5 percent as a coordination
A factor of 1.5 for contaminated phases, and a safety factor of 1.25 frequency overvoltages. For 115-kV for a possible
the
and air gaps are described by strength These distributions will vary depending
and
situations it is probably
strings tower.
accepted
can he described
conservative,
contaminated atmosphere. An added altitude elevation of the given transmission line above
20.
switching
To be more
the critical configuration,
Some
characteristics,
The
is generally
of occurrence.
humidity, air to the
not
overvoltage
frequency
one
in the
a S-percent
by their
of insulator on a full-scale
and gap
crest
at the time
distribution;
etc.)
(altitude)
voltage
operating
The
maximum
system
MANUAL
of safety
maximum
limit.
(chemicals,
density
fault
Factor
l
The
atmosphere air
LINE DESIGN
purposes. The units, should
tables.
problem
of lines
These values.
free,
or because
then of lack
insulation of facts,
coordination have
is a necessity.
chosen
to ignore
some
which results in lines that have many unexplained outages. considered over a period of time._Insulation coordination is
21.
Protectioma series
In 1930, C. L. Fortescue, a consulting transmission line engineer with of articles on lightning investigations that were published in Electrical
Joumm!
He advanced
the theory
strokes
of lightning.
Previous
that
high-voltage
to that
time,
transmission transmission
lines lines
should were
be protected designed
on
from the
direct basis
of
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
Table 16.-Insulation
selection
CLEARANCE
PATTERNS
107
for 345 kV Switching surge impulse, positive critical
Power frequency, 60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge
2.5
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand
1.175
1.175
1.1
1.5
1.15
1.25
f. Contaminated
to critical flashover voltage
atmosphere
g. Factor of safety h. Rise due to line faults Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through
Normal line to neutral, 345/G Total withstand multiplying neutral voltage
(h)
2.78
1291 kV
554 kV
1585 kV
690 kV
= 199.2 kV factor (at sea level) times normal line to
Flashover of 18 insulator units, 146 by 267 mm (5-3/4 by 10-l/2 in), from table B-7 in appendix B Factor for nonstandard
6.48
1585/1291
air density (altitude)
namely,
that
6901554 = 1.25
2154 m (7068 ft)
From table B-10 in appendix B, permissible elevation limit
induced-stroke assumption;
= 1.23
a charge
cloud
in the vicinity
2362 m (7750 ft)
of the transmission
line,
with
its accompanying gradient of voltage to ground, would bind a charge on the line. The discharge of the cloud to any object other than a transmission line, would release this bound charge, which was then free to travel along the line seeking a path to ground. However, induced voltage gradients appearing on transmission lines during account for the damage to the lines. high-voltage lines. Complete protection
nearby lightning discharges have proved to be too low to The direct-stroke theory is now generally accepted for against direct strokes requires a shield to prevent lightning
from striking the electrical conductors, together with adequate adequate drainage facilities so that the discharge can drain conductors. The shielding method does not allow the formation to ground. An alternative nonshielding method tubes or ground fault neutralizers, does allow conductors four basic
but provides requirements
of protection an arc to form
a means for quenching for the design of a line
Adequate the full
clearance effectiveness
level
used
in the
must
line
design.
such as protector structure and the
the theory
be locatd
from the line conductor to the tower or ground of the insulating structure can be obtained.
(3) Adequate clearances from overhead especially at midspan, to prevent flashover voltage
strength
of the structures and without affecting the from the line conductor
by auxiliary devices, between the ground
the arc without interrupting based on the direct-stroke
(1) Ground wires with sufficient mechanical the line conductors from direct strokes. (2) so that
insulation to ground of an arc
ground wires to conductors to the conductors for voltages
line are:
circuit.
to adequately must
The shield
be maintained
must be maintained, up to the protective
TRANSMISSION
108
LINE DESIGN
Table 17.-Insulation
MANUAL
selection for 230 kV Switching surge impulse, positive critical
Power frequency, 60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge
2.5
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand to critical flashover voltage
1.175
1.175
f. Contaminated
1.1
1.5
1.2
1.25
atmosphere
g. Factor of safety h. Rise due to line faults Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through (h)
Normal line to neutral, 230/a Total withstand multiplying neutral voltage
6.76
= 132.8 kV factor (at sea level) times normal line to
Flashover of 12 insulator units, 146 by 254 mm (S-3/4 by 10 in), from table B-7 in appendix B Factor for nonstandard
air density (altitude)
898 kV
369 kV
1105 kV
490 kV
1105/898
From table B-10 in appendix B, permissible elevation limit
overhead ground wires are not normally used ground wires are used for a distance of 0.8 km the entire length of line. On lines of 115 kV for the entire length of the line. On transmission (3/8-in),
7-wire,
above
are used.
high-strength
lines,
13-mm
On lines
or for extra so that the
long extra
saline fogs occur, corrosion resistant overhead extended a straight
where spans, heavy
galvanized
(l/2-in), very
7 -wire, heavy
line
ice loading,
through
the
overhead
maximum angle of 30 o with the vertical. to give a maximum angle of proteetion the
angle
steel
strand radial
is used
for overhead
galvanized
steel
ice thickness
of protection
should
adequately,
ground
strand
of 25 mm
On 230 ground
(1 in) or more,
the
poles
the overhead the terrain to maintain
kV
wires occurs wires where
it is desirable to use a more wires. In order to locate the in wood-pole
of protection at tangent structures. ground wire and the outside conductor
At steel towers, of 20 O. Where be decreased in order
wires.
overhead
steel for the overhead ground sag. In areas near a sea coast,
and in other areas having a contaminated atmosphere, material such as Alumoweld for the overhead ground
drawn
must be obtained. are used on all lines using For standard construction,
and higher, overhead ground wires normally are used lines for voltages up to and including 161 kV, lo-mm
high-strength
the conductors a 30’ cone
3139 m (10 299 ft)
on lines of 46 kV or less. On 69.kV lines, overhead (0.5 mi) in each direction from the substations or for
it is desirable to use extra-high-strength loads may be carried without excessive
ground wires to shield high enough to provide
4901369 = 1.32
= 1.23
2154 m (7068 ft)
(4) Tower footing impedances as low as economically justified To meet the first of these requirements, two overhead ground wires H-frame wood-pole construction and generally on all steel tower lines.
and
2.78
ground
wires
lines
should
be
This means that should make a should
be located
slopes across a transmission line, an angle of less than 30’ for
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
Table 18.~Insulation
CLEARANCE
109
PATTERNS
selection for I I5 kV Switching surge impulse, positive critical
Power frequency, 60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge’
2.8
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand
1.175
1.175
1.1
1.5
1.2
1.25
f. Contaminated
to critical flashover voltage
atmosphere
g. Factor of safety h. Rise due to line faults Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through
Normal line to neutral, 115/fi= Total withstand multiplying neutral voltage
(h)
2.78
503 kV
185 kV
610 kV
255 kV
66.4 kV
factor (at sea level) times normal line to
Flashover of 6 insulator units, 146 by 254 mm (5-3/4 by 10 in), from table B-7 in appendix B Factor for nonstandard
7.57
610/503
air density (altitude)
From table B-10 in appendix B, permissible elevation limit
= 1.21
255/185
1946 m (6386 ft)
= 1.38
3864 m (12 676 ft)
’ A switching surge value of 2.8 is a more realistic value for 115-kV lines than the 2.5 value used for 230- and 345-kV lines.
wood-pole the
lines,
overhead
and
ground
less than wire
earth. If steel towers exceed indicated on figure 43. To
maintain
between voltages lightning
adequate
20 o for steel
and
the
38.1
m (125
clearance
ft)
in height, the
These and the
angles
a line angle
structure
would
be between
perpendicular or protection
and
the
a line
to the should
conductors,
the
through
surface
of the
be reduced air-gap
as
distance
any conductor and the structure should be sufficient to coordinate the impulse flashover of the air gap and the insulation used on the structures, under the conditions at which is likely to occur. Almost all electrical storms occur at temperatures between minus 1 and
designs are based air gap between 15.5 OC (60 is measured
a sideswing
lines.
conductor,
between
32 OC (30 and 90 OF), and are not
insulation suspension
tower
outside
on coordination the conductor
likely
to occur
OF). 0 n wood-pole structures between the conductor and
and the insulator
air-gap clearance strings caused
of 30 O, whichever
between
the overhead
between
the ground
ground wires
and
simultaneously
of the impulse insulation and the structure with
high
winds.
Therefore,
Bureau
of the insulators with the minimum pressure of 0.19 kPa (4 lb/fta) at
having ground wires running the pole ground wire. On
down the pole, steel structures,
the clearance the impulse
to the structure are coordinated for the sideswing angle by a 0.14kPa wind pressure on the conductors at 15.5 ‘C
is greater. wires
with
value a wind
and
For
complete
the conductors
the conductors
will
not
coordination, must
occur
be made before
the great
flashover
clearance
enough occurs
of the or for
at midspan
so that
flashover
at the
structure.
TRANSMISSION
LINE DESIGN
MANUAL
-
(50) 15.2
(70) 21.3
(90) 27.4
(130) 39.6
(110) 33.5
(150) 45.7
TOWER HEIGHT, meters Figure 43.-Reduction
Because than
of the
at the
length and
of angle of protection
impedance
structure.
of span, an outage
shows
the
span
lengths.
and
of the The
the
structure
probability
minimum
overhead
amount
ground
of separation footing
clearances
between
voltages
have
very
little
tabulation
is satisfactory
tabulation,
the sag in the overhead
for voltages
80 percent
of the
sag of the
to the
conductor
115
at this
separation
depends
desired
structure
per year,
ground
height.
at midspan
on the
a 15-ohm of line
wires
and
the
104-D-1071.
must
be greater
protection footing
level, resistance
following
tabulation
conductors
for
various
(15)
4.6 6.1 7.3 9.7 11.3 11.9 13.7 15.5 17.4
(800)
wire
to structure
Midspan spacing, m w
(1000) (1150) (1200) (1400) (1600) (1800)
from ground
mi)
overhead
(700)
relationship
the
Assuming
(600)
183 213 244 305 350 366 427 488 549
according
wires,
161 km (100
Span length, m et)
Line
lightning
(feet)
required
resistance.
of 1 or less per
midspan
against
(feet) ( meters 1
(190) 57.9
(170) 5 I.8
(20) (24) (32) (37) (3% (45) (51) (57)
required
to 500 kV. at 15.5
midspan For
’ C (60
temperature.
spans
_
clearances, longer
’ F) no load,
than should
so the those
preceding
shown
be equal
in the to about
CHAPTER Lightning 60-Hz
performance
value
slightly
III-INSULATION,
usually
less than
the
60-Hz
less. For
based
best
on the
All
structures
because path
pole.
under The
structures,
between
through
to each
desert
is fastened
protection
centerline
of the
tower I5
the
PATTERNS footing,
ohms,
of resistance,
wires
the
resistance
wires
should
111
rather
the
surge
surge
to the
pole
surge
than
the
resistance
resistance should
is
measures
be estimated,
structures, to reinforcing
(such
as in rocky,
one on each 305
mm
and
(12
a ground down
turns
grounding bars
the
brought
into
each
to 18 in) below
ground
the
of the S-pole surface
accomplished or in sandy,
when
a high
level
of
7.6 m (25 ft) from structure
earth
2
the reinforcing
terrain
at least
butt
all 2- and
welding
is used
of No.
of the pole,
the
At
mountainous
are placed
wire
is usually
and
at the top
the face
around
staples.
counterpoise
wires
side,
to 457
carried
impedance
together
(18 to 24 in) below
angles
counterpoise
structures,
spiral
grounded
on a low
be tied
of Copperweld
continuous
be adequately
depends
should
wires,
complete
On steel
stub
resistivity
line,
ground
457 to 610 mm
or a double
are buried
they
On wood-pole
by means
on each pole.
two
protection
wires,
five
placed
The
transmission
ground
wrapped
of high
ground
for lightning
to ground.
by welding
is desired.
overhead
wires
and
counterpoise
wires
values
to the overhead
pole,
footings In areas
counterpoise
of the
up to about
15 ohms,
overhead
connection
the ground
lightning The
is connected
wire
a radial
having
ground
are two
of the
other.
areas)
lines
butt
the concrete
higher above
the impedance
an underground
is made bars
there
wire
for
CLEARANCE
data.
to reduce
ground
but
of these
Where
the
resistance
surge
resistances
resistances
in transmission
Copperweld
passed
on the footing
value,
available
of each structure AWG
For
footing
the effectiveness
to ground.
PROTECTION,
is dependent
measured.
considerably
LIGHTNING
and
surface.
the
attached. Figure
B-5
in appendix An AIEE
B shows ground resistivity values in ohm-meters for the United States. Committee Report published in 1950 [ 131’ was updated and expanded by Clayton and in 1964 [14]. Th e method presented in these reports consists of groups of curves that are based
Young
on typical span
horizontal
lengths,
insulator
to 700 kV.
discussed. For studying
quantities,
that
21.
Conductor
anticipated
Type
l
Loading area where Minimum conductor Angle of protection
l l
of towers
required
Maximum line deflection Ruling span length
l
Insulation
1 Numbers
vertical, at each
sum spans
in brackets
(single
the line spacing (against
l
Maximum adjacent
outages
Patterns.-Before
Longitudinal, ground wires
l
these
The
curves
footing curves,
on
wire
configurations,
cover
a voltage
resistances use surge
transmission
for
range
a desired
resistance
lines
a range
I I5
performance
values
of 345 kV
from
of
as previously
and
above,
it is
a designer
can design
steel
towers
must
afford
for a transmission
be known:
l
l
using
and
ground
be used.
must
l
When
overhead
resistances.
quantities
lightning
[15]
Clearance data
and
and footing
the curves.
reference
following
conductor
of insulator
from the
suggested
the
vertical
Combinations
can be determined
line,
and
or double
circuit)
is to be constructed lightning)
that
and transverse loading attachment point
of adjacent
the
ground
under
wires
full-load
conditions
the for
conductors
conductors
and
angle spans,
and
coordination refer to items in the Bibliography.
the
maximum
distance
between
low
points
of the
TRANSMISSION
112 It is the the 20;
responsibility
required data and insulation
discussed To
in section any
insulation and
line
designer
clearance
conductor
and
the
considering
power
frequency)
required
for the
indicted
on figure
to provide
The angle construction
all of the
of protection of conductor
above
data.
Most
of
is discussed in section clearance patterns, is
19.
adequate
structure
transmission
can be calculated or approximated. coordination, the basis for the
maintain
between surge,
of the
LINE DESIGN MANUAL
three
between structure
each
the
stresses
structure
should
of the three
under
voltage
the
condition are,
and
be sufficient types
the
to coordinate
of voltage
at which
in general,
conductors,
each
described
stress is likely by the
air-gap
the
(lightning
gap
and
the
impulse,
switching
The
clearances
to govern. three
air
distance
superimposed
patterns
44.
///////////
/l////
Figure 44Auperimposed clearance voltage stresses. 104-D-1072.
patterns
1
Insulator
for the three types of
Bureau designs for wood-pole structures are based on coordination of the impulse insulation value of the insulators with the minimum air gap between the conductor and structure, and a wind pressure of 0.19 kPa (4 lb/ft2) at 15.5 ‘C (60° F). On steel structures, the impulse insulation of the insulator string
and
the
air-gap
clearance
to the
structure
are
coordinated
suspension insulator strings caused by a 0.19-kPa wind pressure for a sideswing angle of 30 O, whichever is greater. In the normal string, 10 percent is added to the impulse value of the insulator used
for clearance
to the
structure.
For
the
power
frequency
for
the
sideswing
clearance,
the
maximum
0.43 to 0.48 kPa (9 to 10 lb/ft2), in the area where the line is to be located, swing of the insulator string. An air gap equivalent to the wet 60-Hz flashover string is used for the clearance envelope. An
example
Example Assume 644
mm2
problem
on constructing
the
clearance
patterns
angle
wind,
(1272
transmission, kcmil),
ACSR,
line 45/7
follows.
with: d u pl ex conductor.
The
following
data
usually
is used to define the value of the insulator
Problem a 345-kV
of the
at 15.5 “C on the conductors or or vertical position of the insulator string and an equivalent air gap is
is also
assumed:
CHAPTER Maximum Ruling
initial
III-INSULATION, tension
per
LIGHTNING
PROTECTION,
conductor
span
18 insulator units per string 146 by 267 mm (5-3/4 by Length
per
(single
10-l/2
=
53 378
=
350.5
N (12 000
=
3099
mm
(122
in)
=
3277
mm
(129
in)
=
1500.8
m (1150
PATTERNS
113
lb)
ft)
in)
string
conductor)
(duplex
conductor)
Vertical
CLEARANCE
force
(weight)
per string
N (337.4
lb)
Wind Everyday
maximum
=
0.19
kPa
(4 lb/ft2)
Maximum Design for
design a minimum
=
0.43
kPa
(9 lb/ft2)
Calculations Sag and tension
to be made calculations
low-point
distance
at 15.5 “C are shown
L,“ear
I TEMP.., / oC UNSTRESSED LENGTH1
LOADING /3mm
NO Ice.
-mm 0,kPa
sr AE
to one-third 45 and
Force
the
sum
of adjacent
46.
I
I
,
?
SAG,mm
SAG FACTOR
350.5
SW.N
m
(W’)
Ice Wind (W”‘)
Figure 45.-Sag
and tension
calculation
spans.
Factor
SPANLENGTHW
Ice
No W\nd
equal
(60 “F). on figures
form for clearance
pattern
problem
(metric).
TENSION, N
TRANSMISSION
114
LINE DESIGN MANUAL
;;;FL
SAGCALCULATIONS L43qpJ
CONDUCTOR /'972 Code
Name Rated
Breaking
Dmmeter
Load
,!..&&
Tension
+/Am.
Final.
-//DF AcF
Fml.
6oF
Computed
by ~
“/.I/
366
SC R
lb
Area
50
% 17
lb
TemD.
-
% -lb
TEd”p-I
/.
Wind
(A)
(W”‘)
J!&&!-
Coeff.
0.000
tIllSTRESSED
LEI(CTH(
O//
I
,323
Creep
O.OOQ&2---
/7:
7817
lb/f:
Tolal
0.0009,17
2,
977-3
lblft Modulus,
(E)
Exp.:
z?
Final
9.35
lnltial
per “F
B
Set 0.000
lb/f1
in2 of Linear
Permanent
Ib/ft
5816
1
Final
1 SAC FACTOR
/
SAG.ft
1
wx
AE
InltialAE
SPAH LENGTH(S) //5D
_ lee__
No Wind
(w’)
(w.‘)
Resultant:
_25_
Inch
Ice.
lb
lb
Date
LOADING
weight Ice
jL 2&
Facrors.
Dead
Llmltarlons:
Loaded.
No
lb
180
L$k.y
LOADING h Weight
,?d Inch
l”8,~4,+F
% ___
ACSR “5
km// 1 ern
4 ;
48
x 106
lb/~+?
103
lb/&?
J?Ofl
??/L
SW ih
1
:,”
TENSION. lb
FEET
(W’)
Figure 46.-Sag
and tension
calculation
form
for clearance
pattern
problem
(U.S. customary).
Metric
A 0.191 52-kPa wind per meter of conductor = A 0.430 92-kPa wind per meter of conductor =
(0.430 92) (1000) = 14.722 N/m
U. S. Customary
A 4-lb/ft’
wind per foot of conductor =
A 9-lb/ft2 wind per foot of conductor = The
vertical
plus
one-half
load the
due to conductor
low-point
insulator
per
weight
distance
equal
to one-third
the sum of adjacent
spans
conductor:
Metric
For duplex conductor line: ‘(350*5) 3 (2) (20 .928) + -1500*8 = 4890.2 + 375.2 = 5265.4 N 4
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
CLEARANCE
PATTERNS
For single conductor line: (350.5) (2) (20 928) + -1500.8 = 4890.2 + 750.4 = 5640.6 N 3 * 2 U. S. Customary
For duplex conductor line: (1150) 3 (2) (1 .434) + -337.4 = 1099.4 + 84.3 = 1183.7 lb 4 For single conductor line: (1150)(2) 3 Compute
8 (angle
Metric
(0.191
of insulator 52-kPa
swing)
wind,
0’
line
for
(1 .434)+337.4= 2 the
following
1099.4 + 168.7 = 1268.1 lb
conditions:
angle)
Wind = 350.5 (6.542) = 2293 N fj = tan- 1 - 2293 = tan- ’ 0.435 48 = 23O32’, for one conductor of duplex 5265.4 /J
=
tan-
1
- 2293 = tan- ’ 0.406 52 = 22OO7’, for single conductor 5640.6
U.S. Customary (4-lb/ft2
wind,
Wind = 1150(0.4483)
0
=
tan-l
O”
line
angle)
= 515.55 lb
515.55 = tan- * 0.435 54 = 23O32’, for one conductor of duplex 1183.7
515.55 0 = tan-’ -1268.1 = tan- ’ 0.406 55 = 22OO7’, for single conductor
Metric (0.430
92-kPa
wind,
0’
line
angle)
Wind = 350.5 (14.722) = 5 160.06 N
~9= tan-’
5 160.06 5265.4 = tan- ’ 0.979 99 = 44’25’,
for one conductor of duplex
0 = tan- l 5516$)boi = tan- ’ 0.9 14 8 1 ‘= 42O27’, for single conductor
115
TRANSMISSION
116
U.S. Customary (9-lb/ft2
wind,
Wind = 1150(1.0088) (j = tan’ l ‘1116~~lf
0 = tan-
Metric
wind,
5’
line
angle)
= 1160.12 lb
= tan- 1 0.980 08 = 44O25’, for one conductor of duplex
l ‘11~~~ 112 = tan-
(No
0’
LINE DESIGN MANUAL
line
l 0.914 85 = 42O27’, for single conductor
angle)
2T sin 2S” = 2 (23 916) (0.043 62) = 2086.43
2086.43 5265 4 = tan -l 0.396 25 =21’37’,
0 = tan-’
(j = tan” l 2~~&4~
U.S. Customary (No
for one conductor of duplex
= tan- l 0.369 90 = 20’ 18’, for single conductor
wind,
5 O line
angle)
2T sin 2.5’ = 2 (5377) (0.043 62) = 469.09
e
=
tan-
1
469’09
1183.7 = tan 8 = tan-
Metric
l ‘s
(0.191
= tan-
52-kPa
wind,
- ’ 0.396 29 = 21037’, for one conductor of duplex l 0.369 91 = 20’ 18’, for single conductor
5’
line
angle)
2T sin 2.5’ = 2 (24 985) (0.043 62) = 2179.69
e = tan- l
2179.69 + 2293 = tanl 0.849 45 = 40020’, for one conductor of duplex 5265.4
e = tan- l
2179.69 + 2293 =,tanl 0.792 95 = 38O24’, for single conductor 5640.6
CHAPTER
Customary
U.S.
III-INSULATION, (4-lb/ft2
wind,
LIGHTNING 5 O line
PROTECTION,
CLEARANCE
PATTERNS
angle)
2T sin 2.5O = 2 (5617) (0.043 62) = 490.03
6 = tan- l
490.03 + 515.55 = tan- 1 0.849 52 = 40020’, for one conductor of duplex 1183.7
e = tan-,
490.03 + 515.55 = tan- 1 0.792 98 = 38”24’, for single conductor 1268.1
Metric
(0.430
92-kPa
wind,
5’
line
angle)
2T sin 2.5O = 2 (28 883) (0.043 62) = 2519.75
e = tan-l
2519.75 + 5160.06 = tan- * 1.4585 = 55O34’, for one conductor of duplex 5265.4
8 = tan- l
2519.75 + 5160.06 = tan- 1 1.36 15 = 53O42’, for single conductor 5640.6
Customary
U.S.
(9-lb/f@
wind,
5 O line
angle)
2T sin 2.5O = 2 (6494) (0.043 62) = 566.54
e = tan-I 566.54+ 1160.12 = tan- 1 1.4587 = 55034’, for one conductor of duplex 1183.7 e = tan- 1 566.54 + 1160.12 = tan-’ 1268.1
Metric
(No
wind,
15 ’ line
1.3616 = 53O42’, for single conductor
angle)
2T sin 7.5O = 2 (23 916) (0.130 53) = 6243.51
e
=
tmwl
6243.51
5265.4 = tan e = b-
- l 1.1858 = 49O5 1’ , for one conductor of duplex
i 6243.51 = tan- 1 1.1069 = 47O 54’, for single conductor 5640.6
117
TRANSMISSION
118
Customary
U.S.
(No
wind,
15 O line
LINE DESIGN MANUAL
angle)
2T sin 7.S” = 2 (5377) (0.130 53) = 1403.72 1403.72 = tan- 1 1.1858 = 4905 1’, for one conductor of duplex 1183.7
8 =tan-’
e = TV- 1 1403.72 = tan- ’ 1.1069 = 47O 54’, for single conductor 1268.1
Metric
(0.191
52-kPa
2T sin 79 e = tan-l
wind,
15’
line
angle)
= 2 (24 985) (0.130 53) = 6522.58 6522.58 + 2293 = tan-’ 5265.4
1.6742 = 59OO9’, for one conductor of duplex
e = tan- l 6522.58 + 2293 = tan- 1 1.5629 = 57O23’, for single conductor 5640.6
U.S.
Customary
(4-lb/ft2
wind,
15’
line
angle)
2T sin 7.5’ = 2 (5617) (0.130 53) = 1466.37 e =tan-’
1466.37 + 515.55 = tan’ 1 1.6743 = 59OO9’, for one conductor of duplex 1183.7
8 = tan-’
1466.37 + 515.55 = tan-l 1268.1
Metric
(0.430
92-kPa
wind,
15’
line
1.5629 = $7O23’, for single conductor
angle)
2T sin 7.5O = 2 (28 883) (0.130 53) = 7540.20 I:=Qn
1
7540.20 + 5 160.06 = tan-’ 5265.4
e = TV- 1 7540.20 + 5160.06 = tan-’ 5640.6
2.4119 = 67O29’, for one conductor of duplex 2.25 16 = 66OO3”, for single conductor
CHAPTER
III-INSULATION,
Customary (9-lb/ft2
U.S.
wind,
LIGHTNING 15O
line
PROTECTION,
CLEARANCE
PATTERNS
angle)
2T sin 7.5O = 2 (6494) (0.130 53) = 1695.32
1695.32 + 1160.12 = tan- 1 2.4 123 = 67O29’, for one conductor of duplex 1183.7
0 = tan-’
1695.32 + 1160.12 = tanl 2.2517 = 66OO3’, for single conductor 1268.1
8 = tan-’
Metric
(-0.191
8 = tan-
5%kPa
f 2179..69
wind,
5’
- 2293
5265.4 8 = tan-,
U.S.
Customary
line
angle)
-0.021 52 = -lo 14’, for one conductor of duplex
= tan”
2179.69 - 2293 = tan- 1 - 0.020 09 = -1’09”, for single conductor 5640.6
(-4-lb/ft2
wind,
5 ’
line
angle)
e = tan- 1
490.03 - 515.55 = tm” 1183.7
-0.021 56 = -lo 14’, for one conductor of duplex
8 = tan”
490.03 - 515.55 ztm-1 1268.1
-0.020 12 = -1’09’, for single conductor
Metric
(-0.430
B = tan-l
9%kPa 2519.75
wind,
5 O line
- 5160.06
5265.4 8 = tan-l
U.S.
Custmmy
B = tm-l
angle)
= tan-l -0.501 44 = -26’38’,
2519.75 - 5160.06 =tm-’ 5640.6
(-9-lb/ft2
wind,
5 O line
566.54- 1160.12= tm-l 1183.7
for one conductor of duplex
-0.468 09 = -25OO5 , for single conductor
angle)
-o . 501 46 = -26O38’, for one conductor of duplex
0 = tan- 1 566’54 - ’ ’ 60*1 2 = tan- l k 0.468 09 = -25OOS’ , for single conductor 1268.1
119
120
TRANSMISSION
Metric
(-0.191
52-kPa
wind,
15’
MANUAL
line angle)
e = tan- 1 6522.58 - 2293 = tan-’ 5265.4 13= tan-’
LINE DESIGN
0.803 28 = 38O46’, for one conductor of duplex
6522.58 - 2293 = tan- l 0.749 84 = 36O5 l’, for single conductor 5640.6
U.S. Customary (-4-lb/ft2
wind,
15 O line angle)
e =tan-’
- 5 15.55 1466.371183.7 = tan- 1 0.803 26 = 38O46’, for one conductor of duplex
8 =tan-’
1466.37 - 515.55 = tan” 1268.1
Metric
(-0.430
92-kPa
wind,
0.749 80 = 36O51’, for single conductor
15 o line angle)
8 = tan-’
7540.20 - 5 160.06 = tan- ’ 0.452 03 = 24O 19’, for one conductor of duplex 5265.4
e = tan- 1
7540.20 - 5 160.06 = tan- 1 0.421 97 = 22O52’, for single conductor 5640.6
U.S. Customary (-9-lb/fts
8 =twl
e=ta-l
wind,
15 O line angle)
1695.32 - 1160.12 = tan’ 0.452 14 = 24O 19’, for one conductor of duplex 1183.7 1695.32 1160.12 = tan- 1 0.422 05 = 22O52’, for single conductor 1268.1
Determine the critical positive impulse flashover value and the 60-Hz wet flashover value of the insulator string to be used. Determine the lengths of air gaps that are electrically equivalent to the critical positive impulse flashover, equivalent to the impulse flashover plus 10 percent, and equivalent to the 60-Hz wet flashover. These values may be obtained from catalog data or from the tables in appendix B. For example: 1. For 18 insulator units, the critical positive impulse flashover is 1585 kV (table B-7, app. B). 2. 1585 kV plus 10 percent equals 1744 kV. 3. The SO-Hz wet flashover for 18 units is 690 kV (table B-7, app. B). 4. The equivalent air gaps for l., 2., and 3. are 2642,2921, and 2083 mm (104,115, and 82 in), respectively (table B-8, app. B).
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
CLEARANCE
-Bottom
of crossarm
PATTERNS
121
1524 mm (i-6)
Conductor elevation center of tower
Conductor elevation at edge of tower, high side of 1:5 ground
at
Conductor elevation at edge of tower, level span Conductor elevation at edge of tower, low side of 1:5 ground slope
NOTES: Conductor = 644 mm2 (1272 kcmil), ACSR, 45/ 7. Sag at 15.5 “C (60 OF)=I3 628 mm (44.71 ft) for a 350.5-m (1150-ft) span. Conductor elevation at edge of, cage: bktriC: 1.219/350.5=0.35% of span = 1.5% of sag =204 mm. U.S. Customary: 4/1150 = 0.35 % of span = 1.5% of sog = 0.67 ft= 8.1 in. Assume ground slope of I in 5 equivalent to 244 mm (0.8 ft=9.6 in) additional sag at edge of tower. On low side of tower, total drop of conductor at edge of tower=448 mm (17.7 in). On high side of tower, assume conductor sag cancels effect of ground slope. Fire
47.-Assumed
dimensions
for side view of structure
at conductor
elevation.
104-D-1073.
Figure 4’7 shows the assumed dimensions of the sideview of the tower at the conductor elevation. Clearance patterns for two structure types, a tangent structure and an angle structure capable of taking line angles between 5 O and 15 O, have been constructed for two cases: (1) for duplex conductor, and (2) a single conductor. These clearance patterns are shown on figures 48, 49, 50, and 51. The clearance pattern shown on figure 48 has been noted to illustrate the following discussion on construction of the clearance pattern. After selecting a scale, begin constructing the pattern by striking a 180° arc with a radius equal to the length of the insulator string as it hangs normally; the center of the arc represents the attachment point of the insulator string at the tower. By looking at a side view of the tower (fig. 47), it can be seen that the electrical clearance between the conductor and steel will be most critical at the edge of the tower because of the sag in the conductor. To account for this, draw a second arc parallel to the first, but with the radius increased by the amount of the conductor sag at the edge of the tower. These arcs represent the possible locations of the conductor (short radius at the centerline of the tower, and long radius at the edge of the tower) at the end of the insulator string, or the centerline between conductors if duplex conductors are used. Draw radii representing the insulator string as it hangs normally and at its positions with the different wind
TRANSMISSION
122 pressures edge
and
of the
strike
line
tower
arcs to form
air gaps
previously
equal
to the
drawn
from
t
angles, (fig.
as applicable.
47)
for
an envelope
the
the 0.19-kPa
From
the
4331
8662
mm (28: 5”)
0.19152-kPa 0.43092-kPa -0.19152-kPa -0.43092-kPa pattern
value
1I I
is the
radii
4331
locations conductor
for these
of the plus
conductor
adjusted conductor,
the The
arc
has a radius
radius
of the
of the insulator
mm (Id-2;“)
,/Insulator
at the locations,
arcs are the equivalent
10 percent.
air gap equivalent
structure
wind, wind, wind, wind, wind,
w
string
0” line 0” -line O” line 0” line 0” line
with single conductor.
angle angle angle angle angle 104-D-1074.
arc
impulse
Additional clearance for sloping span due to sloping ground = 244 mm (9.6 in)
no (d-lb / ft2) (g-lb/ ft2) 64-lb /ft2) (-g-lb/ ft2)
for a 30s tangent
the
these
The
position
impulse
tower =204 mm (8.1 in )
Figure BI.-Clearance
points.
position
(Clearance for upslope
a 00 b 1 22’07’. C = 42”27’, b’=-22”07’, C’ =-42’27’,
showing From
‘?wind”
mm (I 41-2;‘)
MANUAL
points
“no-wind”
insulator
w
w
the
conditions.
the conductor
of the
(4-lb/f@)
Locate
applicable
around
determined.
air gap equivalent
LINE DESIGN
CHAPTER
III-INSULATION,
LIGHTNING
flashover value, and the arc radius of the 60-Hz wet flashover value
from the 0.43-kPa of the insulator
corresponding
values,
No
part
wind
of a steel
and line structure
angle
is allowed
are shown to encroach
PROTECTION,
CLEARANCE
PATTERNS
(9-lb/ft2) wind position is the air gap equivalent string. The angles of insulator swing, with their on figures upon
48,49,50,
a clearance
and
51 for ready
pattern
envelope.
9398 mm (30’~101’) 4699 mm (I 5: 5”)
\457 cl
4699 mm ( I 5: 5”)
mm (18 in) Spacing of duplex conductor
0”
b 123’32’: O.i9152-kPa (4-lb/ft*) c = 44’25’. 0.43092-kPa (g-lb /ft*) b’=-23°32’,-0.19152 -kPa (-4-lb/ft*) C’ =-44°25’,-0.43092-kPa (-Wb/ft*) Figure 49Alearance
pattern
for a 30s tangent
123
structure
no wind, wind, wind, wind, wind, with duplex
0” 0” 0” 0” 0”
line line line line line
conductor.
angle angle angle angle angle 104-D-1075.
reference.
124
TRANSMISSION
LINE DESIGN MANUAL
8992 mm (291-6”)
l-2
3099 mm (122 in)
-0.4x92-kPa a =-25’05’, b =-oIO o9’,-O.I9152-kPa C = 20” I8’, d = 22” 52’, -0.43092--kPa e = 36’51’, -0.19152 -kPa f = 38’24’, 0.19152-kPa g = 47”54’, h = 53’42’, o.43092-kPa i = 57O 23’, 0.19152-kPa j= 66OO3’, 0.43092-kPa Fire
SO.-Clearance
pattern
(-g-lb /ft2) wind, 5” line (-4-lb / ft2) wind, 5” line no wind, 5” line (-g-lb / ft2) wind, 15” line (-4-lb /ft2) wind, 15” line (4-lb /ft2) wind, 5” line no wind,-l5O line (g-lb / ft2) wind, 5” line (4-lb / ft2) wind, 15” line (g-lb / ft2) wind, 15” line
for a 30A angle structure
with single conductor.
angle angle angle angle angle angle angle angle angle angle
104-D-1076.
CHAPTER
III-INSULATION,
9652
* c
LIGHTNING
3874
mm (12:8;)
1168
PROTECTION,
CLEARANCE
mm ( 31L8”)
C!
C
5778
mm (18Lll~)
mm (46 in)+
L74fR 3277
mm (129 in)
a =-26’38’,-0.43092-kPa (-g-lb / ft*) b =-01” ~4’,-0.~9~52 -kPa (-&lb/ ft*) c =
d= e= f = 9= h= i= j =
wind, wind, no wind, 21” 36’. 24” I&-0.43092-kPa (-9-lb/ft*) wind, 38” 46’, -0.19152 -kPa (-+lb/ft*) wind, 40020’, 0.19152-kPa (+lb/ft*) wind, 49O5l’, no wind, 55O34, 0.43092-kPa (g-lb / f t*) wind, 5g”W, 0.19152-kPa (+lb/ft*) wind, 67’29’. 0.43092-kPa (g-lb/ft*) wind,
Figure Sl.-Clearance
pattern
for a 30A angle structure
125
PATTERNS
with duplex
line 5O line 5” line 15” line 15” line 5” line 15” line 5” line 15” line 15’ line 5”
conductor.
angle angle angle angle angle angle angle angle angle angle
104-D-1077.
STRUCTURE 22.
General.-For
constructed
for
construction wood-pole is also
main
transmission
loading
line
conditions,
AND GUYING under
consideration,
specific
size and
CHARTS a structure
type
limitation
of conductor,
to be used. The chart is used to determine the type of structure construction that is required at any’ given location in the transmission
constructed
23.
each
the
LIMITATION
to determine
Components
the
nutnber
of Charts.-The
of guys
structure
to be used
limitation
and
IV
with
the
guying
and
is
type
of
for either steel or line. A guying chart
wood-pole
chart
chart the
structures.
consists
of the following
items: l
A suspension-type
structure
limitation
chart
that
determines
required for a given location. The chart also determines points) which must be provided by the conductor to limit for a particular location are outside the limits of any necessary
to use a dead-end-type
is dependent on the magnitude between conductor low points at the structure. l
A guy chart magnitude
that determines of the line angle
self-supporting steel structures references to guys are omitted. l
A summary of guying A table summarizing
l
Notes
l
covering
the
structure.
The
type
of suspension
the number of angle and the lengths of are to be used
for
materials,
and
of structure
required
guys required the adjacent
a transmission
the
structure
the amount of mass (between low insulator sideswing. If the conditions suspension-type structure, it will be
of the line angle, lengths of the adjacent in the adjacent spans, and the required
data for tension structures. the structure types, their span construction
the type
limits, conditions
and
at any
location
actual spans, distance conductor clearances (dependent upon the actual spans). When
line,
the
their
allowable
on which
guy
the
chart
and
line chart
all
angles. is based.
24. Preparation of Charts.-A structure limitation chart for steel towers and a structure limitation and guying chart for H-frame, wood-pole transmission lines are developed in this section. The following numbered paragraphs (1 through 7) describe the procedures for preparing these charts. Paragraph In order established:
1. to establish
a basis
for
preparing
For steel structures, the permissible a. structure is determined from the clearance clearance
pattern
depends
on the
these
sideswing pattern
size and’ type
charts,
following
standards
have
been
of each insulator string on a suspension-type established for the design of the towers. The
of conductor 127
the
and
loading
conditions
for
which
the
128
TRANSMISSION
transmission shall
The and
line
for determining
and
the
following
the strength
minimum
strings
(suspension)
2.5
strings
(tension)
3.0
spans,
the maximum
angle
are established
these
structure
distance
limits
factors
Insulator
to fit
in California, for important
MANUAL
Insulator
deflection
are designed
b. Except voltages and
Calculations
conditions
sum of adjacent
maximum
towers
designed.
on full-load
maximum
the
steel
line is being
be based
LINE DESIGN
between
as required
for
of insulator
strings
of safety:
low points the
of adjacent
transmission
line
spans, and
the
requirements.
the design of all wood-pole lines of lower voltages shall
transmission be in accordance
lines for 69-kV and higher with grade B construction
as shown in the latest edition of NESC. Loading conditions and conductor and overhead ground wire tensions shall also be in accordance with the latest edition of the code, except as modified by figure 1 or by specific heavier loading conditions than those prescribed for the general area for which a line
is being
designed.
The recommended conductor ultimate used on transmission
maximum design tensions (full-load tensions based on 33-l/3 percent of the ’ C (0 ’ F) under initial conditions) for typical conductors strength at minus 18 lines with H-frame, wood-pole structures are shown in the following tabulation:
ACSR, 2417 conductors mm2 RCW
242 282 306 322 403
Maximum
full-load
conductor
Maximum N
(477) E)
33362 35 585 31810 40034 44482
(636) (795)
tension
allowble
on standard
exceed 44 482 N (10 000 lb). Strength calculations for determining permissible guying, and requirements for double insulator strings
USBR
tensions (lb)
(7 500) (8000) (8 500) (9 000) (10 000)
H-frame,
wood-pole
structures
should
not
in paragraph
2 and
the
minimum
Selection of the proper type condition of 0.19-kPa (4-lb/ft2)
factors
of safety
of suspension wind pressure
zones. The three axes of the structure limitation of this loading condition. Table 20 shows the
span lengths, distance between low shall be based on the full-load conditions shown
in table
19.
structure for any location shall be based on a loading on the bare conductor at 15.5 o C (60 o F) in all loading chart shall be calibrated minimum clearance from
to correspond the conductor
ground wire or to the surface of the crossarm; these clearances shall be maintained condition above. If a pole ground wire is not be maintained to the centerline types of structures are shown different
types
of wood
points, shown
to the values to the pole
under the loading
used, the clearances specified to the pole ground wire in table 20 shall of the. poles. The limits for permissible insulator swing on the different for, the various voltage classes in table 21. Drawings of some of the
structures
are shown
later
in this
section.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
Table lg.-Minimum
factors of safety for wood-pole construction’ (grade B) At full load
Wood poles Crossarms Guys (line) Guys (transverse) Insulator strings (suspension) Insulator strings (tension) Insulator pins (bending) Conductor
At 15.5 OC (60 OF), no wind 35.5 35.5
z 22:o 2.61 ‘2.5 i-8 2:o
4.0
r Factors of safety are based on ultimate strengths of the different materials to whith they are applicable. USBR standard. 3 Based on 8.96-MPa (1300-lb/in*) fiber stress for fii, or 6.89-MPa (lOOO-lb/in*) fiber stress for western red cedar.
Table 20.-Conductor
clearance to pole ground wire or crossarm surface-wood-pole construction Conductor
Type of construction, kV
Pole ground wire’ mm (in) 660 1092 1245 1524 1803
69 115 138 161 230
(26) (43) (49)
(60) (71)
clearance Crossarm surface’ mm (in) 508 889 991 1245 1473
(20) (35) (39) (49)
(58)
t USBR standard.
Table 21 .-Angukzr limitations of suspension insulator swing for standard USBR wood-pole structures Structure type HS HSB 3A El 3AD’
69 kV *54 max. *54 max. 30 min. -30 12 min. to +70 -30 to +70
115 kV 36 max. 36 max. 36 min. -16 24 min. to +70 -16 to +70
AnguIar limitation, 138 kV 40 max. 40 max. 39 min. -28 27 min. to +70 -28 to +70
degrees 161 kV 38 max. 38 max. 45 min. 35 min. -16 to +63 -16 to +63
230 kV 42 max. 42 max. 41 mill. 38 min. -17 to +60 -17 to +60
’ Structure types 3AC and 3AD should not be used where either a type 3A or 3AB wiIl satisfy the req$rements of the proposed structure:location. Extreme care should be exercised inchecking for uplift.
129
TRANSMISSION
130 The
following
conductor
minimum
positions
clearance
on wood-pole
LINE DESIGN MANUAL
between
conductor
and
guy
wire
shall
be maintained
at all
construction:
Typeofconsmction kV
C1&?llWlCe’ mm w
69 115 138 161 230
965 1397 1524 1676 1956
(38) (55)
(60) (66) (77)
1 USBR standard.
In
areas
where
conductors
and
length of a single span conductors and overhead (600 ft), full-sag ellipses
should ground should
one-half-sag
be used.
ellipses
may
overhead
ground
wires
be limited to prevent wires due to galloping be- used to determine
are subject
to ice loading,
contact between conductors conductors. For span lengths the required clearances. For
the
maximum
or between up to‘183 m longer spans,
c. In California, the design of wood-pole transmission lines shall be in accordance with grade B construction as shown in General Order No. 95 of the California Public Utilities Commission [l],’ except that grade A construction is required for crossings over railroads and major communication lines. Loading conditions with General Order
and conductor No. 95, except
The recommended conductor ultimate
maximum design tensions (full-load tensions based on 33-l/3 percent of the strength at minus 18 o C (0 ’ F) under initial conditions) for typical conductors lines in California with H-frame, wood-pole structures are shown in the following
used on transmission tabulation:
and overhead ground as modified by figure
ACSR, 2417 conductors
Maximum
full-load
mm2
W-1
242 282 306 322 403
(4771 (556.5)
conductor
Maximum N 33 35 37 40 44
(605) (636) (795)
tension
on standard
should not exceed 44 482 N (10 000 lb). Strength calculations for determining permissible guying, and requirements for double insulator strings in paragraph
’ Numbers
2 and
in brackets
the
minimum
factors
of safety
refer to items in the Bibliography.
wire 1.
tensions
allowble
362 585 810 034 482
USBR
shall
also be in accordance
tensions (lb)
(7 (8 (8 (9 (10
500) 000) 500) 000) 000)
H-frame-type
structures
in California
span lengths, distance between low shall be based on the full-load conditions shown
in table
22.
points, shown
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
131
Table 22.-Minimum
factors of safety for wood-pole construction in California’ Grade A
Wood poles Crossarms Guys, except in light loading rural areas Guys in light loading rural areas Insulator strings (suspension) Insulator strings (tension) Insulator pins (bending) Conductor
Grade B
2t::
24.0 3.0
2.0 2.0
2.0 1.5 22.5 23.0 23.0 2.0
23:o Ei 2.0
’ Factors of safety are based on ultimate strengths of the different to Thich they are applicable. USBR standard. Selection at 15.5 ‘C
of the proper (60 OF) with
type of suspension a 0.19-kPa (4-lb/ft2)
crossarm;
these
for any
location
shall
he based
on conditions
wind pressure in all loading areas. The three axes of shall be calibrated to correspond to the values at the above conditions. clearance from the conductor to the pole ground wire or to the surface
the structure limitation chart Table 23 shows the minimum of the
structure
materials
clearances
shall
be maintained
under
the
above
loading
condition.
Table 23.-Conductor
clearance to pole ground wire or crossarm surface-wood-pole construction in cizlifornia Conductor Pole ground wire’ mm (in)
Type of construction, kV 69 115 138 161 230
(26)
660 1092 1245 1524 1803
(43) (49) (60) (71)
clearance Crossarm surfacer mm (in)
(20)
508 889 991 1245 1473
(35) (39) (49)
(58)
r USBR standard. If a pole
ground
be maintained The limits The conductor
wire
is not
used,
the clearances
specified
to the centerline of the poles. for permissible insulator swing in California
following
minimum
clearance
between
conductor
to the pole are the and
same
guy
positions: T&e of construction kV
Clearance ’ mm (in)
69
965
(38)
115 138 161 230
1524 1397 1676 1956
035)
s USBR standard.
si; (77)
wire
ground
wire
as shown shall
in table in table
be maintained
23 shall 21.
at
all
TRANSMISSION
132 In areas
of California
maximum
length
conductors (600
ft),
where
of a single
and
overhead
full-sag
ellipses
one-half-sag
ellipses
Paragraph
may
span
conductors should
LINE DESIGN and
overhead
be limited
ground
wires
due
should
be used
ground
to prevent
to galloping to determine
MANUAL wires
contact
are subject between
conductors. the
For
required
to ice loading,
conductors
span
lengths
clearance.
For
the
or between up to longer
183 m spans,
be used.
2.
Full-load
conditions
are as follows:
National Electrical Safety Code or California General Order No. 95
Loading for calculations of strength of structures and their components
Light loading districts’ : 0.43-kPa (9-lb/ft2) wind pressure, no ice, plus constant, at -1 OC (30 OF)
0.57~kPa (1 2-lb/ft2 ) wind pressure, no ice’
Medium loading districts’ : 0.19-kPa (4-lb/ft2 ) wind pressure, 6-mm (l/4+1) ice, plus constant, at -9.5 OC (15 OF)
0.38-kPa (8-lb/ft2 ) wind pressure, 6-mm ( l/4&) ice’
Heavy loading districts’ : 0.19-kPa (4lb/ft2 ) wind pressure, 13-mm ( l/2+) ice, plus constant, at - 18 OC (0 OF)
0.38~kPa (S-lb/ft2 ) wind pressure, 13-mm (l/2+1) ice’
California light loading: 0.3 8-kPa ( 8-lb/ft2 ) wind pressure, no ice, at -4 OC (25 OF)
0.38~kPa (8-lb/ft2 ) wind pressure, no ice
California heavy 0.29-kPa (6-lb/ft2 pressure, 13-mm ice, at - 18 OC (0
0.29-kPa (6-lb/ft2 ) wind pressure, 13-mm ( l/2&) ice
loading: ) wind ( l/2-in) OF)
’ Extreme wind loading as shown on NESC figure 250-2 in reference [ 31 should be u;ed if resultant loading is greater. Pa ragrap
h 3.
The data transmission patterns.
The
required for construction of a structure line are discussed at the beginning clearance
patterns
themselves
limitation of section
are important
chart for the design of a steel structure 21, which covers conductor clearance because
they
indicate
the maximum
design
CHAPTER swing
of the suspension
limitation
lines
on the
previously
discussed
maximum
sum
that
shows Example Assume conductor.
insulator
strings
low-point
portion
are basically
of adjacent
the
procedure
Problem
for (steel
a 345-kV Assume
obtaining
conditions. The extreme data are also assumed: initial heavy)
made
30s
=
tangent,
30X
=
tangent
30A 30T 30D
= = =
angle, tangent tangent
for
each
chart.
steel
structure
for
with
a 644-mm2
swing
The
angles
balance
low-point An
become
of the
distance
example
and
problem
limitation
force
wind
pressure
data the
follows
chart.
= per
extreme
per unit length N/m (1.8867 here
for
45/7 wind
duplex pressure.
for the conductor lb/ft) for NESC
example
purposes.
The
(weight)
of steel
transmission V-string
=
63 165 N (14 200 lb) 350.5 m (1150 ft)
=
3556
mm
=
1628
N (366
= =
0.19 0.48
string by per
10-l/2
in)
string
design
suspension,
ACSR,
(16~lb/ftz)
was assumed
maximum
types
(1272-kcmil),
a 0.77-kPa
because the resultant force which is less than 27.5345
Design for a minimum sum of adjacent spans.
are usually
the
maximum
on the
data
is in an area with
267 mm (5-3/4 per string
Maximum
of the different
the
these
chart.
full-load tension
per conductor Ruling span 20 insulator units
Drawings
although are drawn
line
location
not be a factor (1.285 lb/ft),
Vertical Wind Everyday
data,
of structures; limitation
133
CHARTS
construction)
the line
146 by Length
structure
the
AND GUYING
types
of the
limitations
transmission
Maximum (NESC
LIMITATION
on the various
tabled
spans
This wind pressure will would be 18.746 N/m full-load following
IV-STRUCTURE
low-point
distance
structures line.
Steel
on center
to 5 O line angle, suspension line angle, suspension 5 to 15’ to 5’ line angle, tension to 30’ line angle, dead end
equal
are not shown tower phase
kPa kPa
(140
in) lb)
(4 lb/ft2) (10 lh/fts)
to one-third
the
in this manual
designations
and
types
because are:
new
designs
TRANSMISSION
134 Tabular
steel
tower
data
LINE DESIGN
MANUAL
follows:
Metric Tower type Line angle capability Ruling span (m) Maximum single span (m) Minimum line angle Maximum line angle Maximum sum of adjacent spans (m) Minimum line angle Maximum line angle Maximum low point distance (m) Conductor, minimum line angle Conductor, maximum line angle OGW, minimum line angle OCW, maximum line angle Maximum uplift (N) Conductor, minimum line angle Conductor, maximum line angle OGW, minimum line angle OGW, maximum line angle Body heights (m)
Leg extension range (m), at 0.762-m intervals
30s
30x
30A
30T
30D
O0 350.5
00-50 350.5
so-150 350.5
00-50 350.5
00-300 350.5
396 396
487.5 396
487.5 396
548.5 487.5
640
792.5 792.5
975.5 792.5
975.5 792.5
1097 975.5
1280
731.5 731.5 853.5 853.5
975.5 792.5 1036.5 853.5
975.5 792.5 1036.5 853.5
19.8 and 25.9 1.524
19.8 and 25.9 1.524
19.8 and 25.9 1.524
10x
lo:607
10x
1280 1280 1524 1524 305 213.5 396 254 16.8 and 22.9 1.524 lo::7
1371.5 1463
305 396 16.8 and 22.9 1.524 lo::7
U. S. Customary Tower type Line angle capability Ruling span (ft) Maximum single span (ft) Minimum line angle Maximum line angle Maximum sum of adjacent spans (ft) Minimum line angle Maximum line angle Maximum low point distance (ft) Conductor, minimum line angle Conductor, maximum line anae OCW, minimum line angle OCW, maximum line angle Maximum uplift (lb) Conductor, minimum line angle Conductor, maximum line angle OGW, minimum line angle OGW, maximum line angle Body heights 0%
Leg extension range (ft), at 2.5-ft intervals
30A
30T
30s
30x
00 1150
00-50 1150
so-150 1150
00-50 1150
00-300 1150
1300 1300
1600 1300
1600 1300
1800 1600
2100
2600 2600
3200 2600
3200 2600
3600 3200
4200
2400 2400 2800 2800
3200 2600 3400 2800
3200 2600 3400 2800
4200 4200 5000 5000
65 and 85 5
65 and 85 5
65 and 85 5
:5”
ii
;:
1000 700 1300 833 55 and 75 5 :z
30D
4500 4800
1000 1300 55 and 75 5 ii
CHAPTER Calculations
IV-STRUCTURE
for the strength
LIMITATION
requirements
AND GUYING
of insulator
strings
CHARTS
for the various
135
types
of steel
towers
are as follows: Type
30.5,
0 o Ihe
Maximum Maximum Conductor
force
0.38-kPa
(8-lb/ft2)
The
bcm-570
with
conductor
a 0.38-kPa
angle
low-point distance = 731.5 m (2400 ft) sum of adjacent spans = 792.5 m (2600 13 mm
wind force
wind
values
are simply
(l/2
on iced
in)
are shown
twice
of radial
conductor
the
=
ft)
ice =
37.676
22.816
N/m
on figures
values
shown
N/m
(2.5816
(1.5634
lb/ft)
52 and
53. The
on these
figures
force for
lb/ft)
values
shown
a 0.19-kPa
above
for
wind.
(9-78)
Dead Load Force (W’)
/3
mm Ica (W”)&
OakPa Initial *-%,33%-.-Final .oc
,
Loadad,~~.50% Final I- 15.5~ ,COIIIPUW~ by
No Ica. *Wind
N 25
K -N
(We”)
I/.
408
,.,,m
j.3.
ff9
N/m
N
o.ooo osw?
Oats -
*I977
Total O.O0/4Jo Modulus. (I3 Final k&&6-
Area (AlC84md Temp. Coaff. of Linear
-N K-
Resultant.
creep o.oooGG2LL
Nh
Wind
Exp.:
initial Fit?alAE
per%
NEtSC K:r/.374?2
Initial
/1/
& 4//P
GPa 2/
:!
GPa
&,/-‘I
AE 3/
t
(W)
No Ice. Lk Wind (W’)
Fire 52.-Conductor (metric).
sag and tension
calculation
form
for example
problem
on steel structure
limitation
chart
TRANSMISSION
136
DC-K70
LINE DESIGN
MANUAL
(S-78)
CONOUCTOR l&U km;/
ACSR
454
33ifem
Code Name
Rated Breaking Load Diameter Tension
/U.&I
Dead Weight
-lb inch
+ hi”.
L~m~tauonr:
Initial.Final,
-
computed
OF% OFA%-
by -
/. 4340 758 6
lb/f1
AL Lb Wind ..,,:,
‘F33fK
LOrded .FiMl. *OF
(W’)
ICI (W”) Resultant:
-lb Y -
lb lb
Area (A) /. TemD.‘Cooff.
(W”‘) 3.6073
O.WO On
per ‘?=
Set 0.00
Creap
o.oon~-
lb/f1
Totai
0.001
O./O
4
lb/f1
in2 of Linear Exp.: s,g77
$4 -lb Date
Permanent
lb/f1
X=0,30
NEsc
Modulus. (E) Final 9 35 Initial~x Final AE .a Initial AE ,7 159
x 1OS lb/it-$ 106 lb/id lb 276 lb
No Ice. No Wind (W’)
0
Inch Ice
No Ice. Mm Wind (w’)
Figure 53.-Conductor customary).
sag and tension calculation
form for example problem
on steel structure
limitation
chart (U.S.
Metric
Maximum Maximum Resultant
vertical load = (731.52) (37.676) = 27 560.75 newtons per conductor wind load = (792.48/2) (22.816) = 9040.61 newtons per conductor load = [(27 560.75)2 + (9040.61)2]1/2 = 29 005.65 newtons per conductor = 58 011.30 newtons per phase = 145 028.25 newtons per phase with a safety factor of 2.5 Use 177 928-N insulator units for suspension strings. A sketch of a center phase V-string
attachment
for the 30s tower is shown on figure 54.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
137
For center phase V-string, b
-=-a sin A
4
145 028 _ b sin 80° sin SO0
50”
b
~(800)
SillB
a
b = 145
028 (0.766 04) = 112 810.85 N 0.984 8 1
‘“B’
Use 133 446-N insulator units.
Figure S4.-Center phase V-string structure with no line angle.
for type 30s steel
U.S. Customary Maximum
vertical
Maximum Resultant
wind load = (2600/2) load I = [(6195.84)2 +
load
= = Use
40 OOO-lb
=
(2400)
13 041.34 32 603.34
insulator
(2.5816)
pounds pounds
units
for
=
6195.84
(1.5634) = (2032.42)2]r/2 per per
phase phase
suspension
pounds
per
conductor
2032.42 pounds per conductor = 65’20.67 pounds per conductor with
a safety
factor
strings.
For center phase V-string (fig. 54), -=- a sinA 32=
sin 80’
b sinB b
sin SO0
b = 32 603 (o-766 04) = 25 360 57 I,, 0.984 81 Use 30 OOO-lb insulator units. Type 30X, 0 O line angle Maximum Maximum
low-point distance = 975.5 m (3200 ft) sum of adjacent spans = 975.5 m (3200
ft)
of 2.5
TRANSMISSION
138
LINE DESIGN MANUAL
Metric Maximum
vertical
Maximum
wind
Resultant
load
Use
222
load load
=
=
(975.5)
(975.5/2)
=
[(36
=
76 800
=
192 000
410-N
752)a
+
=
36 752
newtons
per
conductor
=
11 128
newtons
per
conductor
(11
newtons
insulator
(37.676) (22.816) 128)a]1/2 per
newtons
=
38 400
newtons
per
conductor
phase
per
phase
with
a safety
factor
of 2.5
units.
U. S. Customary Maximum
vertical
Maximum
wind
Resultant
load
Use
50 OOO-lb
load load = = =
=
=
(3200)
(3200/2)
[(8261.12)2 17 263.06 43 157.65
insulator
(2.5816)
= 8261.12
(1.5634) (2501.44)
= 2501.44 pounds per conductor 2 ] l/2 = 8631.53 pounds per conductor
+ pounds pounds
per per
phase phase
with
pounds
a safety
per
factor
conductor
of 2.5
units.
Type 30X, 5 o line angle Maximum
low-point
Maximum
sum
distance
of adjacent
= spans
792.5 =
m (2600 792.5
ft)
m (2600
ft)
Metric Maximum
vertical
load
Maximum wind load Angle load = 2 T(sin Resultant
Use
177
load
928-N
= = =
=
=
(792.5)
(37.676)
= 29 858
(792.5/2) (22.816) = 9040 a/2) = 2(63 165) (0.043 62)
[(29 858)a + (9040 + 5510)2]1/2 66 428 newtons per phase 166 070 newtons per phase with
insulator
newtons
newtons = 5510 =
per
33 214
a safety
conductor
per conductor newtons per conductor newtons
factor
per
conductor
of 2.5
units.
U.S. Customary Maximum Maximum
vertical load = (2600) (2.5816) = wind load = (2600/2) (1.5634) = = 2(14 200) (0.043 Angle load = 2 T ( sin a/2) Resultant load = [(6712.16)2 + (2032.42 + = 14 933.72 pounds per phase = 37 334.3 pounds per phase Use
40 OOO-lb
insulator
6712.16 2032.42 62) =
1238.81)2]1/2 with
a safety
units.
Type 3OA, 5 ’ line angle Maximum
low-point
Maximum
sum
distance
of adjacent
= spans
975.5 =
m (3200 975.5
pounds pounds 1238.81
ft)
m (3200
ft)
per conductor per conductor pounds per =
7466.86
factor
of 2.5
conductor
pounds
per
conductor
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
139
Metric Maximum
vertical
Maximum Angle
wind load
Resultant
Use
load
222
=
load
=
2 T(sin
load
=
(37.676)
(975.5/2) a/2)
=
[(36
=
80 684
=
201
410-N
(975.5) =
752)2
(22.816) 2(63
+
(11
newtons
710
insulator
newtons
=
36 752
newtons
=
11 128
newtons
165)
(0.043
128
+
per
62)
=
5510)2]r/2
5510 =
per
conductor
per
conductor
newtons
40 342
per
conductor
newtons
per
conductor
phase
per
phase
with
a safety
factor
of 2.5
units.
U. S. Customary Maximum
vertical
load
=
(3200)
(2.5816)
=
8261.12
Maximum wind load = (3200/2) (1.5634) = 2501.44 Angle load = 2 T (sin a/2) = 2(14 200) (0.043 62) = Resultant
load
Use 50 OOO-lb
= = =
[(8261.12)2 I8 136.76 45 341.9
insulator
pounds
per
pounds 1238.81
per conductor pounds per
+ (2501.44 + 1238.81)2]1/2 pounds per phase pounds per phase with a safety
=
conductor
9068.38
factor
conductor
pounds
per
conductor
of 2.5
units.
Type 3OA, 15 ’ line angle Maximum Maximum
low-point distance = 792.5 m (2600 ft) sum of adjacent spans = 792.5 m (2600
ft)
Metric Maximum vertical load = (792.5) (37.676) = 29 858 newtons per conductor Maximum wind load = (792.5/2) (22.816) = 9040 newtons per conductor Angle load = 2 T (sin a/2) = 2(63 165) (0.130 53) = 16 489 newtons per conductor Resultant
Use 222
load
= = =
410-N
[(29 858)2 + (9040 + 16 489)2]1/2 = 39 284 newtons 78 568 newtons per, phase 196 420 newtons per phase with a safety factor of 2.5
insulator
per
conductor
units.
U. S. Customary Maximum
vertical
load
=
(2600)
(2.5816)
=
6712.16
pounds
per
conductor
Maximum wind load = (2600/2) (1.5634) = 2032.42 pounds per conductor Angle load = 2 T (sin a/2) = 2(14 200) (0.130 53) = 3707.05 pounds per conductor 3707.05) 2 ] 112 = 8831.46 pounds per conductor Resultant load = [(6712.16)2 + (2032.42 + = Use 50 OOO-lb
17 662.92
pounds
= 44 157.3 pounds insulator units.
per per
phase phase
with
a safety
factor
of 2.5
TRANSMISSION
140 Type
30T
and
300
tension
LINE DESIGN
MANUAL
structures
Metric Maximum
tension=
63 165 = =
Use double
strings
newtons
126 330 378 990
per
newtons newtons
of 222 ,410-N
conductor
per per
insulator
phase phase
with
a safety
factor
of 3.0
units.
U.S. Clrstor?larv Maximum
tension
Use double
strings
Make the construction a.
I4 200
pounds
per
conductor
= =
28 400 85 200
pounds pourlds
per per
phase phase
of SO OOO-lb
following calculations of the steel structure
Calculate
tabulation. as follows:
=
The
the
conductor
calculations
insulator
(paragraphs 3.a. limitation chart:
tensions are
with
shown
a safety
factor
of 3.0
through
3.g.)
to obtain
units.
to be used
for the
on figures
52 and
loading 53.
conditions From
data
shown
these
figures,
use in the
in the the
following
tensions
are
Tension
Loading condition N
(lb)
63 165
(14 200)
No ice, 0.19-kPa wind, 15.5 OC (60 OF)
29 289
(6 583)
No ice, 0.48-kPa ( IO-lb/ft2 ) wind, 15.5 OC
34 791
(7 821)
No ice, no wind, 15.5 OC
28 083
(6 314)
13-mm (l/2+)
b. the
for
ice, 0.19-kPa (4-lb/ft2)
wind, - 18 OC (0 OF)
Assume a scale to be used for the distance between point of origin), and compute the scale factor:
Metric
Let 1 mm = 7.2 m of bare conductor vertical force. Vertical force of conductor = 20.928 N/m Then, 1 mm = (7.2) (20.928,) = 150.68 N, and 1 N = l/150.68 = 0.006 636 58 mm (scale factor).
conductor
low
points
(vertical
scale
below
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
141
I/. S. Customary
Let 1 in = 600 ft of bare conductor weight, Weight of conductor = 1.4340 lb/ft Then, 1 in = (600) (1.434) = 860.4 lb, and 1 lb = l/860.4 = 0.001 162 25 in (scale factor). Compute the vertical force of the insulator
C.
phase factor:
or one-fourth
the insulator
force
string
per conductor
and
convert
to millimeters
one-half (inches)
the
insulator
using
force
the low-point
per scale
Metric Insulator
string
force
=
1628
1628/4 = 407 newtons (407) (0.006 636 58) =
N
per conductor 2.70 mm
U.S. Customary Insulator 366/4 (91.5)
string weight = 366 lb = 91.5 pounds per conductor (0.001 162 25)= 0.106 in
line deflection angle scale d. Compute calibration equal to the resultant tension
at 15.5
pressure
angle:
in one
conductor
due
to the
line
(horizontal
axis to the o C (60
right
’ F) final
of the origin) with
with
0.48-kPa
the degree
(lo-lb/ft2)
wind
I;‘, = 2T(sin a/2) T = 34 791 N (7821 lb) 2 T = 69 582 N (15 642 lb) Assume be the
line
same
angles
as that
and
compute
computed
resultant
in paragraph
tensions
e. Assume the
point
scale
of origin):
their
scale
2T(sinU/2) N (lb)
sina/2
40 50 60
and
values.
The
scale
must
scale
above
SC& mm
on)
(682)
0.043 62 .087 16
3 035 6 065
(1363)
2)
(0.79) (1.59)
.173 53 .130 65 .216 44 .300 71 .258 82
129 083 15 060 18 009 20 924
(2042) (2716) (3385) (4704) (4048)
ii: 100 139 120
:z; (3:95) - (4.72)
.342 02 .422 62 .500 00
23 798 29 407 34 791
(5350) (6610) (7821)
158 195 231
to be used for the sum.of
factor
3.b.
adjacent
spans
portion
of the chart
E,’ (7:7 1) (9.12)
(vertical
TRANSMISSION
142
LINE DESIGN MANUAL
Metric Let 1 mm Note:
=
6 m of wind
This
scale
sum of adjacent
will spans
span
= one-half
be doubled may
the
in marking
be read
directly
sum the
of adjacent
chart;
instead
that
spans. is, 1 mm
of reading
will
one-half
equal
12 m so that
the sum
of adjacent
the
spans.
0.48-kPa wind on conductor = 16.357 N/m (from force triangle, fig. 52) Then, 1 mm = (6) (16.357) = 98.142 N, and 1 N = l/98.142 = 0.010 189 318 mm (scale factor). U.S. Customary Let 1 in
=
500
ft of wind
span
= one-half
Note: This scale will be doubled the sum of adjacent spans may spans.
the
sum
in marking the be read directly
of adjacent
spans.
chart; that is, 1 inch will equal 1000 instead of reading one-half the sum
feet so that of adjacent
IO-lb/ft2 wind on the conductor = 1.12 1 lb/ft (from force triangle, fig. 53) Then, 1 in = (500) (1.121) = 560.5 lb, and 1 lb = l/560.5 = 0.001 784 12 in (scale factor). f.
Calculate
angle
of bias lines
to be drawn
right
bias lines are used to automatically add or subtract due to a line deflection angle. Because the scale the
same
as that
used
for
the
low-point
tan 8=
scale,
and left of the deflection
angle
the wind pressure to or from factor used for the deflection
the
slope
of the
bias
lines
may
calibrations.
These
the resultant angle scale
tension must be
be determined
by
sum of adjacent spans scale factor low-point scale factor
where 8 is the angle formed by the vary depending upon the choice
e = tan-l
’ = tan-’ g.
Calculate
wind
with
angle
for
0.010 189 318 = tan-l 0.006 636 58 0.001 784 12 = tan-’ 0.001 162 25 the
maximum each
bias lines with of scale factors
type
maximum
insulator
permitted
line
of suspension
angle, tower:
the horizontal previously
axis. The slope of the determined in paragraphs
bias lines will 3.b. and 3.e.
1.5353 = 56O55’ (metric) 1.5351 = 56O55’ (U.S. customary) swing
angles
and
maximum
in each negative
direction wind
by using with
maximum
minimum
permitted
positive line
CHAPTER Vertical plus
load
one-fourth
IV-STRUCTURE
due to conductor the
insulator
For one conductor,
LIMITATION
low-point force
per
distance
equal
to one-third
CHARTS the
sum of adjacent
conductor:
(20.928)
(350:)(2)
AND GUYING
+ y
= 5297.2
N, or
(’ ’ 50)(2) (1 434) + 366 = 1190 9 lb 3 4 * Calculate
swing
angles
for
suspension
insulator
strings:
Metric For
0.48-kPa
wind,
0’
line
angle
(30s
tower
with
positive
wind)
Wind = 350.5 (16.357) = 5733.13 N e = tm-’
For
-0.48-kPa
8 =tan-’
For
0.48-kPa
5733.13 = tan- l 1.0823 = 47O 15’ 5297.2 wind,
O”
line
angle
-5733.13 = tan-’ 5297.2 wind,
5’
line
(30s
and
30X
towers
with
negative
_ 1.0823 = -47015
angle
(30X
tower
with
positive
wind)
2T(sin a/2) = 2 (34 791) (0.043 62) = 3035.17 N 8 = tan-1 3035’17 + 5733’13 = tan-1 1 6553 = 58051’ 5297.2 For
-0.48-kPa
8 = tan’l For
0.48-kPa
wind,
5O line
angle
(30A
3035.17 5733.13 = tm-’ 5297.2 wind,
15 O line
angle
(30A
tower
with
negative
-0.509 32 = - 261059’ tower
with
positive
2T(sin a/2) = 2 (34 791) (0.130 53) = 9082.28 N 8 =tan-’
wind)
9082.28 + 5733.13 = tan- l 2.7968 = 70°‘19’ 5297.2
wind)
wind)
143 spans
TRANSMISSION
144
LINE DESIGN
MANUAL
U.S. Customary For
IO-lb/ftz
wind,
0’
line
angle
(30s
tower
with
positive
wind)
Wind = 1150 (1.121) = 1289.15 lb 1289.15 8
For
=tan-'
-lo-lb/ft2
8 = tan-’ For
llgog
lo-lb/ft2
wind,
= tan-’ 0’
line
1.0825 = 47016’ angle
(30s
and
30X
towers
with
negative
wind)
- 1289.15 llgo.g = tan-’ - 1.0825 = -47O16’ wind,
5’
line
angle
(30X
tower
with
positive
wind)
2T(sin a/2) = 2(7821) (0.043 62) = 682.30 lb (j = tan-’
682’30
+ 128g’15
= tan-l
1 6553 = 58051’
1190.9 For
-lO-lb/ft2
8 = tan-’
wind,
5’
682.30-
line
angle
1289.15
(30A
= tan-l
tower
-0
509
with
lo-lb/ft2
wind,
15’
line
angle
(30A
tower
wind)
= _ 27DoO’
32
1190.9 For
negative
with
positive
wind)
2T(sin a/2) = 2 (7821) (0.130 53) = 2041.75 lb e=tan-'
2041.75+
128g*15=tan-l
27970=7p19'
1190.9
the
The permissible center phase.
insulator swing angle It is desirable to keep
the bottom of the V-string at all times would cause wearing of the metal-to-metal greater use in this respect. With a 50’
for the 30s approximately to prevent contacts insulator
steel
tower will 890 N (200
be limited by the V-string lb) of extra vertical force
one leg of the V from becoming slack, which in the string. We use a 100 o V-string to permit swing:
Metric
tan0 = 1.191 76=
on on
5733.13 N (0.48-kPa wind on 350.5 m of conductor) x (X = low point in newtons)
CHAPTER Thus, a vertical when a 0.48-kPa required
force of X = wind is blowing
to provide
4810
- 407
4403
+
this
(extra =
means
insulator
252.9
the
percent of the line angle,
force
vertical
low
sum
LIMITATION
AND GUYING
CHARTS
4810 N is required to hold the insulator on a sum of adjacent spans equal to
vertical
(one-fourth
890
5293/20.928 This
IV-STRUCTURE
plus
the
force)
force
=
extra
890
4403
on V-string)
145
string at a SO0 angle 701 m. The conductor
N is:
N =
5293
N
m of conductor point
for
the
of adjacent
V-string
spans.
must
Therefore,
8 = tan- ’ (350s5) (*I c;;;;;o.g28)
be at least for
252.9/(2)(350.5)
a V-string
with
=
a 0.48-kPa
0.36,
or 36
wind
and
0’
+ 407 = tan- l 1.007 87 = 45 “13’.
U. S. Customary
tan0 = 1.191 76= Thus,
a vertical
when a lo-lb/ft2 to provide this 1082
1289.15 x
weight
wind weight
- 91.5
of
X =
is blowing plus the
(one-fourth
(1 O-lb/ft2 wind on 1150 ft of conductor) (X = low point in pounds) 1082
lb is required
on a sum of adjacent extra 200 lb is: Insulator
weight)
to hold spans
=
990.5
equal
the
to 2300
(extra vertical weight on V-string) = 830.2 ft of conductor
This percent
the low point for the V-string must be at least sum of adjacent spans. Therefore, for a V-string
line
string
ft. The
at a 50’
conductor
angle
required
lb
990.5 + 200 1190.5/1.434 means of the
insulator
=
1190.5
lb
830.2/(2)(1150) with a lo-lb/ft2
= 0.36, or 36 wind and a 0’
angle,
1289.15 8 = tan- l ( 1 150) (2) (o.36) ( 1.434) + g 1.5 = tan- l 1.008 05 = 4S” 13’. Paragraph To
4.
construct
the
structure
limitation
chart
a. Lay out the axes using the same vertical scale (see pars. 3.b. and 3.d.). provided b. the wind
the Calibrate
degree
deflection
angle
the
horizontal
calibration
equal
pressure
on one
conductor
bias
right
resultant to the
of the tension
line
structures,
proceed:
for the horizontal scale and the lower part scale may be used for the sum of adjacent
are adjusted
axis to the due
steel
scale factor A different
lines
to the
for
of the spans
accordingly. origin
in degrees
at 15.5
’ C (60
deflection
angle
of line OF)
(par.3.d.).
with
angle
deflection
0.48-kPa
(lo-lb/ft2)
with
TRANSMlSSlON
146 c.
Calibrate
calibrations on a bare d.
should conductor
Calibrate
of the bare be displaced (pars.
3.b.
e. lines
the
axis above
the vertical
and
axis below
due
lay
insulator
swing
g. angle)
deflection
h.
Add
i.
List
to the
pertinent
notes
Conductor,
l
Conductor Conductor
l
Ruling Number
Line
in meters
(feet)
pressure spans
for the
of adjacent
spans.
at 0.48 kPa (par. 3.e.).
(10 lb/ft2)
distance
the
low
points should string
radial
angles
each
type
of insulator of structure
swing
draw
in heavy
boundary
angle spans
bias lines at the computed angle, dependent upon scale factors scale and the distance between low points scale (par. 3.f.). These add or subtract
the wind
(par.
and
for
lines
chart
(sum
showing
on the
size and
span and
3.g.).
pressure
to or from
the resultant
tension
of adjacent
steel
chart,
tower
spans,
low-point
distance,
and
line
deflection
data.
including:
type or heavy,
and
maximum
design
wind)
size of insulators
limitation
problem structure
Problem a 115-kV
to be located
charts
for
the
example
problem
on steel
structures
follows that shows the limitation and guying
(wood-pole transmission in an area
construction) line with with
a 0.77-kPa
procedure charts.
a 242-mm2 (16~lb/fts)
for obtaining
(477-kcmil), extreme
the
are shown
on figures
required
to prepare
ACSR, wind
data
24/7
pressure.
not be a factor because the resultant force per unit length of conductor of 18.746 for this condition is less than the 27.5345 N/m (1.8867 lb/ft) force for the NESC The following data is also assumed: Maximum Ruling
between
The
5.
An example the wood-pole Example Assume
the origin
loading (NESC light, medium, maximum tension at full load
The structure 55 and 56.
Paragraph
for the sum
limits
limitation of structure.
a table
l
l
(feet)
angle.
Draw in heavy for each type
l
out
are used to automatically
to a line
in meters
equal to the vertical force of the conductor. The zero point by a distance equal to one-half the vertical force of the insulator
f. Lay out the .deflection used for the sum of adjacent bias lines
origin
3.c.).
a protractor,
the
the
MANUAL
be at a distance above the origin equal to the wind of length equal to one-half the sum of adjacent
(no ice) conductor below the origin
With for
vertical
LINE DESIGN
initial span
conductor
tension
(NESC
heavy)
single
conductor.
However,
this
will
N/m (1.285 lb/ft) full-load condition.
=
33 362
N (7500
=
213.36
m (700
lb) ft)
STRL TURE DATA
v lef I&ion
V Angle.
v
90
(dcp~l
eo
Tower Type Lme Angle Maximum Single Span (m) Minimum Lme Angle Mcxrmum Line Angle Mox. Sum of Adjacent Spans (m Minimum Line Angle Maximum Line Angle Mox. Low Point Distance (m) Conductor Minimum Line Angle Maximum Line Angle Overhead Ground Wire Minimum Line Angle Maximum Line Angle Maximum Uphft (N) Conductor Minimum Line Angle Maximum Line Angle Ovcrhcod Ground Mmimum Line Maximum Line
30s 7 3%
30x 65’
30T a-3i
487.5 396
467.5 3%
975.5 792.5
975.5
792.5
731.5 731.5
975.5 792.5
975.5 792.5
653.5 653.5
1036.5 653.5
036.5 653.5
3% 792.5
792.5
540.5 407.5
640
1097 975.5
1260
1371.5 1524 1524
1463
305 213.5
305
3% 254
3%
t
Wire Angle Angle
NOTES This
chart is based on Conductor size Conductor loodmg Conductor tensions
the
Ruling span Insulators
following: 644 mmf AC%. 4517 (bundle of two, 457-mm spacing) NESC Heavy. maximum wind at lS.S*C-0.46 kPo 63 165 N maximum per conductor, initiol conditions 34 790 N %r conductor with 0.46-kPa wind at IS.S*C 350.5 m 20 Units (146 ty 267 mm)
4 u
?
I
I i iAi i. i ““1 h I’/
-*0
----
Id I - -----
I
-----
I\ I\ $ +taox --I-+-
-10 Insulator
z
:
to S*ing”Angle
Figure
tdegZesl
55.-Example
of a steel structure
limitation
chart (metric).
104-D-1078.
7
I x
STRUCTURE Tower Type he Anale Moorimuk Siqle Span ( ft) Mimmum Line Angle Moximum Line Anqle Max Sum of Adjacent Spans (ft) Minimum Line Angle hbximum Line AnpIe Mar. Low point Dirtonce (ft) conductor Minimum Line Angle Morimum Line Angle Overhead Ground Wire Minimum Line Angle lo Morimum Line Angle Maximum Uplift (lb) Conductor Minimum Line Angle lo Moximum Line Angle Overhead Ground Wire Minimum Line Angle Maximum Line Anole IO
\
1 3osI 0.
IATA 30X
TT
-lo lnrulotor
0 . ‘0 Swing Angle (degrees)
Figure
of a steel structure
limitation
30D 535
lb00 I300
I600
I300
I600 1600
2100
2600 2606
3200 2600
3200 2600
3600 3200
4200
2400 2400
3200 2600
3200 2600
4200 4200
4500
2600 2600
3400 2600
3400 20
woo SW0
4600
1000 700
IO00
1300 633
l3DO
NOTES
This chart is based on the following: Conductor size 1272 hcmil. ACSR. 4517 (bundle of two. 16% spocimll NESC Heavy. maximum wind ot 6VF-IOlblft* Conductor loading 14 200 lb morimum per conductor, initiol conditions Conductor tensions lo 7620 lb. per ConductOr with IO- Iblft’ wind ot 6O.F Ruling spon I IS0 ft. lnsulotors 20 Units (5) by IO~ in.)
4 5 z r
M
56.-Example
301 TF
1300 I300
‘\ -co
30A Tiv
chart (U.S. customary).
104-D-1079.
CHAPTER
IV-STRUCTURE
units per mm (S-3/4
string by 10 in)
Seven insulator 146 by 254 Length
per
Vertical
LIMITATION
AND GUYING
string
force
(weight)
per
string
149
CHARTS
=
1194
mm
=
400
N (90
(47
in)
lb)
Wind Everyday Maximum Design
for
Wood-pole
maximum
=
0.19
kPa
(4 lb/ft2)
with
=
0.38
kPa
(8 lb/ft2)
13-mm
a minimum structure
(l/2-in)
radial
low-point
distance
designations
and
HS
=
tangent,
HSB 3AC 3A
= = =
tangent, suspension, large small line angle, suspension large line angle, suspension
3AB
=
large
3TA = Paragraphs charts. a.
to one-third
the
sum
of adjacent
are:
line
angle,
vertical
and
load
suspension
tensions
calculations
dead end the procedure for the
are shown
loading
on figures
for making conditions 57 and
the
calculations
shown
in the following
Assume a scale to be used for the distance between point of origin), and compute the scale factor:
Metric Let 6 m of bare
lmm= Vertical Then,
conductor
force of conductor 1 mm = (6)(8.968)
1 N =
l/53.808
=
0.018
= =
vertical 8.968 53.808
585
mm
force.
N/m. N, and (scale
factor).
U. S. Customary Let 1 in
=
500
feet
of bare
conductor
Weight of conductor = 0.6145 Then, 1 in = (500)(0.6145) = 1 lb = l/307.25 = 0.003 254
weight. lb/ft. 307.25 lb, 7 in (scale
for
the
tabulation.
Tension N (lb)
13-mm (l/2&) ice, 0.19~kPa (4-lb/ft2 ) wind, - 18 OC (0 OF) No ice, 0.19~kPa (4-lb/ft2) wind, 15.5 OC (60 OF) No ice, no wind, 15.5 OC (60 OF)
the
required
58.
Loading condition
b.
spans.
suspension
the conductor
data
equal
types
tangent to 90’ line angle, 5.a. through 5.~. describe
Calculate
Conductor
ice
and factor).
conductor
low
33 362
(7500)
11 748 10 872
(2641) (2444)
points
(vertical
scale
below
TRANSMISSION LINE DESIGN MANUAL
150
DCm-570
(3.78)
Linear Force Factw Rated Breaking
Slrength ,?l
Diameter.&*
TO,9
N
mm
-&
Teneton Lim~lations:
O&L&Z
Resultant:
Final *-!,25K
-N
Ares (A)&?i%mmd
Loaded,%.so%
-N
Temp. bell. N
%-
by
o.oa
Date -
s
?*/06 . 7q.zyiJ
kPa Wind
-N
Final.~‘,
N/m
mm Ice CW-,,2/.//xd
htiat.%.33f%
computed
j/. 9. ?6fD
Doad Load FQC* (W’)
8.
(W”‘)
4
Permanent Set 0.00 02
Nhn
creep 0.000
N/m
Total 0.0002
N/m Modulus. (E) Final m
x-R=
of Litmar hp.:
4’90
v’.52y/
FiM,
GPa
*,,;itiaia~GP:,
o&L&!-per%
/?77
msc
Initial
n’= 4.3782
AE /sr27/
N
1 TENSION. N
No Ice. No Wind (W’)
-
__
I
kPa Wind (W”‘)
No Ice#oWind
999
-
6 gs
0. flno I
SPA# LEN /pf
I
(W’)
0-m D.O?574kPI wind (WV”)1 - / Permanent set a creep 1
No Ice. No Wind (W*)
Figure 57.-Conductor (metric).
c. force
Compute the to millimeters
Insulator One-half (200.17)
ha&J I
432
15.5 32 4!4
sag and tension
vertical (inches)
I 6.000 I
a33/
I 0.
/959
lo , n.74
/
I
1
/ I I
I
I
I
I
calculation
s-253
621
I4kw.
I
!
I
I I
form for example
problem
force (weight) of the insulator string using the low-point scale factor:
string force = 400.34 N (90 lb) insulator string force = 200.17 N (45 lb) (0.018 585) = 3.720 mm or, (45) (0.003 254
7) =
on wood-structure
and
0.1465
convert
in
one-half
limitation
the
chart
insulator
CHAPTER
DC-676
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
(W’) -r?&/Js
lblft
Permamnt
/.
Wft
151
(6-76)
Rated Breaking
Load
Diameter
8. -946
Tension
Limitatiom:
1.7
doe
+&in.
Initial ,OF331Y-
ICO (w”)
Set O/XX&
creep
O.ooP~--
Total
0.00~
lb
Final ,!F_2L~Laded Fiml. XF
Dead Weight
lb
inch
lb OF -5e -
Modulus. (E) Fimlmx
Am (A) fl&$ki?i2 in2 Temo. ~oeff. of Linear EXP.: * &=0.3~
41 -lb K -lb
Fiml
Initial 3. AE Ijs
10s lb/i& //3
x lOS lb/i&? lb
No ICO. No Wind (W’)
SP4N LENGTH(S)--FEET Wlnd(w”’ Set L Creep
lb/f?
Pernunant
/
’ 2
- 40 1 I n
.na9
ff
6.92
4&O.
/5 \ S43i?
7
I I
Inch ~~ ICI.
I
SPANLENGTH(S)-?a
FEET
I
I
No Ice. No Wind (W’)
60 I
Figure 58Ahductor cu6tomary).
sag and tension calculation
ml
d. Compute deflection calibration equal to the pressure, in one conductor
I
I
form for example problem
angle scale (horizontal resultant tension at 15.5 due to the line angle: r;h
I
=
I
on wood-structure
axis to the right ‘C (60 ’ F) final
2 T(sin 11 748
I
I
limitation
of the origin) with 0.19-kPa
chart (U.S.
with the (4-lb/f?)
degree wind
a/2) N (2641
T = lb) 2 T = 23 496 N (5282 lb) Assume line angles and compute resultant be the same as that computed in paragraph
tensions 5.b.
and
their
scale
values.
The
scale
factor
must
TRANSMISSION LINE DESIGN MANUAL
152
5 10
0.043 .087 .130 .173 .216 .258 342 .422 .500
ii 25 30 40 50 60
e. the
Assume point
62 16 53 65 44 82 02 62 00
(230)
1025 2048 3 067 4 080 5085 6 081 8 036 9 930 11748
(0.75) :i
(460)
scale to be used for the sum of adjacent
E (1143) (1367)
57 76 94 113
:;E; (2641)
184 149 218
spans
portion
::z; (2:99) (3.72) (4.45)
of the chart
(vertical
scale
above
of origin):
Let 1 mm
=
1 inch
6 m of wind
=
span
500 ft of wind
=
span
one-half =
the
one-half
sum the
of adjacent sum
Note: This scale will be doubled when marking the chart, that equal 1000 ft, so that the sum of adjacent spans may be read
will the
sum
of adjacent
spans,
of adjacent
or
spans.
is, 1 mm will equal 12 m, or 1 inch directly instead of reading one-half
spans.
Metric 0.19-kPa
wind
on conductor
Then, 1 mm = 1 N = l/24.696
=
(6)(4.116) = 0.040
4.116
= 24.696 492 mm
N/m N, and (scale factor).
U. S. Customary 4-lb/ft2 wind on conductor = 0.282 lb/ft Then, 1 in = (500)(0.282) = 141 lb, and 1 lb = l/141 = 0.007 092 in (scale factor). f.
Calculate
angle
of bias lines
to be drawn
right
bias lines are used to automatically add or subtract due to a line deflection angle. Because the scale the
same
as that
used
for
the
low-point
scale,
and left
of the deflection
angle
the wind pressure to or from factor used for the deflection
the
slope
of the
bias
lines
may
calibrations.
These
the resultant angle scale
tension must be
be determined
by
tane= sum of adjacent spans scale factor _ low-point scale factor
where 8 is the angle formed by the will vary depending upon the choice 5.e.
bias lines with of scale factors
the horizontal previously
axis. The slope of the determined in paragraphs
bias lines 5.b. and
CHAPTER
IV-STRUCTURE
LIMITATION
0.040 492 = tan-’ 0.018 585
’ = km-’
Compute
maximum
low-point
153
CHARTS
2.1787 = 65o20’ (metric)
0.007 092 = tan-l I9 = tan-1 0.003 255 g.
AND GUYING
distance
2.1788 = 65’20’ (U.S. customary) for
the
type
HS
structure
shown
on figure
59:
Crossarm: 67 by 241 by 7620 mm (2-S/8 by 9-l/2 in by 25 ft) fbd’ Ultimate load = 6~ where: f = ultimate fiber stress of crossarm = 5 1 02 1 kPa (7400 lb/in2 ) for Douglas fir b = width of crossarm = 67 mm (2-S/8 in) d = depth of crossarm = 241 mm (9-l/2 in) L = length of crossarm projection = 1829 mm (72 in) fbd’ _ (51 021) (67) (24w 6L (6) (1829) (1000)
= 18 OS1 N or
= (7400) (2.625) (9-5)2 = 4058 lb (6) (72)
Ultimate load for two crossarms = 36 104 N (8 116 lb) Ultimate load withsafety factor of 4 = 9026 N (2029 lb) Force of conductor with 13-mm (1/2-m) radial ice = 2 1.186 N/m (1.45 17 lb/ft) Allowable low-point distance: ==426m 21.186
2029 -= 1.4517
or
1397 ft
At no load, force of conductor = 8.968 N/m (0.6145 lb/ft) factor of safety =
h. Using
Compute 18 905
maximum N (4250
8116 = 9.45 36 lo4 = 426 (8.968) (1397) (0.6145) low-point
lb),
b ased
distance on test
for data,
type for
HSB metal
structure fittings
shown on knee
on figure braces
60:
at 45’
slope:
TRANSMISSION
154
LINE DESIGN
MANUAL
L -2
..
2-
..
a :n k “I
/
--
NvAngle \ \ ‘\
/
or side guy
For two X-braces., install bolts 457mm (I8 in) apart.
II:
For 22.9-m (75-ft) structure and under, install one X-brace. For 24.4-m (80 ft) structure and over, instal t two x-braces.
TYPE
Fiie
59,Type
HS
STRUCTURE
HS wood-pole
structure.
104-D-1080.
CHAPTER
IV-STRUCTURE
-I
LIMITATION
PLAN
AND GUYING
CHARTS
155
L-
/Angle
or side guy
For two x&braces, install bolts 457 mm (I8 in) apart. Structure ground wires4
“OKge*
A
For 22.9-m (75-f-t) structure and under, install one x-brace. For 24.4-m (80-ft) structure and over, install two x-braces.
TYP E Metric L 2
HSB
STRUCTURE
2490 7 620 3658 7 620 3658 2134 8 839 4267
69 II5
2490
138 I61
2439 IO 668 5182 Fiie
60.-Type
HSB wood-pole
structure.
104-D-1081.
TRANSMISSION
156
LINE DESIGN
MANUAL
Metric
US. Customary
Crossarm load = 18 905 (0.707 1) = 13 367 N Allowable low-point distance:
4250 (0.7071) = 3005 lb
13 367 = 630.94 m 21.186 i. Compute
maximum
low-point
3005 = 2070 ft 1.4517 distance
for
type
3AC
structure
Metric
(7400) (2.625) (9-5)2 = 4870 lb 6 (60)
1217 lb
Ultimate load with a safety factor of 4 = 5414 N Allowable low-point distance for double crossarm:
Compute
insulator to prevent
the
effects
m
21(;;;;) .
of various
sizes of hold
string to increase the effective excessive insulator side swing.
conductor The first
downs
Assume 18 288-mm example because
different formula
allowable sum on the structure:
be attached
to the
bottom
of the
in adjacent spans, and also is the low-point scale factor.
1 lb = 0.003 254 7 in 50-lb weight = 0.163 in loo-lb weight = 0.325 in 150-lb weight = 0.488 in
of adjacent
(60-ft), class 2 western red this is the lowest strength
classes of poles are a function for computing the wind force
may
= 1676 ft
U.S. Customary
1 N=O.O18585mm 222.4-N force = 4.13 mm 444.8-N force = 8.27 mm 667.2-N force = 12.40 mm
this
that
low-point distance value shown below
Metric
k. Compute the maximum determining the wind loading
61:
2-518 by 9-l/2 in
(51 021.52) (67) (241)2 = 2l 662 N (1000) (6) (1524)
j.
on figure
U.S. Customary
Crossarm section = 67 by 241 mm fld= Ultimate load = 6~
2(5415L511 21.186
shown
cedar wood
spans
on a type
poles (western permitted by
of the pole circumference, on a pole may be derived
HS
structure
(fig.
59)
by
red cedar data are used for USBR specifications). The
see table B-3 in appendix using figure 62:
B. The
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
-Structure ground wires--=
TYPE
3,
Metric, 69 115
STRUCTURE
mm
A 2 YT 1982 3658 1372 343 1982 4267 1524 610
Figure 61.-Type
3AC wood-pole
U.S. Customary, ft-in A 6-6 6-6
structure.
2 Y 14-O 4-6 14-O 5-O
104-D-1082.
T l-l&
2-O
157
TRANSMISSION
158
d2
0”
LINE DESIGN
H
AX-
d2- diameter of pole at top dl - diameter of pole a-t b&tom H - height of pole
t dl 1 O Figure 62.~Single-line compute wind force.
sketch
For pole,
of wood
pole showing
values
needed
to
Y-Y1 x-x, =x2 - Xl Y2 - Yl
General form of equation:
Then
MANUAL
y-H x-4 =o - H d, - d,
x = (Y - Hi ,
-
d2 1
-H
+d,=(y-
Let the force of wind on dy l X be F in kilopascals moment of the wind force on a pole above ground is:
H)k+d,,wherek=F
(pounds
per
H c
Fx dy*y,
+ Fx dy*y, + . . .
0
H
=F
yb-H)k+d,ldy / 0
=F
H I
WY2 - kHy + dzy)dy
0
square
4
foot).
-
d2
Then,
the
total
CHAPTER
Substituting (d Imeters
(square
dz)/-Hfor
feet)
IV-STRUCTURE
k,
the
LIMITATION
moment
AND GUYING
in newton-meters
CHARTS
(pound-feet)
on an area
is:
- d,)fi’
=F
(d, - d, )H2 d, H2 2 + 2
1 1
- d2)H2 - 3(d, - d2)H2 d2.H2 -6 + 2
1
d,H’ +2
=F
I
=F
=
H= d, +2.d, -y 3 I( 9
FH 2(d 1 + 2d, ) in lb*ft if diameters are in feet, or 6
= FH2W, + 26,) in Nom if diameters are in millimeters, or 6000 = FH2W, + 24 1.111lb* ft if diameters are in inches. 72
159
in square
TRANSMISSION
160
LINE DESIGN
MANUAL
Metric
Mp =
FHZ’(d, + 26,)
6000
, where
Mp = moment
M =(0.383 04)(1000)(15.850)2
[404.34+2(202.18)]
= 12970N.m
6000
P
U.S. Customary
Mp = The
maximum
IO-mm
allowable
(3/8-in)
high
SAS (sum
strength
of 21 418-N (4815~lb) on figures 63 and 64. DCm-I70
FH2(d, +2d,) 8(52)2 [ 15.92+2(7.96)1 72 = 72
initial
steel,
of adjacent
7-strand
condition.
spans)
overhead
Sag and
L can now
ground
tension
wires
calculations
= 9566 lb-ft be found with
by statics.
a maximum
for
the
ground
Assume
full-load wire
are shown
(S-78)
M
coN0ucTom /o-mm.
-
.-=hJ
.-/JJ+r Rotad
Making
Stmngth
Dimeta
.&mm
Tmaim
Limtatiana:
Initial.FINI
d--&--N
9c.33f* .o,
.-
-N 2s
% -N
LUdDdd.~~.Y)% Finsl
cawutd
NO I-.
-N
*-,--lS.Sg:
w
bv
Date
No Wind
N
-
(W’)
Figure 63Averhead chart (metric).
ground wire sag and tension calculation
form for example problem
on wood-structure
two
tension
limitation
CHAPTER
IV-STRUCTURE
LIMITATION
km2
AND GUYING
CHARTS
$A6CKCUUTloM
161
0. #f&f
6=/5'+Q'
LOAOIWGA&;'* 7-wire Ratad ErakIng Load -lb Dlamotu &d&L inch Tonslat
&b oFA?L%
Final.
-
LM Flml.
,-!A% aO?F
WW-
LOADING
NO la.
bad Weight (W')-d!d;73 + kin. ~a fw") .p.ld7
Limitation:
Inithl.~
OFAL% -
tb
Wol@t Fntm:
-
(L -lb Dam
lb
Am
lb
Tamp. coan.
IbItt
(A)
tw”‘)
/*3/c
of Llnu
In2 Exp.:
Q&Q
o.oooonlPu~
[~[LllwnmlLEwlnJ
lb/n
Wind ,A Resultant:
-lb
Modulw. *x:
&.q
bt=
&ac O.bO
0.00
(E) Flrl3j:x Initlal~.
0
100 IWid I l@ lb/Id
Flnl AE ;zInitlaIAE /a
SMfAcloR 1 SAG,R
7
I
Total
Iblft
*:nn
izIE.
Fumsnont sol O.ooJn~ crap 0.00
lb/h
lb lb
1 SN,Ib
1 TENSJON,lb
No Wind (w’)
F’iie 64.-Overhead ground chart (U.S. customary).
wire sag and tension calculation
Using base:
the
(2 OGW)
sketch
(wind
shown
force
cond.) (wind force allowable moment force
on pole)
Figure 65.~Single-line sketch of one pole of a type HS wood-pole structure.
form for example problem
on figure
on iced
65, and
OGW)
taking
(moment
on iced cond.) (moment on pole) (2 poles)/(safety
(2 poles)]
on wood-structure
moments
arm) arm)
(l/2 factor
(l/2
limitation
about
SAS)
the
+
SAS) = [(max. of 2)] - [(wind
(3.
TRANSMISSION
162
LINE DESIGN MANUAL
Metric (2) (13.222) (15.70) (L/2) + (3) (17.96) (13.87) (L/2) = (250 5255’ (2)- (2) (12 970)
415.1708 L/2 + 747.208 L/2 = 250 555 - 25 940 L12 = 224 615 = 193.24 1162.379 L = 386.48 m U. S. Customary
(2) (0.9066) (5 1.5) (L/2) + (3) (1.23 1) (45.5) (L/2) =
(184 8200) (2) _ (2) (9566)
93.380 L/2 + 168.031 L/2 = 184 800 - 19 132 L/2 =
165 668 = 633.74 261.411
L= 1267ft
1. (fig.
Compute 59)
for
the allowable various
line
maximum
sum
of adjacent
spans
on a type
HS structure
with
angles:
Metric
FH2(d, + 6000
w2)
= (0.383 04) (1000) (3.51)2 i246.63 + 2(202.1-8)] = 512 Lo1 Nem 6000
U.S. Customary FH’(d,
+ 2d,) = (8) (1 1.5)2 19.71 + 2(7.96)1 = 376 .6 lbeft 72 72
X-brace
CHAPTER
IV-STRUCTURE
Using
the
LIMITATION
sketch
shown
AND GUYING
on figure
66, and
CHARTS
taking
163
moments
about
the
base:
(2
OGW)(2 Ga,. sin
OGW) (mbment (l/2
(moment arm)
SAS)
factor
=
a/2)
(moment
arm) (l/2 + (3 cond.) [(max.
of 2)] - [( wind
allowable force
arm)
SAS) ( wind
+
(2 OGW)
(wind
force
+ (3 cond.) (2 T&,x. sin force on cond.) (moment
moment
on pole)
on
pole)
on
a/2) arm)
(2 poles)/(safety
(2 poles)]
Figure 66.-Single-line sketch of top portion of a type HS woodpole structure with X-brace.
Metric (2) (42 836) (sin a/2) (3.35) + (2) (13.222) (3.35) (L/2) + (3) (17.96)(1.52)(L/2) = (56 870) (2)/2 - (2) (512) 287 001 592 063 592 063 6936.88 Assume
A line
L/2 + 305 062 (sin L/2 = 55 849 L = 55 849 L = 654.35
(sin a/2)
+
88.587
(sin a/2) (sin a/2)
+ +
170.700 85.35
(sin a/2) + values for L and
solve
for
a/2)
sin a/2
aI2
654.35 300 0
0 0.051 08 0.094 33
0 2’0’55’ 5O24’
these
tabulated
82.113
L/2 = 56 870 - 1021
values
should
he drawn
a 0 5050’ 10@48’
on the
sum
of adjacent
U. S. Customary (2) (9630) (sin a/2) (11) + (3) (1.231) (5) (L/2) 22 747.2 (sin a/2)
+
(2) (0.9066) (11) (L/2) + (3) (15 = (41 945) (2)/2 - (2) (376.6)
+
L = 2144.86
(1.52)
a:
L, m
representing
+
+ (3) (66 724) (sin a/2)
’
000)
(sin
a/2)
(5)
spans
chart.
TRANSMISSION
164 Assume
values
for
L and
solve
for
ft
L,
for
a working
western
red cedar:
stress,
at 15.5
a
42
0 0.050 33 0.094 29
fiber
MANUAL
a:
sin a/2
2144.86 1000 0 Assuming
LINE DESIGN
0 2053’ 5O24’
’ C (60
o F) with
no wind
load,
$$)
= 5.6 safety factor
ultimate fiber stress = 38.612 MPa or ($ii working stress 6.895 MPa With (1844 (2
a 15.5
‘C
lb) on the
OGW)
(60
(2 Tsin
moment
OF)
overhead a/2)
on wood
no wind
tension
of 10 872
ground
wire,
the
moment
(moment
arm)
+
(3 cond.)
(2 poles)/(safety
factor
pole)
0 5O46’ 1O”48’
N (2444
lb)
equation
on the
would
(2 Tsin
a/2)
of 6.895
MPa
(1000
conductor,
lb/ins)
and
8205
N
be:
(moment
arm)
=
(max.
allowable
of 5.6)
Metric (2) (16 410) (sin a/2) (3.35) + (3) (21 744) ( sin Q /2) 109 947 (sin U/2) + 99 413.57 (sin a/2) = 20 310.71
(1.524)
=
(56
870)
(2)/5.6
209 360.57 (sin a/2) = 20 310.71 sin a/2 = 0.097 01, a/2 = So 34 ’ a = 11’08’ U.S.
Customary
(2) (3688) (sin a/2) (11) sin a/2 = 0.096 99, a/2 a = 11’08’ If this
angle
had
been
+ =
less than
be drawn on the sum of adjacent using the previously tabulated m. Compute 61) for various the
two
(3) (4888) 5’34 ’
(sin
the
angle
spans angles.
largest
conductors
Example
: without
(2 cond.) shear)
(2T,,,.
shear sin a/2)
are guyed
(5)
=
(41
computed
945)
(2)/5.6
previously,
then
chart at 11 o 08 ’ from 0 to the intersection This means that the original line would
the allowable sum of adjacent line angles. Assume conductor
outside
a/2)
from
spans due to bolt on inside of angle pole
on outside
a vertical
line
would
with the line drawn be cut off at 11 o 08 :
shear on a type 3AC structure is guyed to top of middle pole,
(fig. and
of angle.
plates +
(2. cond.)
(wind
force
on iced
cond.)
(l/2
SAS)
=
(allowable
bolt
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
165
Metric (2) (2) (33 362) (sin a/2) + (2) (17.959) (L/2) 133 448 (sin a/2) + 17.959 L = 8123.53 7430.70 (sin a/2) + L = 452.34 Assume values for L and solve for a: sin a/2
Lm
452.34 200 0
=
(10 831.37)
aI2
0 0.033 96 0.060 87
0 lO56’ 3 O29’
(0.75)*
a
0
3O52’ 605 8’
U. S. Customary (2) (2) (7500) 24 378.35 (sin Assume
Example
values
(sin
a/2)
a/2) for
+ L = 1507.92 L and solve for a:
+
(2)
(1.2306)
(L/2)
= (2435) (0.75)*
L, ft
sin a/2
aI2
a
1507.92 1000 0
0 0.020 83 0.061 85
0 1011’ 3O32’
0 2022’ 7004’
a/2
a
: with
shear
plates
Metric 633 448 7430.70
(sin a/2) (sin a/2)
Assume
values
for
+
17.959
+
L =
L
and
L = 26 689.2** 1486.12
solve
for
a:
km
sina/
450 225 0
.0.139 44 .169 72 ,199 99
8OOl’ 9O46’ 1 lO32’
16OO2’ 19032’ 23OO4’
* and l * Data from National Design Specifications for Stress-Grade Lumber and Its Fastenings, 1973 Edition, National Forest Products Association, Washington D.C. l Part VI Bolted Joints: Paragraph 600-K-3.-The tabulated loads (table 12 for double shear) shall be used for a main member which is twice the thickness of the thinnest side members (2-5/8 in x 2 = 5-l/4 in). Permissiile load = 2435 lb = 10 831.37 N. Paragraph 600.G-2.-When joints are to be exposed to weather, .75 percent of the tabulated loads apply. l
* Part V Timber Connector Joints: Paragraph 500-B-2.-An assembly with two connector units of the same size used in contact faces with the connectors concentric with the same bolt axis, the total allowable connector load shall be the sum of the allowable connector loads given for each connector unit used (table 9).
TRANSMISSION
166
LINE DESIGN
MANUAL
U.S. Customary 30 000 (sin a/2) + 24 378.35 (sin a/2) Assume
for
values
for
L, ft
sin a/2
2000 1000 0
0.117 96 .158 98 .200 25
To be practical, assume type HS structure. n.
Compute
Full
load
Find
strength
a/2)
2Tsin
A 60’
tension for
angle
a safety
35 585 N (8000 Let points
=
a 60’
on chart
Then’ ’ N Using
same
line
6046’ 9009’ 1 l/033’
maximum
sum
of single
insulator
33 362
N (7500
of adjacent
(as computed
spans
string
used
(upper
limit)
on angle
type
3AC
as
structures:
under
or
par.
due to the
5.d.)
=
218 mm
(8.6
in)
1 lb =+j=O.OOl
(20 OOO-lb) = 21.186 line
angle,
insulator units N/m (1.4517
gives lb/ft).
and
conductor
V
be the
a working
Then,
HZ + V2 = (35 585 N)2 or (8000 lb)2
H(N)=&35
for
lb)
218 =-=O.O065446mm 33 362
force
131~32’ 18O18’ 23’OO6’
angle:
factor of 2.5 on 88 964-N lb). F orce of iced conductor
H be the horizontal in adjacent spans.
a
aI2
= 2(33 362) (0.5) = 33 362 N, = 2(7500) (0.5) = 7500 lb
30’
line
the
limitation
conductor
2 T(sin
L = 6000**
1.2306
+ L = 4875.67 L and solve for a:
585)2 - Y2 or H(lb) = J(8000)2
- V2
force
maximum between
of low
CHAPTER Solve
for
H by
IV-STRUCTURE
assuming
low-point
LIMITATION
AND GUYING
CHARTS
167
distances:
Metric
Low point, m
H,
V2
v, N
N
0
4 8 12 16 21
23t.2 414.4 711.4 948.8 186.0
233 231 226 218 205 187
35 585 35 332 34 561 33 237 31289 28 591
0
200 400 600 800 1000
17 953 864 71815 455 161584 175 287 261821 448846596
U. S. Customary
Low point, ft 0 500
0
Since
angle
structures
with
0
725.85 1451.70 2177.55 2903.40 3629.25 4355.10
1000 1500 2000 2500
suspension
H, lb
in
8000 7967 7867 7698 7455 7129 6711
9.17 9.14 9.02 8.83 8.55 8.17 7.70
V2
V, lb
2 4 8 13 18
insulators
526 858 107 433 741 124 429 732 171456 966 896
are limited
preceding limitation will not have much bearing. To show the 66 723-N (15 OOO-lb) insulator units are to be considered. Then, have a working tension of 26 689 N (6000 lb) and,
H(N)
Solve
for
= &26
H by assuming
- V2
689)2
low-point
to a maximum effect with
line
of such calculations, a 2.5 safety factor,
or H(lb) = J(6000)2
- V2
distances:
Metric
Low point, m 0 200 400 600 800 1000
v, N
V2
423$2 8 47414 12 711.6 16 948.8 21 186.0
17 953 8640 71815 455 161584 775 287 261821 448 846 596
H, -
N
26 689
26 25 23 20 16
350 308 467 617 231
angle
mm 175 172 166 154 135 106
of 60 O, the assume we would
TRANSMISSION
168
LINE DESIGN
MANUAL
U. S. Customary Low point,
lb 0
6000
526858 2107433 4141 124 8429732 13171456 18966 896
5956
0 7250.85 1451.70 2171.55 2903.25
500
1000 1500 2000 2500 3000
o.
Determine
limitation
angle
of single
3629.25 4355.10
of bias lines
insulator
strings
to be drawn under
H,
V2
17
ft
on the
various
-
6.88 6.83 6.68 6.41 6.02 5.48 4.73
5822
5591 5251 4778 4127
sum of adjacent
combinations
in
spans
chart
for reading
of loadings:
Metric Sm11 of adjacent For SAS = 600
spans scale, 1 mm = 6 m (from par. 5.e.) m, wind span = l/2 SAS = 300 m, 300/6
Conductor with 13-mm ice and 0.38-kPa The wind load on 300 m of iced conductor 1 N = 50/5387.7 = 0.009 280 4 mm
wind, =
wind (300)
=
force = (17.959)
50 mm
on chart
17.959 N/m = 5387.7 N
From figure 67, tan 0.008 280 4
6 (From
= 0.006 o*oog2804=141802 544 6 ’ 8 = 54O48’
paro. fin.)
Figure 67.-Force triangle showing angle of bias lines for wood-structure limitation chart (metric).
U. S. Customa fy Sum of adjacent spans scale, 1 in = 500 ft (from par. 5.e.) = 1000 ft, 1000/500 For SAS = 2000 ft, wind span = l/2 S&I Conductor The wind 1 lb
=
with l/2-in ice and 8-lb wind, load on 1000 ft of iced conductor
2/1231
=
0.001
624
wind =
force = 1.231 (1000) (1.231)
=
2 in on chart
lb/ft = 1231
lb
7 in
From figure 68, ._ 0.001 624 7 = 1 416 85 km8 -0.001 1467 * 0.001 624 7
(From poro. 5.n.)
8 = 54O48’ Figure 68.-Force triangle showing angle of bias tines for wood-structure limitation chart (U.S. customary).
the
CHAPTER p.
Compute
IV-STRUCTURE
conductor
guying
LIMITATION
for H-frame
type
AND GUYING
structures
with
CHARTS
no guys
169
on the overhead
ground
wires:
T
When
a transmission
line
which must be considered side of the angle structure, by the
two
a/2),
legs of the
see figure
wind
blowing
both
spans
case that also
on the
could
use more
heavy
and
areas,
instead
NESC loading
in all design the resultant
work. force
guying,
conductor.
happen.
We
assumption
values
loading
of the
values
The
This
for
value that
usually
pressure,
and
0.57
called
for
in NESC
and medium loading Where extreme wind
the
is highly
areas
areas loading
kPa
force
a force wind
blows
add
250.B.:
result
of
perpendicular
to the
safety
NESC
0.19
worst
factor. for light
kPa
and 0.43 kPa (9 lb/ft2) on the line (rule 250.C.)
to
it is the
(8 lb/ft2)
for
is 2 T(sin
is the
but
kPa
(12 lb/ft2) rule
force
that
improbable, 0.38
created
is the same on each of the angle formed
of the resultant
consider
will
wind
is a horizontal
If the line tension will be on the split
assume
line.
This
practical
line.
there
we also must
transmission
medium
heavy areas.
direction,
transmission
69. For
of the
changes
We
NESC loading
(4 lb/ft2)
in NESC is greater
for light than
the combined ice and wind load (or wind load alone) prescribed in rule 250.B., then the proper values taken from the wind pressure map (fig. 250-2 of NESC) should be used for all structure and guy loading computations. Figure 69.-Force triangle showing resultant conductor force due to line angle.
Example H =
: 2
T (sin
a/2)
+
(wind
force)
(L /2)
Metric H = 2(33 362) (sin a/2) +
(0.383 04) (1000)
1
L/2
= 66 724 (sin a/2) + 17.961 (L/2) = 66 724 (sin a/2) + 8.98 L U. S. Customary H = 2(7500) (sin a/2) + [(F)
(8;l
L/2
= 15 000 (sin a/2) + 0.6155 L Using
11-mm
(14 500 lb),
(7/16-in), a safety
7-wire, factor
high-strength
of 2.67,
and
steel
guy wire
set at an angle
with of 45’
a breaking to the
strength pole:
of 64 500
N
TRANSMISSION
170
LINE DESIGN
MANUAL
Metric
64 500 267 (0.707 1) = 17 080 N of horizontal pull per guy wire U. S. Customary
14 500 267 (0.7071) = 3840 lb of horizontal pull per guy wire . Then,
guying
structures
(2
of the horizontal
is determined
0-9
by
farces the
of the
moment
conductors
and overhead
ground
wires
on H-frame
equation:
%,a,.
sin a/2) (moment arm) (2 (l/2 SAS) + (3 cond.) (2 T,,,. sin a/2) (moment arm) (l/2 SAS) = ( a 11owable
+ (2 OGW) ( wind (moment arm) + horizontal
load
force
on OGW)
(3 cond.)
on guy)
(moment
(wind
force
(moment
arm)
- (wind
poles) Metric (2)
(2) + =
1 344 + 4 120
- For (21
one
418)
guy: (sin
(3) (2) (33 362) (17 080) (12.040)
a/2) (15.697) + (2) (13.231) (15.697) (L/2) (13.868) + (3) (17.961) (13.868) ( sin a/2)
L/2 + 2 775 985.30
793.38
( sin a/2)
+
415.48
L/2 =
179
703.69
+
1162.729
778.68
(sin
a/2)
L/2 = L = 179
4 120 778.68 (sin a/2) + 581.364 7088.12 (sin a/2) + L = 309.107 Assume values for L and solve for Lm
309.107 150 0 For two guys: 4 120 778.68
(sin
7088.12
(sin
a/2)
Assume
values
for
Lm
662.83 300 0
a/2) +
L
(L/2)
- 25 939.51
747.249
+
179
(sin
a/2)
703.69
703.69
a:
sin a/2
al2
a
0 0.022 45 .043 61
0 1417’ 2030’
0 2O34’ 5000’
L = (2)
581.364
(17
080)
(12.040)
- 25 939.51
L = 662.832 and
solve
for
a:
sin
a/2
0 0.046 96 .093 51
a/2
0 2Wl’ 5422’
a
0 5O22’ lOO44’
=
385
arm)
on cond.)
346.89
on
CHAPTER
IV-STRUCTURE
U.S. Customary-For
(sin
(2) (2) (4815)
one
a/2)
LIMITATION
AND GUYING
CHARTS
guy:
(51.5) + (2) (0.906) (51.5) (L/2) (45.5) + (3) (1.231) (45.5) (L/2)
(3) (2) (7500) ( sin a/2) 3840 (39.5) - 19 132
+ =
991 890 (sin a/2)
+ 93.318 L/2 + 2 047 500 ( sin a/2) + 168.032 L/2 a/2) + 261.35 L/2 = 132 548 L = 132 548 3 039 390 (sin a/2) + 130.67 23 260.044 (sin a/2) + L = 1014.372 Assume values for L and solve for a: 3 039
390
For two guys: 3 039 390 (sin 23 260.044 (sin values
sin a/2
at2
0 0.022 11 .043 61
1 O16’
ft
1014.372 500 0
Assume
Compute
conductor
conductor
and
on inside
guyed from the outside overhead ground wires two
conductors,
0
0 2032’ SO00
2”‘30’
at2
a
0 0.050 52 .093 51
0 2O53’ 5”22’
0 5046’ 10044’
overhead
of angle
ground
is guyed
one
wire
to top
pole. Two conductors will will be guyed off together.
guying
of center
be guyed
for pole,
off
a type and
together,
arm) horizontal
+
(2 cond.) load
( wind
656.86
656.86 7429.88 (sin
(sin
one conductor
on guy)
(moment
arm)
a/2)
(13.868)
+
(2)
(17.961)
(13.868)
(L/2)
a/2) + 498.166 L/2 = 205 733.62 a/2) + 249.083 L = 205 733.62 a/2) + L = 825.964 (sin
(fig.
and
on cond.)
= (17 080) (13.564) - (2) (12 969.75)
1 850
structure
outside
force
Metric (2) (2) (33 362) ( sin
3AC
two
conductors and
guy:
(moment (2 c0nd.j (2 Tmax. sin a/2) (l/2 SAS) = (2 guys) ( a 11owable
1 850
548
a
sin a/2
ft
2175.159 1000 0
For
132
a/2) + 130.67 L = (2) (3840) (39.5) - 19 132 a/2) + L = 2175.159 for L and solve for a:
L,
q.
=
(sin
L,
Assume
171
(moment - (wind
arm)
on poles)
61). are two
TRANSMISSION
172 Assume
values
for
L
and
solve
for
LINE DESIGN
MANUAL
a:
La
sin a/2
ai2
600 300 0
0.030 4 1 .070 79 ,111 17
1044’ 4003’ 6O23’
a
3 O28’ 8006’ 112~46’
U.S. Customary a/2) (45.5) + (2) (1.231) + 112.021 L /2 = 170 1 365 000 (sin a/2) + 56.01 L = 151 748 24 370.648 (sin a/2) + L = 2709.302 Assume values for L and solve for Q: (2) (2) (7500) 1 365
000
(sin
(sin
a/2)
L, ft
two
conductors,
0.029 10 .070 14 .lll 17 two
(L/2)
= (3840) (44.5) - (2) (9566)
880 - 19 132
sina/
2000 1000 0 For
(45.5)
a/2
a
1040’ 4001’ 6’23’
3O20’ 8002’ 12O46’
guys:
Metric 1 850 Assume
(sin a/2) + 249.083 L = (2) a/2) + L = 1756.068 values for L and solve for a:
656.86
7429.88
(17
080)
(13.564)
- (2)
(12 969.75)
(sin
sin a/2
Lm
0.155 60 .195 97 .236 35
600 300 0
aI2 8O57’ 11°18’ 13O40’
a
17054’ 22O36’ 27 O20’
U. S. Customary 1 365
000
(sin
a/2)
+
56.01
24 370.648
L =
Assume
solve
(sin a/2) + values for L and
L = (2) (3840) (44.5) - (2) (9566) 5760.186 for a:
L, ft
sin a/2
2000 1000 0
0.154 29 .195 32 .236 36
aI2 8O52’ 11015’ 13O40’
a 17044’ 22O30’ 27 O20’
CHAPTER For
one
conductor
and
IV-STRUCTURE two
overhead
LIMITATION
ground
wires,
AND GUYING one
CHARTS
guy:
Metric (1) (2)
(33
362)
+
(2)
(2)
=
(17
080)
6860.892 Assume
(sin
(21
a/2)
418)
(sin
(14.326)
a/2)
(sin values
(14.326) a/2)
- (12
+
(1)
(14.326)
(17.961) +
(2)
(14.326)
(L /2)
(13.2318)
(14.326)
(L/2)
969.75)
+ L = 728.186 L and solve for a:
for
sin, a 12
aI2
0.018 68 .062 41 .106 14
1004’ 3O34’ 6O05’
Lm 600 300 0
a
2OO8’ 7OO8’ 12010’
U.S. Customary (1)
(2)
(7500)
(sin
a/2)
(47)
+
( sin a/2)
+ (2) (‘4 (4815)
(1)
(47)
(L/2)
(0.906)
(47)
(1.231)
(47)
+
(2)
(L/2)
= (3840) (47) - 9566
22 517.410 (sin a/2) + L = 2390.071 Assume values for L and solve for a:
For
one
L, ft
sin a/2
aI2
a
2000 1000 0
0.017 32 .061 73 .106 14
0°S9’ 3032’ 6Qo5’
lO58’ 7w4’ 12010’
conductor
and
two
overhead
a/2) + + L =
318.213 1497.131
ground
wires,
two
guys:
Metric 2 183 225.096 6860.882 (sin Assume
(sin a/2)
values
for
L and solve
La
for
L = (2) (17 080)
0.130 76 .174 49 .218 21
42
7030’ lPO3’ 12036’
U. S. Customary 1 610 220 22 517.410
(sin a/2) (sin a/2)
+
L = (2) (3840) (47) - (9566) L = 4913.914
71.510 +
.- (12 969.75)
a:
sina/
600 300 0
(14.326)
a
1SOOO’ 20° 06’ 2Pi 2’
173
TRANSMISSION
174 Assume
values
L and solve
for
L,
for
0
762 mm
guy
attachment
(2.5
ft)
two-conductor a total
load
for
(three
conductors
two
attachment
between
the
two
guy
attachment
guys
and
attachment
The
ground
required
points
overhead
with
ground
for the other guy attachment
and two overhead points.
two
very
little
wires
is separated
two conductors and points, it is satisfactory
wires)
number
14O52’ 20000’ 25012’
guyed
of guys load
from
an imaginary
(as calculated)
transferred
the
at each
(2 cond.1 (2 T,,,. (1 cond.)
attachment
(moment on poles)
sin a/2) (moment arm) + (2 cond.) ( wind force on cond.) arm) + (1 cond.) (wind force (2 T,,,. sin a/2) (moment
arm)
(l/2
SAS)
(2) (2) (33 362) (sin a/2)
=
(2 guys)
sin a/2) (moment arm) + (2 OGW) ( a 11owable horizontal load per guy)
(2)
(33
362)
(sin
(13.868) a/2)
+
(2)
(14.326)
(17.961)
4 033 881.960 Assmne
be split between
+
(1)
(17.961)
(sin
(sin
a/2)
values
for
Lm 600 300 0
(14.326) (14.326)
(L/2) (L/2)
a/2)
+ 567.296 L = 437 451.95 L = 771.118 L and solve for a: +
sina/2 0.024 06 .060 63 .108 44
aI2 1022’
3O28’ 6% 3’
arm) (l/2 (moment
(wind force on OGW) (moment arm) - (wind
(L/2)
(13.868)
+ (2) (2) (21 418) (sin a/2) (14.326) + (2) (13.2318) = (2) (17 080) (13.945) - (3) (12 969.75)
7110.718
pole
(moment on cond.)
Metric
(1)
halfway
then
point):
arm) (l/2 SAS) + (2 OGW) (2 T,,,.
+
only
because the to consider point
could
through
by
points.
(one
SAS ) +
conductor
the guy attachment is located between the, two
the
Example For two
7O26’ 10°00’ 12”36’
f rom
load
between these
one
a
al2
0.129 41 .173 82 .218 22
1000
MANUAL
a:
sin a/2
ft
2000
As the
LINE DESIGN
a
2O44’ 6O56’ 12O26’
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
U. S. Customary
(2) (2) (7500) (sin a/2) + (1) (2) (7500) (sin + (2) (2) (4815) ( sin = (2) (3840) (45.75)
(45.5) a/2) a/2) - (3)
+ (2) (1.231) (45.5) (L/2) (47) + (1) (1.231) (47) (L/2) (47) + (2) (0.906) (47) (L /2) (9566)
2 975 220 (sin a/2) + 127.521 L = 322 662 23 331.216 (sin a/2) + L = 2530.266 Assume values for L and solve for a: L,
ft
2000 1000 0
sin a/2
aI2
a
0.022 73 .065 59 .108 45
lO18’ 3045’ 6013’
2036’ 7030’ 12O26’
For three guys (two at upper guy attachment
and one at lower):
Metric
4 033 881.960 (sin a/2) + 567.296 L = (3) (17 080) (13.945) 7110.718 (sin a/2) + L = 1190.970 Assume values for L and solve for a:
- 38 909.25
L, m
sin a/2
aI2
a
600 300 0
0.083 11 .125 30 .167 49
4p46’ 7012’ 938’
9”32’ 14O24 19O16’
U. S. Customary
2 975 220 (sin a/2) + 127.521 L = (3) (3840) 23 331.216 (sin a/2) + L = 3907.921 Assume values for L and solve for a: L,
ft
2000 1000
0
(45.75)
- 28 698
sin a/2
42
0.081 78 .124 64 .167 50
4041’ 7OO9’ 938’
For four guys (two at each attachment
a
9O22’ 14Ol8’ 19O16’
point):
Metric + 4 033 881.960 (sin a/2) + L = 7110.718 (sin a/2)
567.296
1610.822
L.=
(4)
(17 080) (13.945) - 38 909.25
175
TRANSMISSION
176 Assrmle
values
L
for
and
solve
for
LINE DESIGN
a:
sin a/2
Lm
600 300 0
MANUAL
a
aI2
0.142 15 .184 34 .226 53
8OlO’ 10O37’ 13005’
16O20’ 21O14’ 26O 10’
U.S. C11st0maly 2 975
200
(sin
a/2) +
r. Compute For one guy
L = (4) (3840) (45.75) - 28 698 L = 5285.576
127.521
23 331.216 (sin a/2) + Assume values for L and
solve
for
a:
L, ft
sin a/2
2000 1000 0
0.140 82 .183 68 .226 54
conductor guying at each conductor:
for
a
42
structure
16OlO’ 21010’ 26O 10’
8OO5’ 10035’ 13005’ types
3A
(fig.
70) and
3AB
(fig.
71).
Metric 2 T(sin
(2) (33 66 724 66 724
a/2)
+
362) (sin (sin a/2) (sin a/2)
7430.041 Assume
(sin
a/2)
values
for L
(wind
force)
(L /2) =
17 080
a/2) + [(47/1000) (0.383 04) + 17.9607 L /2 = 17 080 L = 17 080 + 8.9803 and
sin a/2
m
at2
0.175 23 .215 60 .256 00
lOOO5’ 12’27’ 14O50’
U. S. Customary (2) (7500) (sin a/2) 15 000 (sin a/2) + 15 000 (sin a/2) +
+ [(1.846/12) 1.231 L/2 0.6155 L =
24 370.43
+
a/2)
17 080
1901.941 solve for a:
600 300 0
(sin
=
L =
+
L
(lOOO)](L/2)
(8)]
= 3840 3840 L = 6238.83
(L/2)
= 3840
a
2o” 10’ 24O54’ 29040’
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
177
PLAN b
‘Minimum clearance between conductor and band or guy-
7
TYPE
1
230
Figure 70.-Type
3A
Structure ground wires’
STRUCTURE
130481762011956 110-O 125-016-5 3A wood-pole
structure.
104-D-1083.
178
TRANSMISSION
LINE DESIGN MANUAL
PLAN
/J c Minimum clearance between conductor and band or guy l-r
TYPE
Voltage, kV 1
69
Fii
3AB
/J
:
/
STRUCTURE
Metric, mm “.‘. fCtus~~mory’ AIZIB
AIZIB
130481442Oi 965 hO-Oh4-6
71-Type
3AB wood-pole
structure.
1 3-2 1
104-D-1084.
Assume
values
CHAPTER
IV-STRUCTURE
for
solve
L and
for
sin a/2
2000
0.173 93 .214 97 .256 00
0 two
guys
at each
AND GUYING
CHARTS
179
a:
L, ft
1000
For
LIMITATION
a
aI2
20002 241O48’ 29O40’
1OOOl’ 12O24’ 14050’
conductor:
Metric
66
724
(sin
7430.041 Assume
a/2)
+
(sin
a/2)
values
for
8.9803 +
L =
L =
L and
(2)
(17 080)
3803.882
solve
for
Lm
a: sin a/2
0.431 21 .471 58 Sll 96
600 300 0
aI2
a
25O32’ 28OO8’ 30°47’
5 I OO4’ 56’O16’ 6 l’O34’
aI2
a
U. S. Customary 15 000 (sin a/2) + (sin a/2) 24 370.43 Assume
values
s. Compute
for
0.6155 +
L =
L =
L and
(2)
(3840).
12 477.66
solve
for
a:
L, ft
sin a/2
2000 1000 0
0.429 93 .470 97 .512 00
overhead
ground
wire
guying
2S0’27’ 281OOS’ 3 0047’ for structure
types
on 2 OGW)
=
3A,
50054’ 56010’ 6 1O’34’ 3AB,
and
3TA
(figs.
72, respectively).
(2
OGV
For one Metric
(2
G,,,.
sin a/2)
+
(wind
load
horizontal
force
to he guyed
guy:
(2) (2) (21 418) ( sin + 85 672 (sin a/2) + 85 672 (sin a/2) 6474.754 (sin a/2)
a/2) + 26.4634 13.2317 +
L =
[ (34.544/1000) L /2 = 17 080 L = 1290:839
17 080 I
(0.383
04)
(lOOO)]
(2) (L/2)
=
17 080
70, 71, and
180
TRANSMISSION
LINE DESIGN
MANUAL
mm (14 ft) Withpost insulator 4877 mm (16 ft) With post insulator out
Structure wires y
ground
TYPE I
I
Figure 72.-Type
3TA
STRUCTURE
POLE
3TA wood-pole
SPACING
structure.
104-D-1085.
I
CHAPTER Assume
values
L
for
IV-STRUCTURE
and
solve
for
Lm
AND GUYING
CHARTS
a:
sin a/2
600 300 0 U.S.
LIMITATION
a/2
0.106 70 .153 03 .199 36
6007’ 8O48’ 11030’
a
12O14’ 17O36’ 23OOO’
Customary
(2) (2) (4815)
(sin a/2) +
[(1.36/12)
(8)]
21 244.209
L = 3840 L = 4235.605
Assume
solve
19 260
For two Metric
(sin
a/2)
+
(sin a/2) + values for L and
for
(2)
(L/2)
= 3840
a:
L, ft
sin a/2
2000 1000 0
0.105 23 ,152 30 .199 37
aI2 6OO2’ 8O45’ 11030’
a 12OO4’ 17030’ 23OOO’
guys:
85 672 (sin a/2) 6474.754 (sin a/2) Assume
0.9066
values
+
13.2317 +
L
for
L =
(2)(17
080)
L = and
2581.679 solve for a:
La 600 300 0
sin a/2
a/2
a
0.306 06 .352 40 .398 73
17O49’ 20°38’ 23O30’
35O38’ 41O16’ 47000’
a/2
a
U. S. Customary 19 260
(sin
a/2)
+
L = (2)(3840)
0.9066
21 244.209 (sin a/2) + Assume values for L and
L
= 8471.211 solve for a:
L, ft
sin a/2
2000 1000 0
0.304 61 .351 68 .398,75
17044’ 20°35’ 23O30’
35O28’ 41010’ 47000’
181
TRANSMISSION
182 For
three
LINE DESIGN
MANUAL
guys:
Metric 85 672 (sin a/2) 6474.754 (sin a/2) Assume
values
+
L
for
L =
13.2317
L =
+
and
(3)(17
080)
3872.518
solve
for
a:
sin a/2
Lm
0.505 43 .551 76 .598 10
600 300 0
a
42
30°21’ 33O29’ 36O44’
60°42’ 66O58’ 73O28’
42
a
U.S. Customary 19 260 (sin 21 244.209 Assume
a/2) + (sin a/2)
vahtes
0.9066 + L
L
for
and
L = (3) (3840) = 12 706.817
solve
for
L, ft
sin a/2
2000
0.503 99 .551 06 .598 13
1000
0 t.
Prepare
Assume
guying
structure
data
for
has 18.3-m
requirements
with
no angle
(OGW)
force
on iced
(wind
(moment arm) force on pole)
a:
(l/2
SAS)
structure (60-ft)
type
30015’ 33O26’ 36O44’ 3TA
western
(fig.
60°30’ 66O52’ 73O28’
72):
red cedar
poles
without
X-braces.
=
OGW) (moment [( max. allowable
arm)
(l/2
SAS)
moment
+ ( cond.)
on wood
(wind
pole)/(safetyLfactor
Metric (13.232)
(15.697) +
207.703 L/2 202.383 L = L =
(L/2)
+ (17.959) L/2 =
197.064
112 307 554.923 m (maximum
125
(10.973) 277 SAS
(L/2)
= (250 555/Z) -
12 970
without
side
guys)
U.S. Customary (0.9066) (51.5) (L/2) 46.690 L/2 + 44.316 45.503 L = 82 834 L = 1820.41
+
Compute
side guy
guys:
(36) (L/2) = = 92 400 - 9566
(1.231)
L/2
ft (maximum
SAS
without
(184
800/2)
side
guys)
- 9566
12 970
force
on iced
cond.)
of 2)] - (wind
CHAPTER With At
IV-STRUCTURE
LIMITATION
AND GUYING
183
CHARTS
X-braces: 5.9436
m (19.5
Circumference Diameter
=
on pole (wind
874 mm
mm
SAS)
(34.4
in)
in)
on pole
to wind
on iced
(l/2
of structure:
(10.95
moment due
force
(moment arm) force on pole)
top
= 278
allowable
Moment
from
of pole of pole
Maximum
(OGW)
ft)
=
81 603
OGW) (moment [( max. allowable
=
Nom
(60
187 lb*ft)
force: arm) (l/2 moment
SAS) + on wood
(cond.) (wind pole)/(safety
force factor
on iced cond.) of 2)] - (wind
Metric FfI’(d,
(13.232) 76.6291
+2d,) 6000 (5.7912)
= [0.38304(1000)(5.9436)21 [278.13 +(2)(202.18)1 6000 (L/2)
+
L /2 + 19.1587 47.894 L = 39 262 m L = 819.7686 U. S. Customary
(17.959)
(1.0668) (L/2) 801 - 1539
=
(81
603/2)
-
= 153g 176 Nem
1539
L /2 = 40 (maximum
SAS
without
side
guys)
FH2 Cd, + 26,) _ K%19.5)21 f10.95 + (2) (7.9611 = 1135 25.,5 lbaft 72 72 (0.9066) 17.2254 10.767
The
(19) (L/2) + (1.231) (3.5) (L/2) = (60 187/2) L /2 + 4.3085 L /2 = 30 093 - 1135 L = 28 958 L = 2689.51 ft (maximum SAS without side guys)
National
Electrical
Safety
Code
does
not
require
- 1135
angle
guys
structures; however, we use one single guy for each conductor up to 60 ‘. These angle guys will keep the structure from leaning for
the u.
3TA
overhead
Determine
single
ground
wires
span
were
limits
on structures
The following paragraphs describe how between conductors and overhead ground and span permissible
(30
length span
with given for a given
For loading conditions OF), determine the Conductor: 242 mm2 (477 Ruling span
conductors structure
of 13-mm conductor kcmil),
computed
in paragraph due
to galloping
to determine the spacing wires to prevent contact
and overhead ground with given conductors
(l/2-in) ice, O.lO-kPa and overhead ground ACSR,
24,/7,
NESC
if line
guys
at tension
for line angles requirements
5.~. conductors: required between conductors and for a particular loading condition
wires; or to determine and overhead ground
(2-lb/ft2) wind pressure, wire sags for the given
heavy
are used
on tension structures into the angle. Guying
the maximum wires.
and at minus span length:
1 ‘C
loading =
213.36
m (700
ft)
TRANSMISSION
184 Maximrun
tension
under
full-load
ice, 0.19-kPa (4-lb/ftz) Sag under a load of 13-mm at -l°C
(30
LINE DESIGN MANUAL conditions
of
13-mm
(l/2-in)
wind, at -18 o C: (0 o F) (l/2&1) ice, O.lO-kPa (2-lb/ftz)
=
33 362N
(7500
lb)
=
5253
(17.23
=
2 13.36
=
21 118 N (4815
=
4353
wind,
“F)
mm
ft)
OG w: lo-mm
(3/8-in)
Ruling
span
Maximum
high-strength
tension
under
steel, full-load
Sag under a load of 13-mm at -1 OC (30 “F) Sag and and
tension
calculation
heavy
loading
conditions
(l/2-in)
forms
NEST
ice, O.lO-kPa
for
this
(0)
for
example
(2-lb/ft2)
were
m (700
ft) lb)
wind,
shown
previously
mm
(14.28
on figures
57,
ft)
58, 63,
64. Determine The
the
angle
couductor
(2-lb/ft2)
wiud
of sideswing
has a force on the
iced
of 21.186
The
overhead
O.lO-kPa Therefore,
ground
(2-lb/ft2)
wire
wind
has a force iced
drawn at the
ellipses: locations
structures, sag valrles
of attachment
the conductors and below the attachment
N/m
of 11.773
N/m ground
or
points
overhead points.
length of the suspeusion hardware suspension insulator string for the
overhead
with (0.3077
= tan-’
overhead
to scale to give an accurate configuration. respective angles of sideswing for the
and
lb/ft)
4.4898
or
e = tan- 1 +f!$i$ Construct First, the
conductors (I.4517
equals
E
on the
the
N/m
conductor
e = tan-’
the the
7-wire,
for
the
(l/2-in)
ice.
Ib/ft).
Therefore,
with
equals
A O.lO-kPa
13-mm
(l/2+1)
ice.
N/m
(0.227
lb/ft).
3.3079
A
0.280 88 = 1SO42’.
conductors
and
the
are then drawn and overhead
ground wires For suspension
are located structures,
for the overhead conductors.
ground
A line which will be the location of the major point at an angle of 28 f ram the line representing
13-mm
lb/ft)
wire
Lines conductors
wires:
0.211 92 = 1 lO58’.
(0.807
= tan-’
ground
overhead
on these lines the sag points wires,
gromld
wires
from the attachment ground wires. For
and
axis of an ellipse is then the conductor or overhead
are
points tension
at their respective must be extended
extended
the
drawn through ground wire
length
of
each sag sideswing.
The major axis of the ellipse is equal to the sag for full-sag ellipses, or one-half the sag for half-sag ellipses, plus 6 percent. The minor axis is equal to one-half of the major axis. The ends and center of the major axis are marked with one end being placed a distance below the
sag point
equal
to 3 percent
of the
applicable
sag or half-sag
value.
The
minor
axis
is marked
perpendicular to the major axis at its center point. The ellipses may then be drawn by any acceptable method. There is no definite length of span where galloping will change from full-sag ellipses to half-sag ellipses. However, our experience has shown that, for our line locations and conditions, we should
use full-sag
ellipses
in spans
up to 183 m (600
ft)
in length.
In longer
spans,
the
conductors
CHAPTER are likely
to gallop
IV-STRUCTURE
in two
or more
percent of the sag, should be used. conductors or between conductors reduced
(see sec. 15).
for the longer must
span
be satisfied
Full-sag
limits
Paragraph 6. To construct a. spans
Lay
the
out
the
scale provided
in one
the and
deflection
b. Calibrate the the degree calibration pressure
5.b.
chart
183-m
type
same
scale
A different bias
horizontal axis to the equal to the resultant due
to the
(600-ft)
of structure
the
for
major
spans
axis
and
wire
of these
ellipses
limitations
limitation
Ellipses
chart
are shown
structures: the
scale
horizontal
factor
are adjusted
deflection
to 53
between is greatly
configuration.
scale
may
and
be used
the
for
lower
the
part
sum
of the
of adjacent
accordingly.
right of the origin in degrees of line angle tension at 15.5 o C (60 ’ F) with 0.19-kPa
line
equal
the half-sag
and case. Each ground
for the structure
wood
factor
lines
with
185
CHARTS
the probability of contact as a result of galloping
and overhead
for
5.d.).
angle
conductor
size ellipses,
do not overlap, ground wires
of the conductor
limitation
axes using
the
for each
AND GUYING
and cases to be considered
structure
(see pars.
so one-half
for the maximum
be made
by the dimensions
for the different structure types on figures ‘73 through 87.
vertical
loops
If these ellipses and overhead
ellipses
should
LIMITATION
angle
(par.
deflection (4-lb/ft2)
with wind
5.d.).
c. Calibrate the vertical axis above the origin in meters (feet) for the sum of adjacent spans. The calibrations should be at a distance above the origin equal to the wind pressure at 0.19 kPa (4 lb/ft2) on a bare d.
conductor
Calibrate
of length
the vertical
equal
to one-half
axis below
of the bare (no ice) conductor be displaced below the origin (pars. 5.b. and 5.c.).
the origin
Lay
out
the
deflection
angle
bias
g.
Layout
lines
showing
h.
Draw
lines
to show
in meters
are offset the vertical
adjacent
(feet)
for the distance
spans
(par.
5.e.).
between
low
the
maximum
(pars. of the
the conductor
at the
computed
vertically from force of each
swing, and draw in heavy (see table 21, par. l.c.). angle
and the distance between add or subtract the wind
permissible
(dependent
low
point
sum of adjacent
limits
the, insulator holddown by
permissible
upon
low points scale, pressure to or from
spans
5.k., 5.1., and S.m.), and maximum low structures (pars. 5.g., 5.h., and 5.i.).
of holddowns to the bottom of the insulator strings holddown is drawn parallel to the insulator string swing These lines multiplying
of the
angles of insulator type of structure
lines
used for the sum of adjacent spans scale These bias lines are used to automatically tension due to a line deflection angle.
types of suspension structures calculated from the strength
sum
points
equal to the vertical force of the conductor. The zero point by a distance equal to one-half the vertical force of the insulator
e. With a protractor, lay out the radial lines for the insulator swing limits for each f.
the
by the
for class point
addition
should string
boundary
scale
factors
see par. 5.f.). the resultant
2 poles
distance
for all lines
of various
as
sizes
(par. 5.j.). A line for each size of insulator limit line for the type HS and HSB structures. string swing the low point
limit line by values obtained scale factor (par. 5.j.).
by
TRANSMISSION
186 i.
Plot
the
single
35 585 N (8000 j. spans The
Add
lb)
insulator for
the bias lines
chart
(par.
structure
string
88 965-N
limit
LINE DESIGN line
(20 OOO-lb)
for determining
at the units
resultant
under
the limitation
MANUAL load
on the
maximum
of single
insulator
loading
insulator
string
conditions
strings
equal
(par.
to
5.n.).
to the sum of adjacent
5.0.).
limitation
charts
for
wood
structures
are shown
on figures
88 through
91.
Paragraph 7. To
construct
a.
Use
b.
Superimpose
calibration C.
under
the
the
same
(sum
From
angle
guying
line
deflection
the
guying
of adjacent
conditions
for
angle chart
horizontal
using
for the number (pars.
suspension
on the
spans)
the calculations
full-load
chart
5.p.,
wood axis
deflection
the
structures:
as used angle
bias
same
scale
used
of angle
guys
required
q., r.,
and
s.), plot
for
lines,
for
lines
the
the
structure
limitation
or repeat structure
the
vertical
limitation
for the various separating
chart.
the
types zones
axis
chart.. of structures for
different
quantities of guys. Some of the limitations calculated may be unnecessary because some of the limit lines may be very close to each other if they are all plotted. Some of these limitations may be combined with others to keep the chart clean, but care must be taken to eliminate the right lines so that all guying
requirements
are satisfied.
required by various guy guys required to satisfy indicated one angle
Standard
arrangements, the calculated
guying
drawings
and the required guy requirements.
quantities The
be checked coordinated coordinated
for the number with the quantities
of guys number should
of be
on the structure guying chart. No guying is required for a line angle up to lo, but at least guy per suspension structure should be used for all line deflection angles greater than lo.
A vertical line at the 1 o mark should be drawn and an angle guy is not required. Guying charts are shown arrangement
must
drawing
for
the
type
3TA
structure
labeled to indicate the area on the chart on figures 92 and 93. A typical standard
has been
included
as figure
94.
where guying
CHAPTER
IV-STRUCTURE
Type HS Structure 289.5 -m (950-ft) Span Based on 213.4-m (700-ft) ruling span 3658-mm (12-ft) l%e spacing NESC Heavy Loading Conductor full-load tension = 33 362 N (7500 lb) OGW f ul I - load tension = 21 418 N (4815 lb) Half-sag ellipses
LIMITATION
AND GUYING
CHARTS
Conductor: 242 mm2 (477 kcmil~B~SR. 2417 9%
Sag Half sag
290
(31.74) ( 15.87) ( 0.95)
5127 2563
(16.82) ( 8.41)
4837
+6%
Major axis Minor axis 8 = I lo 58’ OGW: IO-mm ( i-in) So HaBf saa +6%
~-=
Major axis Minor axis 8= 15’42’
H.S. Steel (tilt) mm 8016 (26.30) 4008 (I 3.15) ii0 ( 0.79) 4248 (I 3.94) 2124 ( 6.97)
4023 mm t=
Fiie
73.~Half-
and full-sag
ellipses for type HS wood-pole
(13.2 ft)
structure
(Sheet 1 of 2). 104-D-1086-1.
187
188
TRANSMISSION
Type HS Structure 183-m (600-ft) Span Based on 213.4-m (700-ft) ruling span 3658-mm (12-ft) Pole spacing NESC Heavy Loading Conductor ful I- load tension = 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb) Full-sag ellipses
LINE DESIGN MANUAL
Conductor: 242 mm2 (477 kcmil) ACSR, 24/7 (if) m 3852 (12.64) Sag +6%
Major axis Minor axis
231 4083 2042
( 0.76) (13.40) ( 6.70)
0= IP58’
OGW: lo-mm
( i-in)
Sag +6%
Major axis Minor axis
H.S. Steel mm (tit) 3 I97 (10.49) 192 3389 1695
( 0.63) (I 1.12) ( 5.56)
8 = 15“ 42’
Figure
73.~Half-
and full-sag
ellipses for type HS wood-pole
structure
(Sheet 2 of 2). 104-D-1086-2.
CHAPTER
IV-STRUCTURE
Based on 213.4-m (700-ft) ruling span 3658-mm (i2-ft) Pole spacing NESC Heavy Loading Conductor full-load tension
Half-sag
ellipses
AND GUYING
IO?7 5 359 321 5 680 2 840
Sag
Half-sog +6%
Major axis Minor axis 9 = I lo 58’ OGW: lo-mm ($-in)
Saa Haif -sag +6%
Major axis Minor axis
189
CHARTS
Conductor: 242 mm2 (477 kcmil)f;XiR,
Type HSB Structure 305.4-m (iooo-ft) Span
= 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb)
LIMITATION
24/7
(3576) (17.58) ( 1.05) ( 18.63) ( 9.32)
H.S. Steel (fi) mm 8882 (29.14) 4441 ( 14.57) 266 ( 0.87) 4707 (15.44) 2353 ( 7.72)
6= 15”42’
F’iie
74.~Half-
and full-sag
ellipses for type HSB wood-pole
structure
(Sheet 1 of 2). 104-D-1087-1.
TRANSMISSION
190
Type HS8 Structure
Conductor:
183-m (600-ft) Span Based on 213.4-m (7oo-ft)
ruling
span
3658-mm (l2-ft) Pole spacing NESC Heavy Loading
Conductor full- load tension = 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb) Full-sag ellipses
Figure 74.-Half-
and full-sag
LINE DESIGN MANUAL
242 mm* (477 kcmil) ACSR, 2417 CY) 3852 (12.64) Sag +6% 231 ( 0.76) Major axis 4083 ( 13.40) Minor axis 2042 ( 6.70) 0 = I l”58’ OGW: IO-mm ($-in) H.S. Steel mm wt) 3197 (10.49) Sag +6% 192 ( 0.63) Major axis 3389 (11.12) Minor axis 1695 ( 5.56) 0 = 15’42’
ellipses for type HSB wood-pole
structure
(Sheet 2 of 2). 104-D-1087-2.
CHAPTER
IV-STRUCTURE
Type 3AC Structure loo Line Angie 304.8-m (IOOO-ft) Span Based on 213.4-m (7oo-ft) ruling span 4267~ITIm (l4-ft) Pole spacing NESC Heavy Loading Conductor full-load tension = 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb) Half-sag ellipses
LIMITATION
AND GUYING
CHARTS
Conductor: 242 mm2 (477 kcmi~ft;LCSR. 24/7 IO?7
WI
(35,16)
Half -sag +6X
Major axis Minor axis 8 = 11’58’ OGW: IO-mm (i-in)
sag
Half-sag +6%
Major axis Minor axis 0 = 15’ 42’
5 680 2 840
( 18.63) ( 9.32)
H.S. Steel mm 8882 4441 266 4707 2353
Kt) (29.14) (14.57) ( 0.87) (15.44) ( 1.72)
2(23 586) sin 5’+
Fii
75.~Half-
and full-sag ellipses for type 3AC wood-pole
structure
(Sheet 1 of 2). 104-D-1088-1.
191
TRANSMISSION LINE DESIGN MANUAL
192
Type 3AC Structure IO0 Line Angle 183-m (600-ft) Span Based on 213.4-m (7oo-ft) ruling span 4267-mm (l4-ft) Pole spacing NESC Heavy Loading Conductor f uI I - load tension = 33 362 N (7500 lb) OGW full-load tension
Conductor: 242 mm2 (477 kcmil) ACSR, 2417 mm K?) 3852 (I 2.64) wl +6%
8 = ll”58’ OGW: IO-t?Im (i-in)
+6%
Full-sag ellipses
2
Fire
75.-Half-
and full-sag
Major axis Minor axis 8 = 15’ 42’
_
t-
( 0.76) (13.40) ( 6.70)
H.S. Steel Hi) mm
swl
= 21 418 N (4815 lb)
z
231 4083 2042
Major axis Minor axis
3 197 192 3389
( 10.49) ( 0.63) (I 1.12)
1695 ( 5.56)
4251 mm (13.95 ft)
ellipses for type 3AC wood-pole
structure
(Sheet 2 of 2). 104-D-1088-2.
CHAPTER
IV-STRUCTURE
Type 3TA Structure Tangent, OGW in tension 213-m (700 -ft) Span 4267-mm (I4 - f t) Pole spacing NESC Heavy loading Conductor full-load tension -33 362 N (7500 lb) OGW full-load tension -21 418 N (4815 lb) Full-sag ellipses
LIMITATION
AND GUYING
193
CHARTS
Conductor : 242 mm2 (477 kcmil) ACSR, 24/7 5g 315 5568 2784
Sag +6 %
Major axis Minor axis 0- ll”58’ OGW: ICFmm (&in)
WI (17.23) (I .03) (18.26) (9.13)
H.S. Steel
Sag +6 % Major axis Minor axis 0= 15’42’
mm
(B)
4353 261 4614 2307
(14.28) (0.86) (15.14) (7.5 7)
3534 mm (28 ft)
Figure 76.-Full-sag 104-D-1089.
ellipses for type 3TA
wood-pole
structure,
tangent,
4267-mm
(14.ft)
pole spacing.
TRANSMISSION
194
Conductor : 242 mm* (477 kcmil)ACSR, Sag
Half sag +6 % Major
axis
Minor axis 8= 11’58’ OGW: IO-mm (i-in)
Sag Half
sag
+6 %
Major Minor 0=
F@e.
axis axis
mm I2 966 6483 389 6872 3436
LINE DESIGN MANUAL
Type 3TA Structure Tangent, OGW in tension
2417
(fa (42.54) (21.27) (1.27) (22.54) (I 1.27)
335-m (IIOO-ft) Span 4267-mm (l4- ft) Pole spacing NESC Heavy loading
Conductor ful l-load tension =33 362 N (7500 lb) OGW full-load tension -21 418 N (4815 lb) Half-sag ellipses
H.S. Steel IO 747 5374
(ti) (35.26) (I 7.63)
322 5696 2848
(1.06) (18.69) (9.35)
8534 mm (28 ft)
lS“42’
77.-Half-sag
ellipses for type 3TA wood-pole
structure,
tangent,
4267-mm
(14.ft)
pole spacing.
104-D-1090.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
195
Type 3TA Structure 90” Line ongle, OGW in tension
Conductor : 242 mm’ (477 kcmil) ACSR. 2417 Cf?) Without post insulator for jumper 4526 (14.86) Sag 198-m (650-ft) Span II 278-mm (37-ft) Pole spacing NESC Heavy loading
+6%
272 4798 2399
Major axis Minor axis
Conductor full -load tension 0 = Ilo 58’ -33 362 N (7500 lb) OGW: IO-mm ($-in) OGW full-load tension 121 418 N (4815 lb) sag Full-sag ellipses +6 % Only one OGW and two conductors Major axis are shown Minor axis 0s
Fiie 78.-Full-sag ellipses for type 3TA wood-pole spacing. 104-D-1091.
(0.89) (15.75) (7.88)
H.S. Steel
(ti) 3751 225 3976 1988
(12.31) (0.74) (13.05) (6.53)
l5O42’
structure,
90”
line angle,
11 278~mm
(37.ft)
pole
TRANSMISSION LINE DESIGN MANUAL
196
15 951 mm (52.33 ft)
Conductor: 242 mm2( 477 kcmil). ACSR, 24/ 7 mm (ft)
m Half-sag +6%
Major ax/s Minor axis 0
e= 11058’ GW: IO-mm (i-in),
m
Half-sag +6%
Major axis Minor axis
II817 5 909 355 6 264 3 I32
(38.77) (19.39) ( 1.16) (20.55) (10.28)
H.S. Steel !E3 4897 294 5191 2596
Type 3iA Structure 90“ Line Angle 320-m (1050-ftj Span II 278-mm (37-ft) Pole spacing NESC Heavy Loading Conductor full- load tension = 33 362 N (7500 lb) OGW ful I- load tension = 21 418 N (4815 lb) Half-sag ellipses O;to;;e OGW and two conductors
(ft 1 (3Z) (I 6.07) ( 0.96) (17.03) ( 8.52)
0 = 15”42’
Figure 79.-Half-sag 104-D-1092.
ellipses for type 3TA wood-pole
structure,
90’
line angle,
11 278-mm
(37-ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type 3TA Structure 60’ Line angle, OGWin tension 213-m (700-ft) Span 4267-mm(l4-ft) Pole spacing NESC Heavy loading Conductor full-load tension -33 362 N (7500 lb) OGW full-load tension =21 418 N (4815 lb) Full-sag ellipses
LIMITATION
Conductor:
AND GUYING
242mm'
Sag +6 % Major axis Minor axis 8 = I lo 58’ OGW: IO-mm (i-in) %I +6 % Major axis Minor axis 8= 15’42’
\
Figure 80.-Full-sag ellipses for type 3TA wood-pole spacing. 104-D-1093.
197
CHARTS
(477 kcmil)ACSR. 2417 (ft) 5% (17.23) 315 (I .03) 5568 (18.26) 2784 (9.13) H.S. Steel mm Ki) 4353 (14.28) 261 (0.86) 4614 (15.14) 2307 (7.57)
7366 mm (24.17f t)
structure,
60’
line angle, 4267-mm
(14-ft)
pole
198
TRANSMISSION
LINE DESIGN MANUAL
Type 3TA Structure Conductor : 242 mm2 (477 kcmi I) ACSR, 2417 60’ Line angle, OGWin’ tension w 213-m (700- ft) Span 5z3 (17.23) sag 8230-mm (27-ft) Pole spacing +6 % 315 (I .03) NESC Heavy loading Major oxis 5568 (18.26) Conductor full-load tension Minor axis 2784 (9.13) =33 362 N (7500 lb) 0 = I lo 58’ OGW full-load tension OGW : IO-mm (i-in) H. S. Steel =2l 418 N (4815 lb) Cfi) mm Full-sag ellipses 4353 (14.28) Sag Only one OGW and two conductors +6 % 261 (0.86) are shown Major oxis 4614 (15.14) Minor axis 2307 (7.5 7) 8=
; _
14 249 mm (46.75 ft)
_ 7125 mm (23.38 ft)
Figure 81.-Full-sag 104-D-1094.
15O42’
ellipses
7125 mm (23.38 ft)
for type 3TA
wood-pole
structure,
60’
line angle,
8230-mm
(27-ft)
pole spacing.
CHAPTER IV-STRUCTURE LIMITATION AND GUYING CHARTS Type 3TA Structure 60” Line angje,OGWin tension 335-m (Iloo-ft) Span 4267-mm(14-ft) Pole spacing NESC Heavy loading Conductor full-load tension =33 362 N (7500 lb) OGW full-load tension -21 418 N (4815 lb) Half-sag ellipses
Conductor : 242 mm’ (477 kcmil) ACSR, 2417 snm (W 12966 (42.54) sag Half -sag 6483 (21.27) +6 % 389 (1.27) Major axis 6872 (22.54) Minor axis 3436 (I I. 27) 8 = I I“ 58’ OGW: IO-mm (&in) H.S. Steel mm Sag Half -sag +6 % Major axis Minor axis 8= 15”42’
Figure 82.-Half-sag 104-D-1095.
ellipses for type 3TA woo&pole
199
structure,
60 ’ line angle, 4267-mm
(14.ft)
pole spacing.
200
TRANSMISSION
LINE DESIGN
Conductor: 242 mm2 (477 kcmi I) ACSR, 24/7 4< (ft)
Sag Half -sag +6%
Major axis Minor axis 0==11”58 OGW: IO-mm (i-in) Sag
Half-sag +6%
Major axis Minor axis
I2%6 6483 389 6872 3436
(4224) (21.27) ( 1.27) (22.54) (I 1.27)
H.S. Steel mm IO 747 5374 322 5696 2848
(f_t) (35.26) (17.63 ) ( 1.06) (18.69) ( 9.35)
MANUAL
14 249 mm (46.75 f t)
b
Type 3TA Structure 60’ Line angle, OGW in tension 335-m (IIOO-ft) Span 8230-mm (27-ft) Pole spacing NESC Heavy loading Conductor full-load tension = 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb) Half-sag ellipses
0= 15’42’
Only one OGW and two conductors are shown
Figure 83.-Half-sag 104-D-1096.
ellipses for type
3TA
wood-pole
structure,
60’
line angle,
8230-mm
(27.ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type ETA Structure
LIMITATION
full-
Full-sag
Sag +6%
Major axis Minor axis
load tension
= 33 362 N (7500 lb) OGW full- load tension = 21 418 N (4815 lb)
CHARTS
201
Conductor: 242 mm2 (477 kcmil) ACSR. 2417
45’ Line angle, OGW in tension 213-m (700-ft) Span 6096-mm (20-ft) Pole spacing NESC Heavy loading
Conductor
AND GUYING
8= Il”58’ OGW: IO-mm ( i-in)
ellipses
Sag +6%
Major axis Minor axis
5E3 315 5568 2784
(ft) (17.23) ( 1.03) ( 18.26) ( 9.13)
H.S. Steel mm 4353 261 4614 2307
CD) (14.28) ( 0.86) (15.14) ( 7.57)
8 =15’42’
II 278 mm
Figure 84.-Full-sag ellipses for type 3TA spacing. 104-D-1097.
wood-pole
structure,
45’
line angle,
6096&n
(20-ft)
pole
202
TRANSMISSION
Conductor: 242 mm2(477 Sag
Half -sag +6%
Major axis Minor axis 8= 11’58’ OGW: IO-mm (i-in) Sag
Half-sag +6%
Major axis Minor axis 8 = 15’42’
Figure (IL-Half-sag 104-D-1098.
MANUAL
kcmil ) ACSR, 24/7
mm I2 966 6483 389 6872 3436
(ti) (42.54) (21.27 ) ( 1.27) (22.54) (11.27)
~~~
Heavy loading Conductor full-load tension NESC
H.S. Steel
= 33 362 N (7500 lb) OGW full-load tension = 21 418 N (4815 lb)
(W I Om7:7 (35.26) 5374 (17.63) 322 ( 1.06 ) 5696 (18.69) 2848 ( 9.35)
ellipses
LINE DESIGN
for type 3TA
T
E z
ul
Half-sag ellipses Only one OGW and two conductors are shown
B d e J / L
wood-pole
structure,
45 ’ line angle,
6096-mm
(20.ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type 3TA Structure 30° Line angle. OGW in tension 213-m (700-ft) Span 4572- mm (l5-ft) hle spacing NESC Heavy loading Conductor full- load tension =33 362 N (7500 lb) OGW full-load tension =2l 418 N (4815 lb) Full-sag ellipses
LIMITATION
AND GUYING
203
Conductor : 242 mm2 (477 kcmil) ACSR. 24/7 sag +6%
Major axis Minor axis 8- 11’58’ OGW: IO-mm (i-in) Sag +6%
Major axis Minor axis 8= l5O 42’
Figure 86.-Full-sag ellipses for type 3TA spacing. 104-D-1099.
CHARTS
wood-pole
structure,
30°
mm 5253 315 5568 2784
(-ft) (17.23) ( 1.03) (18.26) (9.13)
H.S. Steel 4% 261 4614 2307
(ftl (1428) ( 0.86) (15.14) ( 7.57)
line angle, 4572=mm
(IS-ft)
pole
TRANSMISSION
204
Conductor : 242 mm2 (477 kcmiI)ACSR. Sag
Half -sag +6%
Major axis Minor axis 8 = I I’-’58’ OGW: IO-mm (i-in) Sag
Half -sag + 6 “/o
Major Minor e=
axis axis
mm I2 966 6483 389 6872 3436
LINE DESIGN MANUAL
Type 3TA Structure 30” Line angle, OGW in tension 335-m (Iloo- f t) Span 4572-mm (15 - ft) Pole spacing NESC Heavy loading Conductor ful l-load tension
24/7
(-ft) (42.54) (21.27) (1.27) (22.54) (II ,27)
=33 362 N (7500 lb) OGW full-load tension =2l 418 N (4815 lb)
H.S. Steel IO%7 5374 322 5696 2848
Half -sag ellipses
(ft) (3F26) (17.63) (1.06) (18.69) (9.35) I
15” 42’
Figure 87.-Half-sag 104-D-1100.
ellipses for type 3TA
wood-pole
structure,
30’
line angle,
4572-mm
(15.ft)
pole spacing.
(4x1~) suodS
-P\
CHAPTER
+lMD!
F
IV-STRUCTURE 8
?
:t
\
lp \ \y
\
I’
LIMITATION
1
AND GUYING
I
CHARTS
t f
.
,
4’
\
205
5i
900
\
-60
-70
-60
-50
-40
with 88 965-N units -30
-20
-10
30
40
50
Angle’of InsuloGr Swing ~~egrees) Figure 89.-Example
of a wood-structure
limitation
chart (metric).
104-D-1102.
s e
/
I
/I
I4DG I \/
3&3AB & 3TA OGW Gu 3 A & 3AB Co\nd. Gu
!c
I / I/
\‘. I \‘I .
I
\
/
I
IY.. \
blY\V
/I \.
\ \
I I
/
I I //
\
\
\ / In
n
-10
Angle of"lnsulotor Figure 90.-Example
king
k&s)
of a wood-structure
limitation
chart
(U.S. customary).
104-D-1103.
STRUCTURE
NOTES
DATA Voltage Looding
-wet HS HSB 36
269 305 305
3A8
305
3AC
305 O-213
3TA’
13%
2070
213
213-335 0- 213 213-335 0- 213 213-335
o- I96 196-320 lure 94 1 lension. 1 = tension
?i2E&
‘or (tensm)
OGW
mlmul)
OGW (suspension) Angle guys Conductor OGW
S
ted 12
610
60
610
Itit
426
0
S S
3.6 5.5
S
5.2
I2
I6 I7 I4 I4 I4 I4 I4
Conductor Ultimate strength Maximum design tension 33 670 0 4.3 Overhead ground wire 426 4.3 60 Ultimate strength 670 60 4.3 Mokimum design tension -21 426 30 4.6 I5 Guy wire 670 4.6 30 I5 Conductor cteomnce 426 6.1 45 20 to pole ground wire or 670 45 6.1 20 to centerline of pok 1092 mm(43 in) 426 60 6.2 27 to crossarme69 mm(35 in) 670 60 6.2 27 to guy wire 1397 mm(55 in) 396 90 II.3 37 Lightning protective angle -30 degrees 90 II.3 - 37 Span length limits by holf sag elkpse method for suspemion structures Safety fuctws with l3-mm (i-in) ice, 0.36-kPo (&lb/ft) wind Poles 2.0 Cmssorms 4.0 One line double guy per conductor. Total for structure Insulators would be three line double guys each way (3-LDGEW). suspension 2.5 T mor.= 33 362 N (75oolb). I siflgle guy = 22 800 N (5125lb) tension 3.0 horizontal pull. Conductor 2.0 -.._ ^ . . . one line OouMe guy per OGW. TOtal for Structure would uverneoo grouno wire 2.0 be two line double guys each way (P-LDGEW). Guy wire Offset OGW line guys 30. from COnduCtOr t for e IV line line guys.o angles. 22 800 N (5125 lb) times cos 3Ov-19 745 N (4436lb.3 transverse 2.67 Omit OGW line guys for OGW in MpenSiOn (O*-60. line angles). Omit angle guys for 0*-I* and 60*- 90. line ongles. The oppropriateDnetric or U.S. customary) data from Use 3-150 for conductors on line angles up to 60. to keep the this figure should be placed on the structure structure from leaning into the angle. limitation chart to make o complete chart. For OGW in suspension (r- 60’ line angles) or tension ( lV-60v line angles). mad guying rquimments on suspemion guying chart. 1675
-335 O-213
iFi horl
lMkn 3.6
-0.38
wind
1orrongl chu-t
213-335 O-213
near4 570 610 610
Design wind on structures Rles Ultunote fiber stress Crossarms Ultimate fiber stress Insulators
II5 kv NESC Heavy: l3-mm(+in) ice. O.l9-kPo (rib/ft’) mum plus constant ot -l6Y(O*F) kPa (6 Ib/fte) Gloss 2 western red cedar 36.612 MPo(5600 lb/in’) Douglas fir 51.023 MR (7400 lb/in’) 146 by 254 mm (5{ by IO in). 66 964-N (2oOOo-lb) stwndord suspension units 242 mm’ (477 kcmil). ACSR. 2417. Flicker 76 509 N(l7 200 lb) 362 N (7500 lb) under full load conditions IO-mm (i-m) high strength steel, 7 wire 46 040 ND0 600 lb) 416 N (4615 lb) under full load conditions II-mm (fin) high strength steel, 7 wire
Figure 91.-Additional
S
S or T S or T SorT Sor T T T T T T T T T
data required
4.3 4.3
for the wood-structure
limitation
chart.
104-D-1104.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
209
NOTES The required number of guys noted on this chart should be coordinated with the number of guys required by the standard guying arrangement drawing for the structure type used. The coordinated number of guys should then be shown an the final guying chart. The line shown for b. may be omitted because of the small area defined. The H-frame (x-braced) limit and the I-ADG limit far conductors are about identical, so only one line is shown at f. The line shown far g. may be omitted because it falls outside the structure limit ; use structure limit far guy limit. Use the same maximum sum of adjacent spans limit for Type 3Ac as used for the type HS structures. ASG = Angle single guy ADG = Angle double guy
7\7
- I.x,i/ I/ i Y,/ I 74 /I .
IV
.
I /
I/
i ’ \, ‘i
Figure 92.-Example
guying chart
‘\/
Line
for wood-pole
I
DeflectioFAngle
structures
(metric).
/
/
r\ I \
(degreesr
104-D-1105.
/
/
210
TRANSMISSION
LINE DESIGN MANUAL
NOTES The required number of guys noted on this chart should be coordinated with the number of guys required by the standard guymg arrangement drowmg for the structure type used. The coordinated number of guys should then be shown on the final guying chart. The line shown for b. may be omitted because of the small area defined. The H-frame (x-braced) limit and the I-ADG limit for conductors ore about identical. so only one line is shown ot f. The line shown for g.moy be omitted because it falls outside the structure limit; use structure limit for guy hmit. Use the same maximum sum ofadJacentspanslimlt forType 3AC as used for the Type HS structures. ASG = Angle single guy ADG '- Angle double guy 3000
\
c
\ \
s r x v)
v, 2000
\
\
/ /
/ \
\ \
f!i .z Q
\
/
&
/
z
\ \ 1000 \
/
‘c 0
/
\ \
\.
OO,
5
101
I5
20
h
2
30
50
Line
Figure 93.-Example
guying
chart
for wood-pole
Deflectmn4c!Angle (degrees)
structures
\ \,
\
s
\ \
\
E
.
(U.S. customary).
104-D-1106.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS 211
<
ADDITIONAL 25.
Stresses
H-frame
type
in Wood-Pole
structure
will
DATA
Structures.-There
withstand
when
large
V
is a limit conductors
to the
and long
amount spans
of loading
are used.
This
that
the
limitation
becomes even more pronounced when strong winds and heavy ice loadings are also present. Sample analyses have been made to determine the pole strength in column loading for small deflections. Calculations of stresses have been made for the following H-frame structures: 29-m 29-m 29-m
l l l
The
(95-ft) (95-ft) (95-ft)
type type type
HS 230-kV structure HSB 230-kV structure HSB 230-kV structure
calculations
assume:
a The
in a structure
load
Clockwise ,bending Poles are uniformly
l
a
member moments tapered
is positive
with class 2 Douglas fir poles and one X-brace with class 2 Douglas fir poles and one X-brace with class 1 Douglas fir poles and two X-braces
if it is in tension,
are positive with minimum
ANSI
and negative
(American
if it is in compression
National
Standards
Institute)
dimensions a All The
bolted
effect
joints
of wind
mass was neglected be made in tables and This
by using B-l and
B-4.
on the structures
and
Example
L M
F U
R I I,
was taken
on all structures.
Similar
the methods shown in the B-2, and pole circumferences
Development
figure
Let
are rigid
the
of the above
I.-Stress = load
formula
tables
for
maximum
(95.ft)
= =
bending extreme
= = =
axial reaction in pole horizontal reaction on pole
account for
only any
single double
prime sign indicates prime sign indicates
V, Vg
= =
vertical vertical
H,
=
horizontal
conductor overhead conductor
load ground,
height
and structure
or voltage
class
may
moment
of resistance
type
HS 230-kV
vertical load stress horizontal load stress wire
is shown
on figure
B-4.
B.
moment fiber stress
=
on the HS structure,
structure
following examples. Pole resistance moments are shown for different classes of poles are shown in tables B-3
are in appendix
analysis for a 29-m in member
into
analyses
load
load 213
structure
with
class
2 wood
poles:
TRANSMISSION LINE DESIGN MANUAL
214
Hg
=
horizontal
P,
=
pole
LP
=
SAS =
overhead
resisting
distance sum
ground
wire
load
moment
between
of adjacent
low
points
in adjacent
spans
spans
Metric Figure
95 shows
the
structure
outline
and
-G I
other
data.
-
i L
L
2
x 1
N
---
Q
-
Conductor: 403 mm’, ACSR, 45/7 Diameter - 27 mm 0.38- kPo wind on iced (l3-mm radial) conductor = 20.07 N/m Vertical force with 13-mm radial ice = 27.26 N/m OGW: IO mm, H.S. Steel, ‘I-Wire Diameter = 9 mm 0.38 - kPa wind on iced (l3-mm radial 1 OGW= 13.23 N/m Vertical force with l3-mm radial ice = Ii.79 N/m Position 8 or D
Ground
K or M or P or R or
dim5
Pole Circumference, mm 718
L N Q s
Pr , N.m
801
59 778 82 996
983 1148 1326
244 634 376 534
I53 411
Douglas Fir Working Stress = 51.02 MPa
6.706 m Figure 95.-29-m
Vertical
loads,
type HS 230-kV
structure
with class 2 Douglas
fir poles (one X-brace).
V,
=
(27.26)(LP)
v-
Hc
=
(20.07)(SAS/2)
Hg =
3 V, +
2 Vg, are shared
equally
by two
=
(11.79)(LP) (13.23)(SAS/2)
poles:
UK’= U,’ = jyM’fl= UN’= Up’= UQ’= U,’ = U,’ = 1.5v, + vg
104-D-1107.
CHAPTER For
transverse
H,
loads
and
Hg ,
a plane
Y vhf
)
V-ADDITIONAL
PQ exists.
of inflection
215
DATA The
location
of the
plane
is found
by:
Y, =
‘rR
vertical
force
due
vu = Assuming
244-m
The The The For
+ 2Hg(hg) + moment due to wind on poles pole spacing
0.383(16.464)2
[365.2 6
+(2)(202.2)]
037.60N
force and
in the
overhead
downward
force
and
overhead
force
Pole
3H,(h,)
6.706
uplift
conductor,
is:
(13.416)+2(13.23)
V”= conductor,
to uplift
spans:
3(20.07)
=49
+PrM
= 12.649 - 3.662 = 8.987 m
Yl
The
= (12.649) (153 411) = 3 662 m 376534+ 153411 *
in the
braces bending
windward ground
in the
X-brace
ground is
installed
at 45
moments
are:
pole
is
VU minus
leeward
the
vertical
force
of structure,
pole
is
one-half
the
vertical
force
of structure,
VU plus
wire.
0.5 Vu/sin 0 . O, 0.5 Vu 0.707 = 0.707 Vu.
At K, MK = (1 SH,) (3.048) + H,(5.944) MK = 4.572(20.07)(243.84)+ +
one-half
wire.
0.383(6.096)2
+ moment due to wind on pole
5.944(13.23)(243.84)
[254.8 + (2) (202.2)l 6
At M, MIM = (1 SH, + H,)y,
= 43 114 M,m
+ moment due to wind on pole
MM = t(1.5) (20.07) + 13.231 (243.8) (3.662)
+ 0.383(12.802)2
1312.7 + (2) (202.2)1 = 46 291 Nam 6
TRANSMISSION
216
LINE DESIGN
MANUAL
At R, MR = (1 .5Hc + H,)y, + moment due to wind on pole
MR = [(1.5) (20.07) + 13.231 (243.8) (8.987) + 0.383(25.451)2
Crossarm For
[421.9 + (2) (202.2)1 = 12g 1 l4 Nmrn 6
strength:’ a 79-
by
267-mm
laminated
arm,
the
ultimate
fiber
stress
S =
13.79
MPa:
where :
W, = ultimate vertical load, N b
= horizontal thickness of arm, mm d = vertical thickness of arm, mm L = length of arm to load (lever arm), mm w = 13.79(79) (267)2 = 3861 N or 7722 N for a double arm V 6(3352.8) For
the
given
Allowable
conductor,
distance
the
between
vertical
low
force
points
is 27.26
is 7722/27.26
N/m
=
(with
13-mm
283.272
m.
radial
ice).
U. S. Customary Figure
Vertical
96 shows
loads,
the
3
structure
outline
V,
=
H,
= (1.3754)(SAS/2)
V, +
2
and
other
data.
(1.8682)(LP)
V',
are shared
Vg =
(0.8079)(LP)
Hg = (0.9066)(SAS/2) equally
’ Standard Specifications for Structural Glued Laminated Association), table II, combination E, shows this ultimate (79- by 267-mm) laminated crossarm.
by
two
poles:
Douglas Fir (Coast Region) Timber (West Coast Lumbermen’s fiber stress is 2000 lb/ in2 (13.79 MPa) for a 3-l/8- by lo-l/2-in
CHAPTER
,
V-ADDITIONAL
DATA
Conductor: 795 kcmil. ACSR, 45/7 Diameter = 1.063 in 8-lb/ft’ wind on iced (f-in radial) conductor - I. 3754 Ib/ft Vertical force with t-in radial ice = 1.8682 Ib/ft OGW: B - in H.S. steel, 7-wire Diameter = 0.360 in 8-Ib/ft* wind on iced (t-in radial) OGW = 0.9066 Ib/ft Vertical force with i-in radial ice = 0.8079 Ib/ft
F
-
Ground
h Figure 96.-95.ft
22ft
For
transverse
type HS 230.kV
loads
H,and
Hg,
structure
a plane
Pole Circumference, in
Posit ion 8 or cl K or L
28.26 31.52
44 100 6 I 059
M or N POT0 R or s
38.69
113244
45.20
180421
52.19
277 731
with class 2 Douglas
of inflection
fir poles (one X-brace).
PQexists.
The
location
by: Y (PM
1
(41.5) (113 244) y” =PrR +PrM = 277731+113244
yt The
vertical
force
due
vu =
= 41.5
to the
3H,(h,)
- 12.02
uplift
= 29.48
Pr, Ibeft
Douglas Fir Working stress = 7400 lb/in*
ww-
.
217
= 12 o2 ft
’
ft
is:
+ 2Hg(hg) + moment due to wind on poles pole spacing
104-D-1108.
of the
plane
is found
TRANSMISSION
218 Assuming
800-ft
LINE DESIGN
spans:
3(1.3754) (F)(
44.02) +2(0.9066)(?)(53.52)
vu =
The
uplift
and
overhead The
At
force
in the
braces bending
windward
pole
is
VU minus
one-half
the
weight
of structure,
conductor,
in the
leeward
pole
is VU plus
one-half
the
weight
of structure,
conductor,
wire. X-brace
is 0.5 VU/sin
8 .
installed
at 45 O, 0.5 VU/O.707
moments
are:
=
0.707
V,
K,M, = (1 SH,) (10) + I&( 19.5) + moment due to wind on pole MK = 15 (1.3752) (800) + 19.5 (0.9066) (800) + = 31 799
At
+ 2(7’96)1)
wire.
ground
force For
in the
ground
downward
Pole
[;38
lb
force
overhead The
+ 2 ((8)(54’02)’
22
= 11 026.87
and
MANUAL
8(20)2 [ 10.03 + (2) (7.96)] 72
lb*ft
M,MM = (1 .5HC + H,)y,
+ moment due to wind on pole
MM = [( 1.5) (1.3752) + 0.90661, (800) (12.02) + 8t42)2 [ 12’y2+ (2) (7*96)1 = 34 087
lb*ft
At R, MR = (1 .5Hc + H,)y, + moment due to wind on pole MR = [( 1.5)
(1.3752)
+ 0.90661
(800)
(12.02)
+ 8(83’5)2
[ ‘“‘;;
+ (2)
(7’96)1
= 95 231 lb-ft Crossarm For
strength: a 3-l/8-
by
10-l/2-
in laminated
arm,
the
ultimate
fiber
stress
S =
2000
where :
W,,= ultimate vertical load, lb b = horizontal thickness of arm, in d = vertical thickness of arm, in L = length of arm to load (lever arm), in w = 2000(3.125) (10.5)2 = 870 lb or 1740 lb for a double arm V 6(132)
lb/G.
CHAPTER For
the
Allowable
Example Metric Figure
given
conductor,
distance Z.-Stress
97 shows
the
between analysis
the
vertical low
force
points
for a 29-m
structure
V-ADDITIONAL
outline
(95-ft) and
type other
1
L
X 1 1
-
is 1.8682
HSB data.
219
(with
=
931
230-kV Using
l/2-in
ice).
ft.
structure the
radial
with
nomenclature
class 2 wood from
example
Vertical force with l3-mm ice - 11.79 N/m Pole Position Circumference, mm
N
(Ground
or D or L or N or Q
’ Or ’
718 801 983 II48 1326
radial
Pr, N*m 59 82 I53 244 376
Douglas Fir Working Stress - 51.02 MPa
tan QI =m sin cos
Figure 97.-29-m
6.706 m
L
= 0.7727
u = 0.6114 a = 0.7913 u = 37O41’ type HSB 230-kV
1,
OGW = 13.23 N/m
8 K M P
,
poles:
Conductor: 403 mm,’ ASCR, 45/7 Diameter = 27 mm 0.38 - kPo wind on iced (l3-mm radial) E conductor = 20.07 N/m Vertical force with l3-mm radial ice = 27.26 N/m OGW: IO mm, H.S. Steel, 7-wire Diameter = 9 mm 0.38 - kPa wind on iced (B-mm radial)
C
._-
lb/ft
is 1740/1.8682
F
:
DATA
structure
with class 2 Douglas
fir poles (one X-brace).
104-D-1109.
778 946 41 I 634 534
220
TRANSMISSION
Load
in adjustable
V,
=
H,
= (20.07)(SAS/2)
(27.26)(LP)
braces
load
in nonadjustable
braces
EF:
force
in crossarm
L,’
For
transverse
FC: = 0.5Vc/sin a = 0.8181/,
= L,’
Band
I- -L,,’
C and
= - v,/tan
D and
between
C:
u = - 1.294&
GF:
in crosstie
loads,
1.635V,
‘=-vc/tana=-1.294vc
- LDE
between L,,
Vertical
&/ha=
‘= L,‘=
CC and
L,,’
Load
(11.79)(LP)
Hg = (13.23)(SAS/2)
I-
Compressive
=
in crossarm:
LAB
Load
MANUAL
v-
AC and
LAG
Compression
LINE DESIGN
3
V,
loads
= LAG’
cos
2 Vg, are shared
and
a - L,,’ equally
H, and Hg , a plane
of inflection
cos
a = 0.647 V,
by two
poles:
HJexists.
The
location
by:
x (p,B ) X0 =& +P,, Xl
A plane
of inflection
PQalso
3.048W 778) =82946+59778
= 1 277 m *
= 3.048 - 1.277 = 1.771 m
=x-x,
exists.
Its
Y (PrM 1
y” = PrR + PrM =
location
is found
by:
12.649(153 411) 376534+153411=3*662m
y1 = y - y. = 12.649 - 3.662 = 8.987 m
^
of this
plane
is found
CHAPTER When
position
considered
is known,
wind
points
forces
of zero
on conductors
the structure
may
be separated
into
parts
and
each
part
at J caused
reaction
dividing
by the
moment
‘?J
UJ Taking
and overhead
ground
wires
are resisted
equally
by each
pole
moment.
R, Axial
221
DATA
separately.
Horizontal at the
of zero moment
V-ADDITIONAL
moments
f)
by
arm
-- R;’ = Rp” = Rd”=
horizontal
(pole
wind
- ISH,
force
is found
- Hg by
taking
moments
Hand
about
spacing).
,, _ (3H,) (1.277) + <=Q 6.706
(4.173)
= 0.571H, + 1.244H,
” = - ufy
B
about
in the
pole
above
the
plane
of inflection
(fig.
98),
gives
the
Figure 98.-Free body diagram of pole above plane of inflection to the crosstie (metric example 2).
force&“:
and
“c +“g 1.277(1.5H,
FG 11--
The
outside
CF, carry
braces,
90 percent.
AC and Load
L,
,, -0.9FG” --= cos a
L,
u --L,” -
+H,)+ 2.591
EF, carry on the
inner
2.896H,
10 percent braces
of
1
=-0.739H,
FG” and FHtr CFis:
while
- 1.611H,
the
inside
CG and
0.9(-0.739H, - 1.611H,) = -0.841H, 0.7913
- 1.832H,
braces,
CG and
TRANSMISSION
222 The
load
in the
outer
,, _ -O.l&”
The
load
=AG
-
L,"
= -LA;
in the
crossarm
L,,”
LB, The
load
AG
braces
=
cos a
-O.l(-0.739H,
BC
portions
= l.l65H,
+ 1.448Hg
=A,
- 1.61 lH,)
= O.O934H, + 0.2036H,
0.7913
cot?, a + 0.5&
in the
EFis:
and
= (-J&-G”)
" =-
LINE DESIGN MANUAL
CD is:
and
- (- 0.841H, - 1.832H,) (0.79 13) + OSH,)
=
=CD”
crossarm
AB
portions
” = -(LAG”
and
DE
is:
cos a + H,) = - (O.O934H, + 0.204H,) (0.79 13) - H,
=- l.O74H, - O.l61H,
LAB” = -L&V” The
moment
at
MD
B and D is
given
by:
+Hg)=
“=-xo(1.5Hc
- 1.277(1.5H,
+Hg) =- 1.915H, - 1.277Hg Nom
MB 1)-MD" For
the
portion
MK
of the
pole
“=x1(1.5Hc
between
+Hg)=
the
planes
of inflection,
1.771(1.5Hc+Hg)=2.657Hc
the
moment
at K and
L
is:
+ 1.771H, N*m
ML M-MK" The
area
of the pole
at K and
L
, excluding
the
23.8-mm-diameter
hole
for
mounting
the X-brace
is:
??D2 - 23.80 =;(254.84)2 AK ~4 A, =A,
- 23.8(254.84)
= 5 1 006 - 6065 = 44 941 mm2
CHAPTER The
section
modulus
L
at K and
V-ADDITIONAL
is:
7TD3 23 Joe2 = $ (254.84)3 - y 32 6
‘,=
223
DATA
(254.84)2 = 1 624 810 - 257 609
= 1 367 201 mm3
The
horizontal
reaction
in the
poles
P and
at 1) -
RP The
axial
reaction
in the
poles
3H, + 2Hg ‘Q” = up”
The
force
“=-l.SH,
-RQ
Pand
- Hg
Q is:
(12.139) + 0.571H, + 1.244H, = 6.002Hc + 4.864H,
= - UQ”
K
at
6 . 706
at
Q is:
E i= b,’ L
can
be found
-1.5 IH -
K
by
taking
moments
about
point
M (fig.
99):
H, + Hg F(
E E (d
Figure 99.-Free body diagram (metric example 2).
E a 8 tii.-
FK
planes of inflection
i;;--Fi’ P
=-
I.5 H, + Hg
+Hg)+3.662WHc
” =-
FK ”
of pole between
6.706
FM”
+Hg)
1
=- 2.715H, - 1.813H,
224
TRANSMISSION
The
force
KN
in X-braces
2.715H, + 1.813H, = -3.84OH, - 2.564H, sin 45O >
11 -
- -L,,”
L,,
The
net
area
A,
=y
A,
=A,
section
of the
LMis:
and
LKN” = -
The
pole
(less the
X-brace
- 23.80 =%(312.80)’
modulus
LINE DESIGN MANUAL
at Mand
mounting
hole)
- 23.8(312.80)
at
M
and
Nis:
= 76 846 - 7445 = 69 401 mm2
N is:
(312.80)3 - y
(312.80)2 = 3 004 693 - 388 114
= 2 616 579 mm3
z, =z, Taking
about point
moments
M(fig.
99):
” = -3.662(1.5H, Ml44
+ Hg) = -5.493H,
- 3.662H,
MM 11--MN”’ By superposition, and horizontal by its respective Stress At
in the point
the
loading total poles
values
of the
forces
and
can he combined
for total
load
factors
and
safety
bending loading.
tabulated.
is:
L :
sL=--*--
UL
ML
AL
ZL
where : UL” = UJ” + 0.707L,,”
kd U, = UL’+ULn
moments The
strength
computed of each
separately member
for vertical can he divided
CHAPTER
” = 0.571H,+
UL
U,‘=
V-ADDITIONAL
1.244H, + 0.707(3.84OH,
+ 2.564HJ
1.5v, + vg
U, = U,’ + UL” = 1.5 V, + Vg + 3.286H, + 3.057H, A, = 44 941 mm2 ML” = 2.657H, + 1.771H, N-m Z, = 1367 201 mm3
s,
+ Vb + 3.286H,
=
44 941
+ 3.057H,
mm2
+
At point N: uN sN
MN
=A,%
where : UN UN UN
” = ue”
and
UN
= UN’
+ UN”
‘= 1.5vc + v, ” = 6.002H, + 4.864H,
UN = UN’+ UN ” = 1.5vc + vg + 6.002H, + 4.864H, AN = 69 401 mm2 MN
” = - 5.493H, - 3.662H, N-m
zN = 2 616 579 mm3 1.5 V, + V8 + 6.002H, s,
=
69 401
+ 4.864H, +
225
DATA
= 3.286H, + 3.057H,
226
TRANSMISSION
Adjustable
braces
AG
and
EF: L AG’ = 1.635 Vc
183-m Spans, LP = 366 m
LINE DESIGN MANUAL
LAG" =0.0934Hc+0.2036Hg
L AG=LAG'+L*G"
16 312
343.06+492.92=836
17 148 N
18 987
399.29 + 573.74 = 973
19 960 N
21750
457.38 + 657.22 = 1115
22865 N
I',=9977 N 2 I ;g ; H; = 2421 N 213-m Spans, LP = 426 m V,=ll
613N
V = 5 023N $= 4275N Hg= 2818N 244-m Spans, LP = 488 m
V,=13303N $1 ii;;; H;= 3228N 274-m Spans, LP = 548 m
24424
513.61+
738.05 = 1252
25 676N
27 188
571.70 + 821.53 = 1393
28 581 N
29 862
627.93 + 902.36 = 1530
31 392 N
32625
686.12 + 985.83 = 1672
34297N
35 300
742.34 + 1066.66 = 1809
37 109 N
vc = 14 938 N v'= 6 461 N H,= 5 499N
Hg= 3625N 305-m Spans, LP = 610 m vc = 16 629 N vg= 7192N H,= 6121N
Hg= 4035 N 335-m Spans, LP = 670 m V,=18264N
v-= 7 899N Hc= 6723N Hg= 4432N 366-m Spans, LP = 732 m vc = 19 954 N
vg= 8630N H,= 7 346N f&= 4 842N 396-m Spans, LP = 792 m vc = 21 590 N vg= 9338N
H,= 7948N f$.= 5 239N
CHAPTER Adjustable
braces
AG
and
V-ADDITIONAL
227
DATA
EF-Continued
LaG”= 0.0934
L AG’= 1.635 Vc 427-m Spans, LP = 854 m
38 063
H, +0.2036 Hg
800.44 + 1150.14 = 1951
L &.=L/&+L*d 40 014 N
v, = 23 280 N Vg=10069N ff, = 8 570N Hg = 5 649 N
Nonadiustable
braces
Spans, m
LP, m -
183 213 244 274 305 335 366 396 427
366 426 488 548 610 670 732 792 854
Crosstie
GC and L&
FC : = 0.818 vc, N
Lee”= 0.841
8 9 10 12 13 14 16 17 19
3088.99 3595.27 4118.38 4624.66 5147.76+ 5654.04 6177.99+ 6684.27 7207.37
161 499 882 219 603 940 322 661 043
H, + 1.832 Hg, N
+ + + +
4 435.27 = 7 524 5 162.58 = 8 758 5 913.70 = 10 032 6 641.00 = 11 266 7392.12=12540 + 8 119.42 = 13 773 8 870.54 = 15 049 + 9 597.85 = 16 282 + 10 348.97 = 17 556
LGC = LGc) + LGc) N 15 18 20 23 26 28 31 33 36
685 257 914 485 143 713 371 943 599
GF :
AB
Crossarms
and
DE
w, 366 426 488 548 610 670 732 792 854
= 0.647 Vc,
LP, m
N
183 213 244 274 305 335 366 396 427
366 426 488 548 610 670 732 792 854
6455 7 514 8 607 9 665 10 759 11 817 12 910 13 969 15 062
-
(compressive): L &=
-1.294 N
m
183 213 244 274 305 335 366 396 427
L&
Spans, m
-12 -15 -17 -19 -21 -23 -25 -27 -30
910 027 214 330 518 634 820 937 124
vc,
= -1.074 LABN -3944.80 -4591.35 -5259.38 -5905.93 -6573.95 -7220.50 -7889.60 -8536.15 -9204.18
-
H, - 0.161 Hg, N
389.78 = 453.70 = 519.71 = 583.63 = 649.64 = 713.55 = 779.56.= 843.48 = 909.49 =
-4 -5 -5 -6 -7 -7 -8 -9 -10
335 045 779 490 224 934 669 380 114
-17 -20 -22 -25 - -28 -31 -34 -37 -40
245 072 993 820 742 568 489 317 238
TRANSMISSION
228 BC and
Crossarms spans, m
-
Poles
LP, m
LCD) = -1.294
366 426 488 548 610 670 732 792 854
-12 -15 -17 -19 -21 -23 -25 -27 -30
KN and
X-braces
(at
point
MANUAL
CD (compressive): L ,,“=-l.l65H,-
vc,
N
-
183 213 244 274 305 335 366 396 427
LINE DESIGN
1.448Hg, N
910 027 214 330 518 634 820 937 124
-4279.05 -4980.38 -5705.01-6406.34 -7130.97 -7832.30 -8558.09 -9259.42 -9984.05
- 3505.61 = -7 - 4080.46 = -9 4674.14 = -10 - 5249.00 = -11 - 5842.68 =-12 - 6417.54 = -14 - 7011.22 =-15 - 7586.07 = -16 - 8179.75 = -18
LCD = LCD’ + L&‘, N
785 061 379 655 974 250 569 845 163
-20 -24 -27 -30 -34 -37 -41 -44 -48
695 088 593 985 492 884 389 782 287
LM: Spans, m
LP, m
183 213 244 274 305 335 366 396 421
366 426 488 548 610 670 732 792 854
L&l=
- 3.840 H, - 2.564 Hg, N
-14 104 - 6207=-20311 -164167 225 = -23 641 -18 735 - 8277r-27012 -211129295=-30407 -23505-10346=-33851 -25 816- 11364=-37180 -28209-12415=-40624 -30520-13433=-43953 -32909-14484=-47383
L ):
1.5 Vc t Vg + 3.286H,
+ 3.057H8 +
s, =
44 941 mm*
[
183-m spans, 366-m LP s
= L
+ 4315 + 3.286(3673)
+ 3.057(2421)
44 941
+ 2.657(3673)
+ 1.771(2421)
1367.201
1
(1000) = 11 136 kPa
213-m spans, 426-m LP 613) + 5023 + 3.286(4275)+
3.057(2818)
+ 2.657(4275)
44 941
+ 1.771(2818)
1367.201
1
(1000) = 12 962 kPa
244-m spans, 488-m LP s
L
=
303) + 5754 + 3.286(4897) 44 941
+ 3.057(3228)
+ 2.657(4897)
+ 1.771(3228) 1367.201
1
(1000) = 14 848 kPa
CHAPTER
V-ADDITIONAL
DATA
229
274-m spans, 548-m LP SL =
c
1.5 (14 938) + 6461+ 3.286(5499) 44 941
+ 3.057(3625)
+ 2.657(5499) + 1.771(3625) 1367.201
1
+ 3.057(4035)
+ 2.657(6121) + 1.771(4035) 1367.201
1
+ 3.057(4432)
+ 2.657(6723) + 1.771(4432) 1367.201
1
+ 3.057(4842)
+ 2.657(7346) + 1.771(4842) 1367.201
1
+ 3.057(5239)
+ 2.657(7948) + 1.771(5239) 1367.201
1
(1000) = 16 673 kPa
305-m spans, 610-m LP 629) + 7192 + 3.286(6121) 44 941
s, =
(1000) = 18 559 kPa
335-m spans, 670-m LP 264) + 7899 + 3.286(6723) 44 941
(1000) = 20 385 kPa
366-m spans, 732-m LP s
=
(19 954) + 8630 + 3.286(7346) 44 941
L
(1000) = 22 273 kPa
396-m spans, 792-m LP 590) + 9338 + 3.286(7948) 44 941
(1000) = 24 098 kPa
427-m spans, 854-m LP 280) + 10 069 + 3.286@570) 44 941
Poles
(at point
+ 3.057(5649)
+ 2.657(8570) + 1.771(5649) 1367.201
1
(1000) = 25 984 kPa
N):
Vc + Vg' 6.002Hc+4.864Hg s,=
+
69 401
183-m spans, 366-m LP s,=
1.5(9977)
[
+4315 + 6.002(3673)
+ 4.864(2421)
69 401
+ 5.493(3673)
+ 3.662(2421)
2616.579
1_
(1000) = 11864 kPa
2 13-m spans, 426-m LP 613) + 5023 + 6.002(4275) 69 401
+ 4.864(2818)
+ 5.493(4275)
+ 3.662(2818)
2616.579
1
(1000) = 13 809 kPa
TRANSMISSION
LINE DESIGN MANUAL
244-m spans, 488-m LP s
_
(13 303) + 5754 + 6.002(4897) 69 401
N-
+ 4.864(3228)
+ 5.493(4897) + 3.662(3228) 2616.579
1
+ 4.864(3625)
+ 5.493 (5499) + 3.662(3625) 2616.579
1
(1000) = 15 818 kPa
274-m spans, 548-m LP sN =
1.5 (14 938) + 6461+
6.002(5499) 69 401
[
(1000) = 17 763 kPa
305-m spans, 610-m LP 1.5(16 629) + 7192 + 6.002(6121) 69 401
sN=
+ 4.864(4035)
+ 5.493(6121) + 3.662(4035) 2616.579
1
(1000) = 19 772 kPa
335-m spans, 670-m LP s
= N
264) + 7899 f 6.002(6723) 69 401
+ 4.864(4432)
+ 5.493(6723) + 3.662(4432) 2616.579
+ 4.864(4842)
+ 5.493(7346)
1
(1000) = 21 716 kPa
366-m spans, 732-m LP sN=
(19 954) + 8630 + 6.002(7346)
+ 3.662(4842)
2616.579
69 401
1
(1000) = 23 728 kPa
396-m spans, 792-m LP sN=
590) + 9338 + 6.002(7948)
+ 4.864(5239)
+ 5.493(7948)
+ 3.662(5239)
2616.579
69 401
1
(1000) = 25 673 kPa
427-m spans, 854-m LP sN=
280) + 10 069 + 6.002(8570)
+ 4.864(5649)
+5.493(8570)
69 401
Table 24 shows a summary point distances.
of loads in the structure
+ 3.662(5649) 2616.579
members
1
(1000) = 27 682 kPa
for various span lengths
and low
CHAPTER
V-ADDITIONAL
DATA
231
Table 24.-Summary of loads in structure members for various span lengths and low-point distances (metric example 2) SAS/Z, m 183 Member
213
244
274
305
335
366
396
421
Position LP, m
Adjustable braces, N Nonadjustable braces, N Crosstie, N Crossarm (compressive), N Crossarm (compressive), N X-brace, N Pole, kPa Pole, kPa
AC& CC & GF AB & BC & KN& L N
EF FC DE CD LM
366
426
488
548
610
670
732
792
854
17 148 15 685 6455 17 245 20 695 20 311 11136 11864
19 960 18257 7514 20012 24088 23 641 12962 13809
22 865 20914 8607 22993 27593 27 012 14848 15818
25 676 23485 9665 25820 30985 30407 16673 11763
28 581 26143 10759 28742 34492 33 851 18559 19172
31 392 28713 11817 31568 31884 37 180 20385 21716
34 291 31371 12910 34489 41389 40 624 22213 23728
37 109 33943 13969 37317 44182 43 953 24098 25673
40 014 36599 15062 40238 48281 47 393 25984 27682
U. S. Customary Figure
100 shows the structure
Load in adjustable
outline
and other data.
V, = (1.8682)(LP)
Vg = (0.8079)(LP)
H, = (1.3754)(SAS/2)
Hg = (0.9066)(SAS/2)
braces AG and EF: )-
LAG
Compression
‘= V,/sina=
- LEF
load in crossarm:
L AB’ = L,,’ Load in nonadjustable
force in crossarm
= LF,’ = 0.5 V,/sin a = 0.8 18 V, between )-
LB,
Load in crosstie
= - V, /tan a = - 1.294 V,
braces GC and FC :
L,,’ Compressive
1.635T/,
-LDC
B and C and between D and C :
‘=-V,/tana=-1.294Vc
GF: LGF
’ = LA,’
cos
u - L,,’
cos
a = 0.647Vc
-
232
TRANSMISSION
LINE DESIGN
MANUAL
Conductor: 795 kcmil, ACSR 45/ 7 Diameter = 1.063 in 8-lb/ft’ wind on iced ($-in radial) E conductor = I .3754 lb/f t Vertical force with $-in radial ice - 1.8682 I b/ft OGW: f - in, H.S. Steel, 7-wire Diameter = 0.360 in 8-lb/ft.’ wind on iced (t-in radial) OGW= 0.9066 Ib/ft Vertical force with $-in radial ice = 0.8079 lb/ft’
\
Position ---
8 or K or M or R or CCround w
ton cn = y-
0 L N S
Pole Circumference, in 28.26 3 1.52
Pr, lb* ft 44 100 61 059
38.69 52.19
II3 244 277 731
Douglas Fir Working stress = 7400 lb/in 2
0.7727
sin cy = 0.6114 cos a = 0.7913 a - 37041’ Figure
Vertical
lOO.-95-ft
loads,
3
type HSB 230-kV
V,
and
2
Vg,
structure
are shared
with class 2 Douglas
equally
by
two
fir poles (one X-brace).
poles:
104-D-1110.
CHAPTER For
transverse
H,
loads
Hg,
and
V-ADDITIONAL
a plane
of inflection
DATA
HJexists.
233 The
location
of this
plane
is found
by:
A plane
PQ also
of inflection
exists.
Its
Y c&f
location
is found
by:
>
41.5 (113 244) y” =PrR +PrM= 277731+113244=12’02ft = 41.5 - 12.02 = 29.48 ft
Yl =y-Yo When
position
of zero moment
is known,
considered separately. Horizontal wind forces on conductors at the points of zero moment.
the
and
structure
overhead
R, N -- R;’ = &.,” = Axial dividing
reaction by the
at J caused moment arm
by horizontal (pole spacing).
may ground
Rd’=-
wind
force
be separated wires
lSH,
into
are resisted
parts equally
and each
part
by each
pole
- Hg
is found
by
taking
moments
about
Hand
u ,, _ (3H,) (4.19) + 2Hg (13.69) = O.S71H, + 1.244H, J22
Taking
moments
about
B in
the
pole
above
the
plane
4.19 (1.5H, + Hg) + 9.5H, 8.5
&“Z-
of inflection
1
(fig.
= -0.739H,
lOl),
gives
the
force
Fen:
- 1.61 lHg
FF v -F,” The Ce
outside
carry
AG
braces,
90 percent.
L,,” L,
Load
and
EF,
on the
carry
10 percent
inner
braces
CG
Fc” and FH” and CF is:
of
while
the
inside
0.9FG u 0.9 (- 0.739H, - 1.611HJ = z= = - 0.841H, - 1.832H, 0.7913 11 -
- - L,,”
braces,
CG and
234
TRANSMISSION
LINE DESIGN MANUAL
Figure lOl.-Free body diagram of pole above plane of inflection crosstie (U.S. customary example 2).
The
load
in the
outer
braces
,, _ -O.l(F,“) LAG
u --
L,, The
load
cos a
in the
AG =
EFis:
and
-O.l(-0.739H, - 1.61 lHg) = O.O934H, + 0.2036H, 0.7913
- LAG”
crossarm
portions
BC
and
CD
is:
L,c” = (-LCG”) cosa + OSH, = - (-0.841H, = l.l65H,
load
- 1.832H,) (0.7913) + OSH,
+ 1.448H,
11 -
- - L,”
L,, The
and to the
in the
LAB
crossarm
portions
AB
and
DE
is:
" = - (LAG" cos a + H,) = - (O.O934H, + 0.204H,)
(0.7913) - H,
= - l.O74H, - O.l61H, LAB” = - L,,” The
moment
at
B
and
D
is given
by:
MD” = - x0 (lSH,
+ Hg> = -6.285H,
- 4.19H, lb*ft
MB 1)--MD” For
the
portion
of pole
between
the
planes
of inflection,
MK ” =x1 (1.5H, +Hg) = 5.81 (1.5H, +i$)
ML” = MK”
the
moment
at
K and
L is:
= 8.715H, + 5.81J$ lb*ft
CHAPTER The area of the pole at Kand
V-ADDITIONAL
235
DATA
L , excluding the 15/16-inch-diameter
hole for mounting
the X-brace
is:
- 2 (10.03)=
$I=;(10.03)'
79.06 - 9.40 = 69.66 in2
A, =A, The section modulus z,
=g
at K and L is:
_ '~~y+-)03)3
- 0.15625(10.03)2
= 99.06 - 15.72 = 83.34 in3
z, = z, The horizontal
reaction
in the poles at Pand RP
The axial reaction
Qis:
f’ -RQ ” = - 1.5H, - Hg
in the poles at P and Q is:
u
Q
(39.83) + 0571H,.
+ 1.244H, = 6.002Hc + 4.864H,
‘P” = - ‘Q ” The force at K can he found by taking
Q”=-
+H,)+
moments
about point
12.02(1.5H, 22
+Hg)
M (fig. 102):
1
= -2.715H,
- 1.813H,
Figure lOZ.-Free body diagram of pole between planes of inflection customary example 2).
(U.S.
TRANSMISSION
236 The
force
KN
in X-braces
L,”
LM
and
LINE DESIGN MANUAL
is:
2.715H, + 1.813H,
=-
sin 45’
_
- -3.84OH, - 2.564H,
>
L KN f! -- - LLM" The
net
area
of the
pole,
less the
AM =‘$
The
section
modulus
at
M
X-brace
- ED
and
mounting
hole,
at
Mand
N is:
= 119.12 - 11.54= 107.58 in2
N is:
183.36 - 23.70 = 159.66 in3
Taking
moments
about
MM
point
M(fig.
102):
“=-
12.02(1.5H,
+Hg)=-
18.11H, - 12.02H,
MM )f -MN" By superposition, and horizontal by its respective Stress At
in the point
the
loading total poles
values
of the forces
and
can be combined
for total
load
factors
and
safety
bending loading.
tabulated.
is:
L:
SL=-f-
moments The
UL
ML
AL
ZL
strength
computed
separately
of each member
for
vertical
can be divided
CHAPTER
V-ADDITIONAL
DATA
where : ” and U, = U,’ + UL”
UL” = UJ” -I- 0.707L,,
uL” = 0.571H, + 1.244H, + 0.707(3.84OH, U,’ = l.W,
+ 2.564H,) = 3.286H, + 3.057H,
+ vg
U, = U,’ + UL” = 1.5 V, + Vg + 3.286H, I- 3.057H, A, = 69.66 in’
ML)) = 8.715H, + 5.81H, lbeft Z, = 83.34 in3 s, =
1.5& + V’ + 3.286H, f 3.057H, + 69.66 in2
N:
At point
where : u “=u N
“adu Q
N
=u
N
‘+u
UN
’ = 1.5v, + vg
UN
” = 6.002H, + 4.864H,
N
”
UN = UN’ + UN’) = 1.5 V, + V, + 6.002H, + 4.864H,
AN = 107.58 in2 MN
” = - 18.1 lH, - 12.02H,
ZN = 159.66 in3 s, =
1.5 V, + Vg + 6.002H, + 4.864H, 18.11H, + 12.02H, + 107.58 in2 159.66 in3
237
238
TRANSMISSION
Adjustable
braces
AG
and
MANUAL
EF: L ,&
600-ft Spans, LP = 1200 ft
LINE DESIGN
= 1.635 Vc
L /&
= O.O934H, + 0.2036Hg
LAG = LllGl + LAG”
3666
77.06 + 110.76 = 188
3854 lb
4277
89.94 + 129.29 = 219
4496 lb
4887
102.74 + 147.61 = 250
5137 lb
5499
115.63 + 166.14 = 282
5781 lb
6110
128.43 + 184.67 = 313
6423 lb
6720
141.31+
202.99 = 344
7064 lb
7331
154.11 + 221.52 = 376
7707 lb
7941
167.00 + 240.04 = 407
8348 lb
8553
179.89 + 258.37 = 438
8991 lb
Vc = 2242 lb V = 9701b I$=
Hg=
825 lb 544Ib
700-ft spans, LP = 1400 ft
Vc = 2616 lb v =1131lb g= 9631b Hg= 6351b 800-ft Spans, LP = 1600 ft
Vc = 2989 Ib V = 12931b 4
= 1100 lb 725 lb
Hg=
900-ft spans, LP = 1800 ft
V, = 3363 lb V = 1454 lb z$ = 1238 lb 8161b
Hg=
lOOO-ft Spans, LP = 2000 ft
Vc = 3737 lb V =16161b 4
= 1375 lb
Hg = 907 lb llOO-ft
Spans, LP = 2200 ft
V, = 4110 lb V = 1777 lb t(
= 1513 lb
Hg=
997 lb
1200-ft Spans, LP = 2400 ft
Vc = 4484 lb 2:
:;g;
H; = 1088 lb 1300-ft Spans, LP = 2600 ft
Vc = 4857 lb V = 2101 lb g
= 1788 lb
Hg = 1179 lb 1400-ft Spans, LP = 2800 ft
Vc = 5231 lb V =2262 lb 4
= 1926 lb
Hg = 1269 lb
CHAPTER Nonadiustable spans, ft 600 700 800 900 1000 1100 1200 1300 1400
Crosstie
V-ADDITIONAL
DATA
239
braces GC and FC : LP, ft
L Gc’= 0.818V,,
1200 1400 1600 1800 2000 2200 2400 2600 2800
1834 2140 2445 2751 3057 3362 3668 3973 4279
-
LGC)) = 0.84111, + 1.832Hg, lb
lb
694+ 996=1690 810+1163=1973 925 + 1328 = 2253 1041+1495=2536 1156+1661=2817 1272+1826=3098 1388+1993=3381 1504+2160=3664 1620 + 2324 = 3944
3524 4113 4698 5287 5874 6460 7049 7637 8223
GF : LP,
Spans, ft 600 700 800 900 1000 1100 1200 1300 1400
Crossarm
=1bo.647 Vc,
1200 1400 1600 1800 2000 2200 2400 2600 2800
1451 1693 1934 2176 2418 2659 2901 3142 3384
AB and DE (compressive):
Spans, ft 600 700 800 900 1000 1100 1200 1300 1400
Crossarm
LG;
ft
LP, ft
L&’
= -1.294yc lb
1200 1400 1600 1800 2000 2200 2400 2600 2800
-2901 -3385 -3868 -4352 -4836 -5318 -5802 -6285 -6769
L/ ’
= -l.O74H, lb
- ‘0.161Hg,
-886 - 88 = -974 -1034-102=-1136 -1181-117 =-1298 -1330-131=-1461 -1477146=-1623 -1625-161=-1786 -1772 - 175 = -1947 -1920-190=-2110 -2069-204=-2273
LAB=kg’ +LAB: -3875 -4521 -5166 -5813 -6459 -7104 -7749 -8395 -9042
BC and CD (compressive):
spans, ft
LP,
600 700 800 900 1000 1100 1200 1300 1400
12DO 1400 1600 1800 2000 2200 2400 2600 2800
ft
L a’
= -1.294v,, lb -2901 -3385 -3868 -4352 -4836 -5318 -5802 -6285 -6769
L cD’ = -l.l65H,
- 1.448H& lb
-961788 = -1122 - 919 = -1282 - 1050 = -1442 - 1182 = -1602-1313=-2915 -1763-1444=-3207 -1922-1575=-3497 -2083-1707=-3790 -2244-1838=-4082
-1749 -2041 -2332 -2624
LCD = LC”’ ~4 -5 -6 -6 -7 -8 -9 -10 -10
+ LCD:
650 426 200 976 751 525 299 075 851
240
TRANSMISSION
KN
X-braces
LP,
L &’
ft
600 700 800 900 1000 1100 1200 1300 1400
(at point
MANUAL
LM :
and
Spans, ft
Poles
LINE DESIGN
= -3.84OH,
- 2.564Hg,
lb
1200 1400 1600 1800 2000 2200 2400 2600 2800
-3168-1395= -3698-1628= -4224-1859= -4754-2092= -5280 - 2326 = -5810-2556= -6336-2790= -6866-3023= -7396-3254=-10650
-4563 -5326 -6083 -6846 -7 606 -8366 -9126 -9889
L):
1.5 Vc + Vg + 3.286H,
+ 3.057Hg
SL =
+ ~‘715;;;‘8’Hf)(!?)
= lb/i,,2
69.66
600-ft spans, 1200-ft s, =
LP
1.5 (2242) + 970 + 3.286(825)
+ 3.057 (544)
+
= 1615 lb/in2
69.66
700-ft spans, 1400-ft LP 1.5(2616)+ s, =
1131 + 3.286(963)
+ 3.057(635)
69.66
+
= 1886 lb/in2
800-ft spans, 1600-ft LP SL =
1.5 (2989) + 1293 + 3.286(1100)
+ 3.057 (725). +
69.66
8.715(1100)
+
83.34
900-ft spans, 1800-ft LP SL = 1.5(3363)
+ 1454 + 3.286(1238)
+ 3.057(816)
69.66
+
= 2424 lb/in2
lOOO-ft spans, 2000-ft LP s, =
1.5(3737)
+ 1616 + 3.286(1375)
+ 3.057(907)
69.66
+
= 2693 lb/in2
1 lOO-ft spans, 2200-ft LP s
= 1.5(4110) L
+ 1777 + 3.286(1513) 69.66
+ 3.057(997)+
8.715(1513)
+5.81(997) 83.34
12 >( -i >
= 2961 lb/i2
CHAPTER
V-ADDITIONAL
DATA
241
1200-ft spans, 2400-ft LP SL =
1.5(4484)
+ 1939 + 3.286(1650)
+ 3.057(1088)
+
= 3231 lb/in2
69.66
1300-ft spans, 2600-ft LP sL=
1.5 (4857) + 2101 + 3.286(1788)
+ 3.057(1179)
+,
69.66
8.715
+ 12 (1788) 5.81(1179) )( > = 3501 lb/i2 83.34 r
1400-ft spans, 2800-ft LP 1.5(5231)
+ 2262 + 3.286(1926)
s, =
Poles
(at
+ 3.057(1269)+
69.66 point
1.5 V;'
N):
Vg+ 6.002H, +4.865Hg
sN=
+
107.58
= lb/in’
600-ft spans, 1200-ft LP sN=
1.5(2242)+
970 + 6.002(825)+4.865(544)+
18.11(825) + 12.02(544) 12 = 1725 lb/in2 159.66 x -i- >
107.58
700-ft spans, 1400-ft LP t$,,=
1.5(2616)
+ 1131 + 6.002(963)
+ 4.865(635)
+
= 2013 lb/in2
107.58
800-ft spans, 1600-ft LP
s,= 1.5(2989)
+ 1293 + 6.002(1100) 107.58
+ 4.865(725)+
18.11(1100)
+ 12.02(725) 12 159.66 x T 1 = 2300 lb/in2
900-ft spans, 1800-ft LP s,=
1.5(3363)
+ 1454 + 6.002(1238)
+ 4.865 (816)
107.58
+
18.11(1238)
+ 12.02(816)
159.66
12 x> 1
= 2589 lb/i2
lOOO-ft spans, 2000-ft LP sN=
1.5(3737)+
1616 + 6.002(1375)+4.865(907)+, 107.58
= 2876 lb/in’
242
TRANSMISSION
LINE DESIGN MANUAL
1 lOO-ft spans, 2200-ft LP s,=
1.5(4110)+
1200-ft
spans, lS(4484)
sN=
1777 + 6.002(1513)+4.865(997) 107.58
18.11(1513)
+
+ 12.02(997) 12 159.66 >( 1 > = 3163 lb/in*
2400-ft LP + 1939 + 6.002(1650)
+ 4.865(1088)+
= 345 1 lb/in*
107.58
1300-ft spans, 2600-ft LP 1.5 (4857) + 2101+ s,=
6.002 (1788) + 4.865 (1179)
+
18.11(1788)
107.58
+ 12 12.02(1179) >( > = 3739 lb/in* 159.66 r
1400-ft spans, 2800-ft LP lS(5231)
sN=
Table point
+ 2262 + 6.002(1926)
18.11(1926)
+ 4.865(1269)+
107.58
25 shows
a summary
+ 12.02(1269) 159.66
of loads
in the
structure
members
12 )( r >
for
various
= 4027 lb/in*
span
lengths
and
low
distances.
Table 25.~Summary of loads in structure members for various spans lengths and low-point distances (U.S. customary example 2) SAS/Z, ft Member
Position
600
700
800
900
1000
1100
1200
1300
1400
2 400
2 600
2 800
8 348 7 637 3 142 8 395 10 075 9 889 3 501 3 739
8 991 8 223 3 384 9 042 10 851 10 650 3 770 4 027
LP, ft 1200 AG&EF GC&FC GF AB&DE BC&CD KN&LM L N
Adjustable braces, lb Nonadjustable braces, lb Crosstie, lb Crossann (compressive), lb Crossarm (compressive), lb X-brace, lb Pole, lb/in* Pole, lb/in*
Example and
double
3.-Stress
analysis
1400
3854 3524 1451 3 875 4650 4 563 1 615 1725
4496 4113 1693 4521 5426 5 326 1 886 2013
for a 29-m
(95-ft)
1600
1800
5137 4 698 1934 5166 6 200 6083 2 154 2300
type
5781 5 287 2 176 5813 6 976 6 846 2424 2589
HSB
2000
2 200
6423 5 874 2418 6459 7751 7 606 2 693 2876
7064 6 460 2659 7 104 8525 8 366 2961 3 163
230-kV
structure
--
7 707 7 049 2 901 7 749 9 299 9 126 3 231 3451
with
class
1 wood
poles
X-brace:
Metric Figure
103
shows
the
structure
outline
and
other
data.
Using
the
nomenclature
from
example
1,
CHAPTER V-ADDITIONAL
DATA
243
Conductor:
403 mm : ACSR, 45/7 27 mm 0.38-kPo wind on iced (l3-mm radial) conductor - 20.07 N/m Vertical force with l3-mm radial ice 27.26 N/m OGW: IO mm, H.S. Steel, 7-wire Diometer - 9 mm 0.38- kPo wind on iced (l3-mm radial) OGW= 13.23 N/m Vertical force with l3-mm radial ice II.79 N/m DiOmeter:
I---
1 1
Pole Circumference, mm
Position 8 or K or M or R or
Pr, N*m
771 857 1247 1401
13 L N s
74 208 IO1 754 312 751 444 314
Douglas Fir Working Stress - 51.02 MPa 6,706m tan
- +j&
= 0.7727
sin a - 0.6114 cos a - 0.7913 a - 37O41’ Figure
103.-29-m
type HSB 230.kV
V,
=
H, = Load
in adjustable
braces
structure
(27.26)(LP)
vg
(20.07)(SAS/2)
Hg =
AC
and
load
=
fir poles (two X-braces).
(11.79)(LP) (13.23)(SAS/2)
EF:
LAG’ = L,’ Compression
with class 1 Douglas
= V,/sin a = 1.635Vc
in crossarm: )-
LAB
- L,’
= - Vc/tan a = - 1.294Vc
104-D-1 111.
244
TRANSMISSION
Load
in nonadjustable
braces
Compressive
force
in crossarm
between
I- -
L, loads U,’ For
3 V, and = U,’
transverse
B and
C and
‘=-V,/tana
‘=L,,
D
between
and
C :
=-1.294V,
GF:
in crosstie
Vertical
= 0.5 V,/sin a = 0.8 18 V,
= L,’
LBC Load
FC:
CC and
L,,’
LINE DESIGN MANUAL
COS
2 Vg are shared
= UK’
loads
L,,’
H,
= u,
equally
’ = U,’
Hg , a
and
a - L,,’
= UN’
plane
a = 0.647Y,
COS
by two = Up’
of inflection
poles:
= Ue’
= u,
’ = Us’
HJexists.
The
= 1.5 v,
location
+ vg
of this
plane
parts
and
is found
by:
X(PrB)
3.048(74 208) +P,B = 101 754+74208
xo =& Xl
A plane
exists.
Its
location
Y C&M 1
considered
moment
Axial
444314+312751
is known,
points
wind
forces
of zero
’
the structure
may
be separated
into
each
part
on conductors
reaction by
the
and
overhead
ground
wires
are resisted
equally
by each
pole
moment: RI;’
dividing
= 2 266 m
separately.
Horizontal at the
of zero
by:
= 5.486 - 2.266 = 3.220 m
Yl =y-Yo position
is found
5.486(312 751)
y” =PpR +PrM=
When
’
= 3.048 - 1.285 = 1.763 m
=x-x,
PQ also
of inflection
= 1 285 m
at Jcaused moment
‘J UJ”
arm
by (pole
CR, f) --R/z horizontal
Rd’=-1.5H,-H, wind
force
is found
by
,, _ (3H,) (1.285) + Cur,> (4.181) = 0.575H, 6.706 = q/
taking
moments
spacing):
+ 1.247H,
about
Hand
CHAPTER Taking
moments
B
about
in the
pole
V-ADDITIONAL
above
the
plane
DATA
245
of inflection
(fig.
104)
gives
force
&“:
Figure 104.-Free body diagram of pole above plane of inflection and to the crosstie (metric example 3).
-F/ -1.5
Hc + Hg 1.285(1.5H,
FG8)---
+I$)+
1
2.896H,
_
- -0.744H,
2.591
[
- 1.614H,
FF” = FG” The
outside
( fi’ . carry
carry
on the
FGRand FH” CF is:
10 percent
of
braces
CG and
inner
cos a
L,, load
EF,
and
Load
,, _ 0.9FG" 0.9(-0.744H, --=
L,
The
AG
braces,
90 percent.
- 1.614H,)
0.7913
while
the
inside
braces,
=-0.846H, - 1.836H,
--L,"
8) -
in the
outer
L*(y=
braces
-O.lF&’ cos a
AG
=
and
EFis:
-O.l(-0.744H, - 1.614H,) = O.O94OH,+0.204H, 0.7913
L,, e --L,," The
load
in the
crossarm
LBc)) =(-L,") = l.l69H, LBC
II -
--
LCD”
portions
BC
and
CD
is:
cos.a + O.SH, =-(-0.846H, + 1.453H,
- 1.836H,)(O.7913)+
O.SH,
CG and
246 The
load
in the
crossarm
TRANSMISSION
LINE DESIGN MANUAL
portions
DE
AB
and
is:
LAB " = -(LAG ” cos a + H,) = - (O.O94H, + 0.204H,)
L, The
(0.7913) -H, = -
- O.l61H,
l.O74H,
rt -- -L& moment
B
at
D is
and
given
by:
MD “=-xo(l.5Hc
+Hg) = - 1.928H, - 1.285H, N-m
MB” = MD” For
the
portion
of pole
between
the
MK ” =x1 (lSH,
planes
of inflection,
the
moment
at
K
and
L
is:
+ Hg) = 2.645H, + 1.763H, Nom
ML” = MK” The
area
of the
pole
at
K
and
L,
excluding
the
23.8.mm-diameter
hole
for mounting
the
X-brace
is:
AK=x-
nD2
23.80 =a (272.8)2 - 23.8(272.8) = 58 449 - 6493 = 51 956 mm2
A, =A, The
section
zK=x-
modulus
at
K
and
L
is:
71D3 23.8D2 = 5 (272.8)3 (j
_ 23’8(;72’8)2
= 1993 118- 295 198= 1 697920mm3
z, =z, The
horizontal
reaction
in the
poles
RP The
axial
reaction
‘Q” = UP
in the
poles
at P and
Q is:
11 -
-RQ ” = - 1 .5Hc - Hg
at P and
Q is:
3H, + 2Hg (17.898) + 0.575H, + 1.247H, = 8.581H, + 6.585H, 6.706
” = - UQ"
The
force
at K can
he found
CHAPTER
V-ADDITIONAL
by
moments
+H
taking
247
DATA
about
point
M (fig.
105):
9
F lgure 105.-Free body diagram of pole between (metric example 3).
+H
Q
15.632(1.5H,
" =-
FK
planes of inflection
+I$)+
2.266(1.5&
+Hg)
1
= - 4.003H, - 2.669H,
6.706
FK u --FM” Since the
the
division
installation,
VN,
WM
and
of load
assume
L,,
net
area
A,=4A, The
all load
X-braces
KUand
is taken
by
LTand
one
X-braces
set of braces.
The
VNand force
WMdepends in X-braces
of the
nD2
4.003H, + 2.669Hg
Of-
--
sin 45O
M- - L,,
pole
(less
M- L,”
the
X-brace
= -5.662H,
- 3.775H,
)
= -L,,”
mounting
hole)
23.80 = 2 (396.80)2 - 23.8(396.80)
at
Mand
N is:
= 123 661- 9444 = 114 217 mm2
=A,
section
modulus
nD3 ZM=F-
at
Mand
N is:
23.8D2 6 = & (396.80)3 - ‘9
= 5 509 039 mm3
z,
upon
KU, LT,
is:
=KU
The
between
that
= z,
(396.80)2 = 6 133 592 -- 624 553
TRANSMISSION
248 Taking
about point
moments
u MA4
the
By superposition, and horizontal
loading
by its respective Stress At
in the point
total poles
M(fig.
-
- - 2.266
values
LINE DESIGN
105): (1
.5Hc + HE) = - 3.399H, - 2.266H,
of the forces
and
can be combined
for total
load
factors
and
safety
MANUAL
bending
moments
loading.
The
strength
computed of each
separately member
for
tabulated.
is:
L :
SL =-
UL
+-
AL
ML ZL
where : UL” = UJ” + 0.707LL,” UL
and UL = UL’ + UL”
” = 0.575H, + 1.247H, + 0.707 (5.662H, + 3.775H,) = 4.578H, + 3.9 16Hg
U,’ = 1.5v, + vg u, = U,’ + UL” = 1.5V, + Vg + 4.578H, + 3.916H, A, =51 956mm’ ML” = 2.645H, + 1.763H, N-m
Z, = 1 697 920 mm3 s
lSV, L
At
point
+ Vg +4.578H, 51 956 mm*
+ 3.916H,
+
N:
‘N SN=ANfZN
MN
vertical
can be divided
CHAPTER
V-ADDITIONAL
DATA
249
where : UN” = Ue” and UN = UN’ + UN” U,‘=
1.5vc + vg
UN” = 8.58lH,
+ 6.585H,
UN = UN) + UN)) = 1.5 v, + vg + 8.581H, + 6.585H, A,
= 114217mm2
MN
” = - 3.399H, - 2.266H,
zN = 5 509 039
+ vg + 8.581H, + 6.585H, 114 217 mm2
s, = Adiustable
mm3
braces
AG
and
1000,,,,,, + 3.399Hc+2.266Hg 5 509039 mm3 ) ()](lOO~zmm’)
El;: L AG’ = 1.635V,
183-m Spans, LP = 366 m
+ 1000 = kPa
LA/'
O.O94OH,+0.204H,
LAG=LAG'+LAGA
16 312
345.26+493.88= 839
17 151 N
18 987
401.85 + 574.87 = 977
19 964 N
21 750
460.32 + 658.51=
22869N
24424
516.91+
V,=9977N V =4315N 4~3673~
iTI"=
N
213-m Spans, LP = 426 m
V,= 11 613N V = 5023N d= 4275N Hg= 2818N 244-m Spans, LP = 488 m
1119
V,=13303N 2: ii;;; H;= 3228N 274-m Spans, LP = 548 m
Vc= 14938N v-
6461 N
f(= 5499N Hg= 3625N
739.50 = 1256
-
25680N
250
TRANSMISSION
Adjustable
braces
AG and
LINE DESIGN
MANUAL
IS-Continued
LAG’ = 1.635 Vc 305-m Spans, LP = 610 m
LAG))= O.O94OH,+0.204Hg
LAG=L*Gt+L*G)
27 188
575.37 + 823.14 = 1399
28587N
29862
631.96 + 904.13 = 1536
31 398 N
32625
690.52 + 987.77 = 1678
34 303N
35 300
747.11+
1068.76 = 1816
37 116 N
38063
805.58+ 1152.40 = 1958
40 021 N
V,=16629N V = 7 192 N $= 6121N
Hg= 4035N 335-m Spans, LP = 670 m
V,=18264N V = 7899N l(= 6723N I+= 4432N 366-m Spans, LP = 732 m F= = 1gg54N 8630N l(= 7346N Hg= 4842N 396-m Spans, LP = 792 m
V,=21590N V = 9338N ig= 7948N fig= 5239N 427-m Spans, LP = 854 m
V,=23280N V = 10 069 N f(= 8570N Hg= 5649N
Nonadjustable
spans, m 183 213
244 274 305 335 366 396 427
braces
LP, m
366 426 488 548 610
670 732 792 854
GC and
FC :
Lee' = O.S18V,, N
N
8 161 9 10 12 13 14 16 17 19
L Gc"= 0.846H,+ 1.836Hg,
499 882 219 603 940 322 661 043
3107 + 4 445 = 7 552 3617+ 5174= 8791 4128+ 5927=10055 4652+ 6656=11308 5178+ 7408=12586 5688+ 8137=13825 6215 + 8 890 = 15 105 6724+ 9619=16343 7250+10372=17622
LGC = L&
+ L&
15 713 18 290
20937 23572 26 189 28765 31427
34004 36665
CHAPTER Crosstie
V-ADDITIONAL
DATA
251
GF : spans, m
LP, m -
183 213
366 426 488 548 610 670 732 192 854
244 214 305 335 366 396 421
Crossarm
183 213
LP, m
-
11 12 13 15
817 910 969 062
L m” = -l.O74H,
- O.l61H& N
-12 910
-3945-390=
-4335
-15 021
-4591-454=
-5045
-17 214
-5259-520= -5906-584= -6574-650= -1221-114= -1890-780= -8536-843=
-5 719 -6490 -7224 -7935 -8670 -9319
-19 330 -21518 -23634 -25 820 -21937 -30124
-9204-909=-10113
LAB = LAB’ + LAB” -. N ’ -17245 -20012 -22993 -25 820 -28142 -31569 -34490 -31316 -40231
BC and CD (compressive):
spans, m
LP, m -
183
366 426 488 548 610 610 132 792 854
244 274 305 335 366 396 427
LAB’ = -1.294 vc, N
366 426 488 548 610 670 732 192 854
244 214 305 335 366 396 421
213
6455 1514 8607 9665 10 159
AB and DE (compressive):
spans, m
Crossarm
L ,;=0.64lv,, N
L&
= -1.294 vc, N -12 910 -15 027
L &=
-l.l69H,
- 1.453Hg, N
-4294-3518= -4991-40951
-1812 -9092
-5725-4690=-10415 -6428-5267=-11695 -7155-5863=-13018 -7859-6440=-14299 -8587-7035=-15622 -9291-7612=-16903 -10018-8208=-18226
-17 214
-19 330 -21518 -23634 -25 820 -21937 -30124
X-brace: spans, m 183 213 244 214 305 335 366 396 427
m,
L,;=-5.662#-
366 426 488 548 610 670 132 192 854
-207969139=-29935 -24205-10638=-34843 -27721-12186=-39913 -31 135 - 13 684 = -44 819 -34 651- 15 232 = -49 889 -38066-16731=-54191 -41593-18219=-59812
3.175Hg,
-m
-45002-19171=-64779 -48523-21325=-69848
LCD = ‘SD’
+ LCD:
-20722 -24 119 -21629 -31025 -34536 -37933 -41442 -44 840 -48350
252
TRANSMISSION
Poles
(at
point
L):
1.5 Vc + Vg + 4.578H, s,
LINE DESIGN MANUAL
+ 3.916Hg
=
+
51956
mm2
183-m spans, 366-m LP s
=
1.5(9977)
+ 4315 + 4.578(3673)
L
+ 3.916(2421)+
2.645(3673)
+ 1.763(2421) (1000) = 9113 kPa
1697.92
51 956
I
2 13-m spans, 426-m LP SL =
C
1.5(11 613) + 5023 + 4.578(4275) 51956
+ 3.916(2818)
+ 2.645(4275)
1
+ 1.763(2818)
(1000) = 10 607 kPa
1697.92
244-m spans, 488-m LP s
= L
1.5 (13 303) + 5754 + 4.578(4897) 51956
+ 3.916(3228)
+ 2.645 (4897) + 1.763 (3228) 1697.92
1
(1000) = 12 150 kPa
274-m spans, 548-m LP s
= L
1.5(14 938) + 6461 + 4.578(5499) 51956
+ 3.916(3625)+2.645(5499)
+ 1.763(3625) 1697.92
1
(1000) = 13 644 kPa
305-m spans, 610-m LP s
L
4.578(6121)
=
+ 3.916(4035)
51956
+ 2.645(6121)
+ 1.763(4035) 1697.92
1
(1000) = 15 187 kPa
335-m spans, 670-m LP s = 1.5(18 264) + 7899 + 4.578(6723) L
+ 3.916(4432)
51956
+ 2.645 (6723) + 1.763(4432) 1697.92
1
+ 2.645 (7346) + 1.763(4842) 1697.92
1
(1000) = 16 681 kPa
366-m spans, 732-m LP (19 954) + 8630 + 4.578(7346) 51956
+ 3.916(4842)
(1000) = 18 225 kPa
396-m spans, 792-m LP SL =
1.5 (21 590) + 9338 + 4.578(7948) 51’956
+ 3.916(5239)
+ 2.645(7948) + 1.763(5239) 1697.92
1
(1000) = 19 719 kPa
CHAPTER
427-m spans, 854-m
l’oles .-
(at point
253
+ 3.916(5649)
+ 2.645 (8570) + 1.763(5649) 1697.92
1
(1000) = 21262
kPa
N):
I .5 V, + Vg + 8.581H,
+ 6.585Hg
&TN=
3.399H, + 2.266Hg +
[
DATA
LP
(23 280) + 10 069 + 4.578(8570) 51956
s, =
V-ADDITIONAL
114 217 nun2
5 509 039 mm3
1ooo mm )(~](looo~~m2)
+lOOO= kPa
183-m spans, 366-m LP S,=
1.5(9977)
+ 4315 + 8.581(3673) 114 217
+ 6.585(2421)
+ 3.399(3673) + 2.266(2421) 5509.039
1
(1000) = 3846 kPa
213-m spans, 426-m LP S,=
1.5(11 613) + 5023 + 8.581(4275) 114 217
+ 6.585(2818)
+ 3.399(4275) + 2.266(2818) 5509.039
1
(1000) = 4477 kPa
244-m spans, 488-m LP sN=
1.5 (13 303) + 5754 + 8.581(4897)
+ 6.585(3228)
+ 3.399(4897)
+ 2.266(3228)
1
(1000) = 5128 kPa
114 217
5509.039
274-m spans, 548-m LP shl=
1.5(14 938) + 6461 + 8.581(5499) 114 217
+ 6.585(3625)
+ 3.399(5499) + 2.266(3625) 5509.039
1
(1000) = 5759 kPa
305-m spans, 610-m LP slv=
1.5 (16 629) + 7192 + 8.581(6121) 114 217
+ 6.585 (4035) + 3.399(6121)
+ 2.266(4035)
1
(1000) = 6410 kPa
5509.039
335-m spans, 670-m LP s,=
1.5(18 264) + 7899 + 8.581(6723) 114 217
+ 3.399(6723) + 2.266(4432) 5509.039
1
+ 6.585 (4842) + 3.399(7346) + 2.266(4842) 5509.039
1
+ 6.585(4432)
(iOO0) = 7040 kPa
366-m spans, 732-m LP SN’
1.5(19 954) + 8630 + 8.581(7346) 114 217
(1000) = 7693 kPa
254
TRANSMISSION
LINE DESIGN
MANUAL
396-m spans, 792-m LP (21 590) + 9338 + 8.581(7948)
S,=
+ 6.585 (5239) + 3.399(7948) + 2.266(5239) 5509.039
114 217
1
(1000) = 8323 kPa
427-m spans, 854-m LP 1.5 (23 280) + 10 069 + 8.581(8570) 114 217
SN’
Table point
26 shows
a summary
of loads
+ 6.585 (5649) + 3.399(8570) + 2.266(5649) 5509.039
in the
structure
members
for
various
1
(1000) = 8974 kPa
span
lengths
and
low
distances.
26.~Summary of loads in structure members for various span lengths and low-point distances (metric example 3)
Table
SAS/Z, m 213
183 Member
244
274
335
366
396
427
670
732
792
854
34303 31427 12910 34 490 41442 59872 18225 7 693
37116 34004 13969 37 316 44840 64779 19719 8 323
40021 36665 15062 40 237 48350 69848 21262 8 974
LP, m
Position
Adjustable braces, N Nonadjustable braces, N Crosstie, N Crossarm (compressive), N Crossarm (compressive), N X-brace, N Pole, kPa Pole, kPa
305
AG&EF GC&FC %&DE BC & CD KN&LM L N
366
426
488
548
610
17151 15 713 6 455 17 245 20722 29935 9113 3 846
19964 18 290
22869 20937 8 607 22 993 27629 39913 12150 5 128
25680 23572 9665 25 820 31025 44819 13644 5 759
28587 26 189 10759 28 742 34536 49889 15187 6 410
2: iii 24119 34843 10607 4 477
31398 28765 11817 31569 37933 54797 16681 7040
U. S. Customary Figure
Load
106
shows
in adjustable
the
structure
outline
and
other
data.
V,
=
(1.8682)(LP)
Vg =
(0.8079)(LP)
H,
= (1.3754)(SAS/2)
Hg =
(0.9066)(SAS/2)
braces
AG and
EF:
LAG’ = LEF) = &/sin a = 1.635Vc Compression
load
in crossarm:
tLAB
Load
in nonadjustable
braces
- LDE
CC and
L,.’
= L,’
‘=-
K/tana=-1.294V,
FC: = 0.5 V, /sin a = 0.8 18 V,
CHAPTER
L
V-ADDITIONAL
Conductor: 759 kcmii, ACSR, 45/7 Diameter - 1.063 in 8- lb/f t ’ wind on iced (+-in radial) conductor - I.3754 lb/ft Vertical force with i-in radial ice - 1.8682 Ib/ft oGw:i-in, H.S. steel, 7-wire Diameter - 0.360 in 8-Ib/ft’ wind on iced (i-in radial) OGW- 0.9066 lb/f t Vertical force with t-in radial ice = 0.8079 Ib/ft
I
x X 1
255
DATA
I
Position
Pole Circumference, in
8 or D KWL
30.37 33.74
M or
49.08
N
ROTS
Pr, Ib=ft 54 75 230 328
55. I5
730 047 976 655
Douglas Fir Working stress = 7400 lb/in* .
tan
a - v
sin
a -
cos
a = 0.7913
- 0.7727
37O 41’
106.-95-ft
Compressive
I
0.6114
a Figure
22 ft
type HSB 230.kV
structure
force in crossarm between LBC
Load in crosstie
‘=L,,
with class 1 Douglas
B and ‘=-
fir poles (two X-braces).
C and between
V,/tana=-1.294
D and C :
V,
GF: LcF) = LAG’ 00s a - L,,’
cos a = 0.647 V,
104-D-1112.
256
TRANSMISSION
Vertical
loads
3
&I ’ = For
transverse
V, u;
and
2
Vg are
= UK’ = u,’
H,
loads
shared
equally
by
= (j-,’
= UN’
= (J,’
Hg,
and
LINE DESIGN
a plane
two
MANUAL
poles:
= Ue’
of inflection
= U,’
HJexists.
= Us’ = 1.5 v,
The
location
+ vg
of this
plane
parts
and
is found
by:
x (prB1
lO(54
xo =PrK +-Prs = Xl =x-x() A plane
of inflection
PQ also
75 047
= lo-
exists.
Its
When
position
considered Horizontal at the
of zero
separately. wind forces
points
of zero
- Y,
moment
Axial
is known,
on conductors
J
reaction
at
by the
moment
moments
= 4*22
ft
655
- 7.43
by:
976) + 230
976
= 10.57
ft
the structure
and overhead
may ground
= 7’43
ft
be separated wires
into
are resisted
equally
each
part
by each
pole
moment:
caused arm
about
B
&“=m
Rd’=R$=-l.SH,-
by horizontal (pole
u ,, = (3H,) J
Taking
328
= 18.0
Rt;‘=R;=
dividing
is found 18(230
Y(PrM)
=Y
+ 54 730
4.22=5.78ft
location
y” =PrR +PrM =
Yl
730)
(4.22)
+ (*H,)
is found
(13.77)
22
pole
(1
above
the
plane
.5Hc + Hg) + 9.5H, 8.5
FF u -- FG”
force
by
taking
moments
about
107)
force
Hand
spacing):
in the
4.22
wind
Hg
I
= 0.575H, +
1.252H,
of inflection
(fig.
= - 0.745H,
- 1.614H,
gives
Fc”:
CHAPTER
-0 4 1
-In a6
The
CF,
HC+Hg AG and E&
braces,
Load
90 percent.
LCG
load
in the
load
LB,”
L, The
load
braces,
of
F,
CG and
” and
CF,
FH”
while
the
inside
braces,
is:
- 1.6 14H,)
= - 0.847H,
- 1.836H,
0.7913
- LCG”
outer
-
in the
10 percent
0.9 (- 0.745H,
=
AG
braces
,, _- 0. I&”
The
inner
cos a
LAG
L,y,
carry
on the
0.9FG”
rr=-
L CF 1)-The
257
Figure 107.-Free body diagram of pole above plane of inflection and to the crosstie (U.S. customary example 3).
Fe”
-I.5
outside
carry
DATA
;n#? 9 -
-z dI
V-ADDITIONAL
-0.1
COSa
and
EF
is:
(-0.745H,
=
-
1.614H,) = 0.0941Hc
0.7913
0.204H,
+
M -
- - LAG”
crossarm
BC
portions
and
CD
is:
= (-a&“)
cos a + 0.5H, = - (- 0.847H, -
= l.l7OH,
+ 1.453H,
1.836H,)
(0.79
13) +
0.204H,)
(0.7913)-
OSH,
rt -
- - L,”
in the
LAB
crossarm
portions
” =- (LAG” = - l.O74H,
LABu --
L,,”
cos
AB
and
a + H,) = -
- O.l61H,
DE
is:
(O.O941H,
+
H,
CG and
TRANSMISSION
258 The
moment
B
at
D
and
is given
For
the
portion
of pole
MANUAL
by:
MD ” = - x,, (1 SH, MB”
LINE DESIGN
+ I$)
= -
6.33H,
- 4.22H,
lb* ft
= MD”
hetween
the
planes
of inflection,
the
moment
at
K and
“=x,(1.5Hc+Hg)=5.78(1.5Hc+Hg)=8.67Hc+5.78Hg
MK
L
is:
lb.0
ML” = MK” The
area of the pole
L
at Kand
, excluding
the 15/16-inch-diameter
hole
for mounting
the X-brace
is:
.rrD2
A,=TAL The
‘K
section
=
=t (10.74)2 - E (10.74) = 90.59 - 10.07 = 80.52 in2
=A, modulus
TD3 -32
15 ED
at
K
15D2/16 6
L
and
is:
= &(10.74)3
- 0.15625(10.74)2
= 121.62-
18.02 = 103.6in3
z, =z, The
horizontal
reaction
in the
poles
P
at
and
Q is:
Rp” = Rp” = - 1.5Hc - Hg The
axial
reaction
in the
poles
u*” = (34;2fJ
at
P
and
Q is:
g ) (58.71) + 0.575H, + 1.252Hg = 8.581H, + 6.589Hg
‘P” = - ‘Q ” The
force
at
FK
FK
K
can be found
”=-
by
51.28(1.5H,
” = - F,”
taking
moments
about
+Hg> + 7.43(1.5H, 22
point
+Hg)
M (fig.
1
108):
= -4.003H,
- 2.669H,
CHAPTER
V-ADDITIONAL
DATA
259
Figure 108.-Free body diagram of pole between (U.S. customary example 3).
Since
the division
installation,
assume
of load that
between
all load
X-braces
is taken
KUand
LTand
by one set of braces.
X-braces The
planes of inflection
VNand
force
WMdepends
in X-braces
KU,
upon
LT, VN,
WMis:
and
4.003H, + 2.669H,
II LKU -L KU ” = The
net
area
of the
pole
The
section
>
n -- - LWM”
X-brace
= $(1~62)~
= - 5.662H, - 3.775H,
mounting
- E
(15.62)
hole)
at
Mand
= 191.62
-
N is:
14.64
= 176.88
= 373.48
- 38.21
in2
=A, modulus
nD3
at Mand
15D2
/16
6
‘hf=x-
Taking
w -L, -
LLT
(less the
ED
A,
sin 4S”
(
moments
about
N is:
- 0.15625(15.62)2
= 0.098(15.62)3
point
MM“=-
M (fig. 7.43(1.5H,
MM n --MN”
108):
+Hg)=-
ll.l4H,
-
7.43H,
-
= 335.36
in3
260
TRANSMISSION
By superposition, and horizontal by
its respective Stress At
the
loading total
in the
poles
values
of the
LINE DESIGN MANUAL
forces
and
can be combined
for total
load
factors
and
safety
bending
moments
loading.
The
strength
computed of each
separately member
for vertic:tl can be divicl~~ll
tabulated.
is:
L:
point
s, =- UL &-ML AL
ZL
where : UL
)) = UJ” + 0.707L,,"
and UL = UL' + UL"
UL" = O.S75H, + 1.252H, +0.707(5.662H,
+3.775H,)=
U,’ = l.SV, + vg U, = UL'+ UL" = 1.5Vc + Vg + 4.578H, + 3.921H, A, = 80.52 in2 ML"
=
8.67H,
+
5.78H,
lb*ft
ZL = 103.60 in3 s, =
= Poles
(at
(%;LuL”
+(~)(ni)
1.5Vc + VK + 4.578H, + 3.921H,
+
80.52 in2 point
N):
‘N SN=ANfZN
where : UN
“= UQ" and UN = UN'+ UN"
MN
4.578H, + 3.921H,
CHAPTER
V-ADDITIONAL
DATA
261
UN’ = 1.5vc + vg UN” = 8.581H, + 6.589H, UN = UN’ + UNf’ = 1.5 V, + Vg + 8.58 lH, + 6.589H, AN = 176.98 in2 MN
“=-1l.l4H,
- 7.43H,
ZN = 335.36 in3 s, = Adjustable
1.5V, + V’ + 8.581H, + 6.589H,
braces
176.98 in2 AC
and
600-ft Spans, LP = 1200 ft
+
11.14Hc + 7.43Hg 335.36 in3
EF: L AG' = 1.635V,
LAGn = O.O94OH,+ 0.204Hg
LAG = LAG' + LA/
3666
77.63 + 110.98 = 189
3855 lb
4277
90.62 + 129.54= 220
4497 lb
4881
103.51+
147.90 = 251
5138 lb
5499
116.50 + 166.46 = 283
5782 lb
6110
129.39 + 185.03 = 315
6425 lb
Vc = 2242 lb V = 9701b f( = 825 lb Hg=
544Ib
700-ft Spans, LP = 1400 ft
V, = 2616 lb V = 11311b g=
9631b
Hg= 635 lb 800-ft Spans, LP = 1600 ft
V, = 2989 lb V = 12931b l$=llOOlb
Hg = 725 lb 900-ft Spans, LP = 1800 ft
Vc = 3363 lb v I(
= 1454 lb = 1238 lb Hg= 8161b lOOO-ft Spans, LP = 2000 ft
vc = 3737 lb v = 1616 lb g=1375lb Hg= 907 lb
262
TRANSMISSION
LINE DESIGN
MANUAL
Adjustable braces AG and E&Continued ’ + LAG”
L AG’ = 1.635 V,
LAG” = O.O94OH, + 0.204Hg
6720
142.37 + 203.39 = 346
7066 lb
7331
155.27 + 221.95 = 377
7708 lb
1300-ft Spans, LP = 2600 ft
7924
168.25 + 240.43 = 409
8351 lb
1400-ft Spans, LP = 2800 ft
8553
181.20 + 258.92 = 440
8993 lb
1100-ft Spans, LP = 2200 ft
LAG
= LAG
Vc = 4110 lb v = 1777lb 4=15131b Hg = 997 lb 1200-ft Spans, LP = 2400 ft
Vc = 4484 lb 2
: ;g
;
H; = 1088 lb
Vc = 5231 lb V = 2262 lb I$ = 1926 lb
Hg = 1269 lb
Nonadiustable Spa% ft 600 700 800 900 1000 1100 1200 1300 1400
Crosstie
braces
GC and
FC :
LP, ft
L Gc’= 0.818V,, lb
lb
1200 1400 1600 1800 2000 2200 2400 2600 2800
1834 2140 2445 2751 3057 3362 3668 3973 4279
699 + 999 = 1698 816+ 1165 = 1981 932+1332=2264 1049 + 1498 = 2547 1165 + 1665 = 2830 1282+1831=3113 1398+1998=3396 1515+2164=3679 1631+2330=3961
-
L cc” = 0.847H,
+ 1.836Hg,
GF : Spans, ft
LP,
600 700 800 900 1000 1100 1200 1300 1400
1200 1400 1600 1800 2000 2200 2400 2600 2800
ft
L ‘$
= 0.647 Vc, lb 1451 1693 1934 2176 2418 2659 2901 3142 3384
3532 4121 4709 5298 5887 6475 7064 7652 8240
CHAPTER
AB
Crossarm
and
DE
LP, ft
L AB’ = -1.294Vc, lb
600 700 800 900 1000 1100 1200 1300 1400
1200 1400 1600 1800 2000 2200 2400 2600 2800
-2901 -3385 -3868 -4352 -4836 -5318 -5802 -6285 -6769
BC
and
263
DATA
(compressive):
Spans, ft
Crossarm
V-ADDITIONAL
L ABn = -l.O74H, lb
- 0.161Hg,
-88688= -974 -1034-102=-1136 -1181-117=-1298 -1330-131=-1461 -1477-146=-1623 -1625-161=-1786 -1772-175=-1947 -1920-190=-2110 -2069-204=-2273
-3875 -4521 -5166 -5813 -6459 -7104 -7749 -8395 -9042
CD (compressive):
spans, ft
LP, ft
L cD’= -1.294Vc, lb
600 700 800 900 1000 1100 1200 1300 1400
1200 1400 1600 1800 2000 2200 2400 2600 2800
-2901 -3385 -3868 -4352 -4836 -5318 -5802 -6285 -6769
L &=
-l.l7OH, lb
- 1.453H
8.
-966791=-1757 -1127922=-2049 -1287-1054=-2341 -1448 - 1186 = -2634 -1609-1317=-2926 -1770-1449=-3219 -1931-1581=-3512 -2092-1713=-3805 -2253-1844=-4097
L CD = “7” -4 -5 -6 -6 -7 -8 -9 -10 -10
+ bD: 658 434 209 986 762 537 314 090 866
X-brace:
Poles
(at
point
spans, ft
LP,
600 700 800 900 1000 1100 1200 1300 1400
1200 1400 1600 1800 2000 2200 2400 2600 2800
ft
L KG = -5.662Hc lb
- 3.775Hg,
-4673-2054= -6727 -5451-2396= -7847 -6230-2738= -8968 -7009-3080=-10089 -7788-3422=-11210 -8566-3765=-12331 -9345-41Oi=-13452 -10124-4449=-14573 -10903-4791=-15694
L):
1.5 V, + Vg + 4.578Hc + 3.921Hg SL = 80.52 ina
600-ft spans, 1200-ft LP s, =
1.5(2242)
+ 970 + 4.578(825) 80.52
+ 3.921(544)
+
= 1320 lb/in2
264
TRANSMISSION
LINE DESIGN
MANUAL
700-ft spans, 1400-ft LP 1.5(2616)+
S,=
1131+4.578(963)
+ 3.921(635)
+ = 1541 lb/in2
8052
800-ft spans, 1600-ft LP SL =
1.5(2989)+
1293+4.578(1100)
+ 3.921(725)
+
8.67(1100)
80.52
+ 5.78(725) 103.60
12 >(
T
= 1760 lb/in2 >
900-ft spans, 1800-ft LP SL =
1.5(3363)
+ 1454 + 4.578(1238)
+ 3.921(816)
+
8.67(1238)
80.52
+ 5.78(816)
103.60
12 I( -7 >
= 1980 lb/in2
lOOO-ft spans, 2000-ft LP s, =
1.5(3737)
+ 1616 + 4.578(1375)
+ 3.921(907)
80.52
8.67(1375)
+ (
+ 5.78(907)
103.60
12 )O T
= 2200 lb/in2
1 lOO-ft spans, 2200-ft LP s, =
1.5(4110)+
1777 +4.578(1513)+
3.921(997)
+
8.67(1513)+
80.52
5.78(997)
103.60
12 )O r
= 2420 lb/i2
1200-ft spans, 2400-ft LP 1.5 (4484) + 1939 + 4.578(1650) s,
=
+ 3.921(1088)
8.67 (1650) + 5.78(1088) +
80.52
103.60
-12 JO 1
= 2640 lb/in2
1300-ft spans, 2600-ft LP s
= 1.5(4857)+
2101 +4.578(1788)
L
+ 3.921(1179)
+
= 2861 lb/in2
80.52
1400-ft spans, 2800-ft LP SL =
Poles
(at
1.5 (5231) + 2262 + 4.578(1926) 80.52
point
N):
l.5Vc+Hg+8.581Hc+6.589Hg s,=
176.98 in2
+ 3.921(1269)
+
8.67(1926)
+ 5.78(1269) 12 103.60 )O T
= 3081 lb/in2
CHAPTER
V-ADDITIONAL
DATA
265
600-ft spans, 1200-ft LP S,=
1.50242)
+ 970 + 8.581(825)
+ 6.589(544)
+ 11.14(825)
176.98
+ 7.43(544)
335.36
(
)O
12 = 558 lb/in2 1
700-ft spans, 1400-ft LP S,-=
1.5(2616)+
1131+ 8.581(963)
+ 6.589(635)
+
176.98
800-ft spans, 1600-ft LP S,=
1.5(2989)
+ 1293 + 8.581(1100)
+ 6.589(725)
+
176.98
11.14(1100) (
+ 7.43(725)
335.36
12 )O
r
= 744 lb/in2
900-ft spans, 1800-ft LP S,=
1.5(3363)+
1454 +8.581(1238)
+ 6.589(816)+
176.98
lOOO-ft spans, 2000-ft LP s,=
1.5(3737)
+ 1616 + 8.581(1375)
+ 6.589(907)
+
176.98
1 loo-ft spans, 2200-ft LP s,=
1.5(4110)+
1777+8.581(1513)+6.589(997)+ (
176.98
11.14(1513)+7.43(997) 335.36
12 )O - = 1023 lb/in2 1
1200-ft spans, 2400-ft LP s,=
1.5 (4484) + 1939 + 8.581(1650)
+ 6.589(1088)
+
176.98
1300-ft spans, 2600-ft LP SN’
1.5(4857)
+ 2101+ 8.581(1788)+
6.589(1179)
176.98
)O
1400-ft spans, 2800-ft LP sN=
1.5 (5231) + 2262 + 8.581(1926) 176.98
+ 6.589(1269)
+
12 = 1209 lb/in’ 1
TRANSMISSION
266 Table point
27 shows
a summary
of loads
LINE DESIGN MANUAL
in the
structure
members
for
various
span
lengths
and
low
distances.
Table 27.-Summary
of loads in structure members for various span lengths and low-point distances (U.S. customary example 3) SAS/Z, ft 600
Member
700
800
900
1000
1100
1200
1 300
1400
2000
2200
2400
2600
2800
6425 5881 2418 6459 7762 11 210 2200 930
7066 6475 2659 7104 8537 12 331 2420 1023
7708 7064 2 901 7749 9 314 13452 2640 1116
8351 7 652 3142 8 395 10090 14573 2861 1209
8993 8240 3 384 9042 10 866 15 694 3081 1 302
Position LP, ft
Adjustable braces, lb Nonadjustable braces, lb Crosstie, lb Crossarm (compressive), lb Crossarm (compressive), lb X-brace, lb Pole, lb/in2 Pole, lb/in2
26.
Structure
location, wood-pole
Data
(a)
l
necessary
1800
3855 3532 1451 3875 4658 6727 1320 558
4497 4121 1693 4521 5434 7841 1541 651
5138 5782 4709 5298 1934 2176 5166 5813 6209 6986 8968 10089 1760 1980 744 837
spatting is a term line structures and bracing
Required.-The
following
to the
structure
plan-profile
limitation
scales and
for
guying
for
the For
and
line: These the
process
equipment
drawings
are
required
are prepared
specified
conductor,
and
a conductor
charts,
by the
field
span,
and
ruling height
table
Process ofSpotting.-Figure
Code
109 shows
or the
the details
plan and profile drawing with the sag template spotting structures. Figure 110 also shows the
applicable
State
for the various
or
clearances over ground, railroads, highways, communication circuits, and These clearances should be calculated in accordance with the latest edition Safety
at the structure
for
Reqnired conductor other power lines.
Electrical
ground
the
the conductor
National
above
of determining
on the plan and profile drawings. is also determined for each location.
template showing types and heights.
of the
height
used
data
of structures on a transmission drawings of the transmission line.
Plan
l
(b)
and Equipment the locations and profile
forces. A sag template made loading conditions. The
1600
type of transmission the amount of guying
l
l
1400
Structure
Spotting.-
height, and structures,
determining
AG&EF GCLFC GF AB & DE BC & CD KU< L N
1200
or municipal
of the sag template,
and figure
structure
code. 110 is a typical
superimposed showing the method of using it for method of using the 15,5 OC (60 “F) curve of the
template to determine the proper conductor and structure heights. The curve labeled “15.5 ‘C (60 o F) Final” represents the conductor position. The lower two curves, marked “8.2-m (27-ft) are exactly the same curves as the 15.5 ’ C final curve, but clearance” and “8.8-m (29-ft) clearance” displaced vertically the corresponding the
8.8-m
clearance
8.2 and 8.8 m, respectively. Therefore, point on the 8,2-m clearance curve curve.
Referring
again
to figure
110,
any point on the final curve is 8.2 m above or 8.8 m above the corresponding point on the
8.8-m
clearance
curve
just
touches
the
CHAPTER ground the
line
8.8-m
of the
profile.
clearance
line
Therefore, touches
the
the
V-ADDITIONAL conductor
ground
DATA
267
is 8.8 m above
the
ground
at the
point
where
line.
Ccnductw: 201 md (387.5 kcmil), ACM, 2W7 Ruling Span =213.4 m (700 f t ) Max. Tension = 32 472 N (7300 lb), 45% Ult. NESC Heavy Loading: IS-mm (IL&in) ice with a 0.38-kPa (8-lb& wind at -18 OC (0 OFI
cut out to prrmit drawing curve on the plan-profile
/
the I sheetr.
TYPE
low point span.
Figure
The
process
109.-Typical
of spotting
usually
2083 + 50 on figure 110, and the position described above. in U.S. customary span to the right is selected, either the various
types
sag template
(plastic)
progresses
the spans to the Please note that
used for spotting
from left the
left
to right
structures.
on the
of it are spotted station numbering
ter of ES the in each
21.3 IO.3 15.2 12.2
Ill m Ill Ill
HS
@Ott)@Oft& QofO{ &oft)-
GROUND -
104-D-1113.
profile.
The
structure
at Sta.
before the template is placed in referred to in this section are
units. After the required position of the conductor has been determined for the of the structure at Sta. 2083+50, the location and height of the next structure by scaling or by use of a pole template. For convenience, the pole template for of structures
is marked
on the margin
of the template.
For
the span
under
discussion,
the structure location selected is at Sta. 2090 +20, the structure is a type HS with 18.3-m (60-ft) poles, and the span length is 204 m (670 ft). This information should be recorded on the drawing. The template is then moved to the right and the next span and structure located by repeating the process.
TRANSMISSION Although
the process
the profile
of spotting
for several
spans
or railroad
crossings,
powerline
which
require
will
special
structures
ahead
because
ahead
there
to one of the fixed
is a choice
to determine that
of structure
of equal
heights.
The
points at each of the as much as possible. transmission
(c)
may
example,
and
high
it is best to examine angle
or low
of the structure.
points,
points Such
and
work
backward.
be desirable
desirable ruling
profile
to make
layout
In the
highway
in the profile
conditions
more
is to have
span,
a smooth
is a sign
of good
sections
often
than
one
of line layout
spans of nearly
conductor design.
The
where
in order
uniform
profile,
and
length
structures
conductor
structures should lie in a smooth flowing curve to equalize This is called grading the line and is an important part
UplifLUplift, in a rough profile
occur
refer
to the three
conductor sag is drawn conductor will contract 60 o F), the conductor template. supports
conductor
crossings,
as line
attachment
structure of the
loading design
of a
line.
Determining
Uplift
the
left to right, such
and it is usually a matter of determining the most these fixed locations. Sometimes it is desirable to
it may most
less than
smooth
line
locations
The
from
be conditions
the location
structure, between
locations,
to or slightly
progresses
may
and affect
structure
the best arrangement.
are equal
usually there
or communication
consideration
fix the location of a transmission line desirable arrangement of the structures move
LINE DESIGN MANUAL
Therefore, of alternate
or upstrain, where the
structures
is a condition which conductor supports
at Sta. 2105+35,2112+40,
should be avoided, if possible. are at different elevations. For and
2121+70
on figure
for a temperature of 15.5 ‘C (60 ’ F), but as the temperature and the sag will decrease. When the temperature reaches minus assumes the position indicated by the minus 51 ‘C cold curve
minus 51 OC curve on the template between the conductor 2 105 + 35 and 2121+70), it can be determined whether the support of the intermediate structure (Sta. 2112+40) is above or below the cold curve. 21.3-m (70-ft) structure at Sta. 2112 +40, the conductor support is approximately on the
conductor For the
by placing structures
lll.‘The
decreases, the 51 ‘C (minus shown on the
the (Sta.
cold curve. Suppose, however, that the 21.3-m (70-ft) structure is replaced by a 19.8-m (65-ft) structure. The conductor support would then be below the cold curve and the conductor would exert an upward pull on the structure-this upward pull is the uplift or upstrain. Uplift at a structure will cause the conductor to pull the insulators cause the conductor to pull away from crossarm. Uplift may possibly be avoided
up into the crossarm, and with pin-type insulators it might the insulator and possibly pull the insulator pin out of the by adjusting structure locations on the plan-profile drawing,
to take advantage of terrain, by using a higher structure at the point of uplift or by attaching weights to the conductor. If these methods fail, then the conductor must be dead-ended. Structures should not be located at uplift points if it can be avoided because the only function of such a structure is to hold the conductors conductors during hot
Insulator
(d)
that
tends
from
to swing
the
swinging force
of the
to the distance of the
adjacent
wind
pressure
Sideswing.-Suspension
pressure. Conductor to limit the sideswing on the conductor
against weather.
clearance in order an insulator
spans
suspended adjacent
to the
insulator between
fall
of the
The
rapidly
away
vertical
conductor
low
the
to sideswing by insulator insulation.
is equal force
structure,
supported the
caused
length
of the
by horizontal
wind
sideswing, so it is necessary The horizontal wind pressure
tends
by the
of the adjacent
a short
to one-half
that
supported
of conductor points
from
to support
are subject is reduced conductor
The
length
conductor
sometimes
on a structure
spans.
force
string. the
insulators
to the structure to maintain proper
in the two is equal
and
the
to keep insulator
by the spans. conductor
total string
insulator
On rough low
wind
pressure
the insulator
terrain points,
plus string
string one-half is equal
where
each
as indicated
CHAPTER by the
conductor
template,
the low points from
is still
swinging.
the
Too
structure.
distance
To
the
checked
the point
much
insulator
falls
sideswing
might
(e) the
instructions
allowable,
low-point
distance,
of structure
could
for
extra
proper
angle
be used In
for
by a broken
conductor
policy and
of 230
kV
and
When strainextra clearance on both
sides
adjacent
span
or pin-type for broken is not
the
to a special
maximum
the
be added
the
this
If
value
area,
Structure at the
value
chart.
be used,
outside
the
heights
bottom
lengths
and
structure
heights
used
for
pole
lengths
over.
strength
structure
of 13.7
Class
1 poles
of the
are given
is needed
limitation
number
of guys,
as shown
major
highways,
major
for
any
chart, on the
m (45 ft) are used
in
or less; for extra
reason.
should guying
be used charts,
at a
should
adjacent
to the crossing span. Other states broken (1977), d o not require
required
clearance for
broken
to maintain
over
the
circuits,
clearance
edition
lines
communication
sufficient
latest
NESC
structures conductors.
of a crossing,
Whenever the under the outside The
This
railroads,
conductor
clearance
major
conditions
and
required
are governed conductor
highways,
major
on transmission
lines
above.
the
enough
it is necessary
be reduced structure.
with
communication
or lake crossings
one-half
may
falls
is necessary.
could
m (50 ft) and
additional
railroads,
of the spans in
to provide major
When sagged
over
which,
River than
correction
the
limitation
type
point
or
limits,
be used.
by the
correct
be provided in either
rules
powerlines,
or where
The
the
hardware,
plan-profile.
structure
structure
weights
the allowable
structures.
should
considerations. It is our
of 15.2
as indicated
all crossings
NESC
are normally
line.
some
span
3 poles
structures,
on the
between
the insulator
line.
for lengths
of structure,
wood-pole
powerlines
the
class
in a transmission
California,
major
tall
type
transmission
used
and
insulators,
suspension If
distance
to hold
is within
is measured
limits.
the
vertically
in the
the specified
prescribed
However,
insulators
on the
regarding
each
lines,
are normally
spans,
The
by
the
more
spans.
a failure
spans
spans
273
as acting
of the
area in which
than
type
for
On all wood-pole class 2 poles
line
be greater
or another
can cause
adjacent
General Instructions.-Instructions
design
long
the
be within
adjacent
sideswing
of adjacent
within
to provide
strings,
the
of the
sum
will will
be adjusted
insulator
points the
of the
DATA
to be considered
distance
whether
low
sideswing
outside
low-point
against
so defined
of insulator
fall
of conductor
determine
between
is then
may
the length
V-ADDITIONAL
ruling
are used on both sides of a crossing, it is not necessary For lower voltages, when suspension-type structures
increased
involving span,
decrease
special
to use spans
ruling
sag in the
to seriously
the
crossing the
structures
longer
than
conductors
or long spans approximately
should
tension
due
to a broken
in most
cases.
are to be handled 1.7 times
be dead-ended
conductor as special
the
ruling
span
at both
ends
of the
in an studies.
or shorter span
and
span.
terrain slopes across the right-of-way, conductor on the high side to meet
approximately Other policies
span
clearance
to allow are used
in conductors
and
overhead
50 percent in the regarding substations
1. It is Bureau policy a substation or switchyard.
sufficient clearance all requirements. ground
span terminating and switchyards
to install self-supporting In general, this means
structures that the
wires on are:
under the
should full
load
substation
(no guys) within structure adjacent
be maintained should
normally
or switchyard 183 m (600 ft) of to the substation
274
TRANSMISSION
or switchyard conductor 2.
will and
When
is not
the
reduced,
should
he a steel
overhead
may
be varied
and
any special
to meet
The
method
that
is designing
of approach the
tension
requirements
between
span
structures
before
angle
in the transmission
and design
roads, should
proceeding
where
with
the
and
overhead ground
final
tension
ground
wires
wire
substation
power
tensions
or switchyard
or communication
be discussed the
in the
conductor
overhead of the
and
tensions
yard.
conductors
structural
as railroads,
unbalanced
the
in a span
the
or switchyard
steel
the into
of conductor
of the such
to the substation
slack
is reduced
of reduction
requirements
of accepting
to the
clearance
amount
the
crossing
due
wire
midspan The
capable
wire
ground
sufficient
be maintained.
structure
ground
overhead
LINE DESIGN MANUAL
with
design
the
of the
lines.
design
group
transmission
line. 3.
The
be made deflection
deflection
as small as possible. angle reduces the
or switchyard
structure.
On wood-pole
lines
all guyed
structures
27.
Right-of-Way
transmission
line
strings require wide enough clearance Sufficient
should
sandy
that imposes
soil or other
have
a separate
and Building
design.
Today’s
soil with
poor
anchorplate
Clearance
higher
this angle additional
voltages,
obstruction is essential
that may to avoid
for
each
.-Right-of-way wider phase
adjacent to the right-of-way. are hanging in their no-wind
It is legally possible for someone right-of-way, and occasionally this
be at the flashover
or switchyard
characteristics
guy
clearance
should
is encountered,
strand.
is a very spacings,
important consideration in and unrestrained insulator
ever before. A right-of-way in a high-wind situation,
edge of the right-of-way to trees, buildings, pole
Some of these position.
structure
be less than loo because a larger transverse load on the substation
bearing
a wider right-of-way and greater clearances than to give adequate clearance between conductors
from any clearance
obstruction conductors
where
line at the substation
It is preferred clearance and
hazards
on private lines, and
are not
obvious
to erect a structure, such as a building, at the is done. The only way we can protect ourselves
very and
must be and also property. any other when
the
edge of our others is to
make our right-of-way wide enough to provide a minimum electrical clearance between the outer conductor, at a maximum wind condition of 0.43 kPa (9 lb/ft2), and an imaginary building with a wall on the edge of the right-of-way. Tables 28 and 29 show the horizontal distance required as clearance between Tables 30 through ruling spans.
a conductor and a building for various line voltages 35 show the required right-of-way for transmission
Sometimes there is a tendency to reduce the right-of-way require shorter spans (to keep the conductors safely within would
be more
expensive
than
initially
because
of the
and elevations above sea level. lines of different voltages and
width to keep costs down, but this would the right-of-way) and the line probably
additional
structures
required.
CHAPTER
V-ADDITIONAL
DATA
275
Table 28 .-Minimum
horizontal clearance to buildings- USBR standard for NESC light, medium, and heavy loading (metric)
kV
Ruling span, m
Conductor
69
84 mm2 ACSR 6/l
115
135 mm2 ACSR 26/7
138
242 mm2 ACSR 2417
161
242 mm2 ACSR 2417
230
483 mm2 ACSR 4517
345
483 mm2 ACSR 4517 duplex
213 305 213 305 213 305 213 305 305 366 427 305 366 427
Basic clearance, m
3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048 3.048
Increase for voltage,’ m
0.2003 .2003 .3420 .3420 .4836 .4836 .9086 .9086 .9086 1.6170 1.6170 1.6170
Increase for elevation, m
Minimum horizontal clearance to buildings,2 m
3 percent of ‘increase for voltage” for each 305 m of elevation over 1006 m
3.048 3.048 3.249 3.249 3.389 3.389 3.532 3.532 3.956 3.956 3.956 4.666 4.666 4.666
r The increase for voltage is: ’ At 1006-m elevation and a
Table 29.-Minimum
horizontal clearance to buildings-USBR standard for NESC light, medium, and heavy loading (U.S. customary)
kV
Conductor
69
No. 4/O AWG ACSR 611
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 2417
161
477 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 4517 duplex
Ruling spa ft
Basic clearance, ft
700 1000 700 1000 700 1000 700 1000 1000 1200 1400 1000 1200 1400
10 10 10 10 10 10 :: 10 10 10 :8 10
l The increase for voltage is: 2 At 3300-ft elevation and at 60 “F with a 9-lb/ft’
wind.
Increase for voltage,’ ft
0.66 0.66 1.12 1.12 1.59 1.59 2.98 2.98 2.98 5.31 5.31 5.31
Increase for elevation, ft
3 percent of ‘increase for voltage” for each 1000 ft of elevation over 3300 ft
Minimum horizontal clearance to buildings,2 ft 10.00 10.00 10.66 10.66 11.12 11.12 11.59 11.59 12.98 12.98 12.98 15.31 15.31 15.31
Table 30.-Right-of-way Maximum
kV’
69
Conductor
Ruling span, m
conductor tension,2 newtons per conductor
84 mm2 ACSR 6/l
213
a12 900
115 138
135 mm2 ACSR 26/7 242 mm2 ACSR 2417
213 213 305
a24900 a16400
161
242 mm2 ACSR 24/l
213
230
483 mm2 ACSR 4517
305 305
a23 100 a24900 a23 100 a31100
366 427 305 366
a30200 a29 300 a31 100 a30200
427
a29 300
305
305
345
483 mm2 ACSR 4517
duplex
b16 900
Insulator string length, mm
Conductor swing 0.43kPa wind l/3 low point Degrees m
869 869
65O19’ 65O19’
1219 1372 1219
3746 7 705 8 964
3745 7576 3460 73746 116
a12900
r 69 through 161 kV are H-frame wood-pole construction; 2 Maximum conductor tensions are limited by:
Conductor sag at 15.5 oc, mm
values-NESC Iigh t loading (metric)
Right-of-way,4 m
2 %
63OO2' 57OO9’ 63OO2'
3.048 3.048 3.658 4.267 3.658
3.048 3.048 3.249 3.389 3.249
21 28 23 24 29
g
1372 1676 1676 2286
57OO9’ 57009’ 57OO9’ 50°38'
7.6255 4.5550 7.8809 8.6982
4.267 5.182 5.182 7.620
3.389 3.532 3.532 3.956
;; 34 41
Iz m u
12851 17676 8 964 12851
2286 2286 3658 3658
50°38' 50°38' 50°38' 50°38'
11.7036 15.4341 9.7590 12.7644
7.620 7.620
9.144 9.144
3.956 3.956 4.666 4.666
47 55 48 54
17676
3658
5OO38'
16.4949
9.144
4.666
61
230 and 345 kV are steel tower construction.
3 At 1006-m elevation, and at 15.5 OC with a 0.43kPa wind. 4 At 1006-m elevation, and rounded off to next highest meter.
Minimum horizontal clearance to buildings,3 m
7.6736 4.1705 4.2996 7.4292
7 705
a 18 percent ultimate strength at 15.5 oC fmal, no load. b 25 percent ultimate strength at -18 OC final, no load.
4.1925
Outside phase to structure centerline, m
$
E n z 5
z ?
Table 3 1.-Right-of-way
kV’
69
Conductor
No. 4/O AWG ACSR 6/l
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 24/l
Ruling span, ft
411 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 45/l duplex
Conductor sag at 60 OF, ft
Insulator string length, ft
12.28 24.86 11.34 23.27 12.28 25.25 12.28 25.25 29.31 42.09 57.89 29.37 42.09 57.89
2.5 2.5 4.0 4.0 4.5 4.5 5.5 5.5 7.5 7.5 7.5 12.0 12.0 12.0
700
a2900
a29oo
700
b3800 a3700 a5600 a5200 a5600 a5200 a7000 86800 a66oo a7000 86800 a66oo
700
1000 161
Maximum conductor tension,* pounds per conductor
1000 1000 700
1000 1000 1200 1400 1000 1200 1400
values-NESC light loading (US. customary)
r 69 through 161 kV are H-frame wood-pole construction; * Maximum conductor tensions are limited by:
Conductor swing 9-lb/ft* wind l/3 low point Degrees Et 65O19’ 65O19’ 63OO2' 63OO2' 57009’ 57OO9’ 57009’ 57009’ 50°38' 50°38' 50°38' 50°38' 50°38' 50'38'
230 and 345 kV are steel tower construction.
a 18 percent ultimate strength at 60 OF fmal, no load. b 25 percent ultimate strength at 0 OF fmal, no load. ’ At 3300-ft elevation, and at 60 OF with a 9-lb/ft* wind. 4 At 3300-ft elevation. and rounded off to next highest 5 feet.
Outside phase to structure centerline, ft
Minimum horizontal clearance to buildings,3 ft
Right-of-way,4 ft
10 10
10.00 10.00
70
24.86 13.67 24.31 14.10 24.99
90
s
12 12 14 14
10.66 10.66
75 95 80
!z
14.94
17
25.83 28.51 38.34 50.56
:5’ 25 25
13.43
31.99 41.82 54.04
i8 30
11.12 11.12 11.59 11.59 12.98 12.98 12.98 15.31
105 90 110 135 155 180 155
15.31 15.31
175 200
7
$ 0 =i 5 z :
2
Table 32.-Right-of-way
kV’
Conductor
69 115 138
84 mm2 ACSR 6/l
213
135 mm2 ACSR 26/7
213
242 mm2 ACSR 24/l
161
242 mm2 ACSR 24/l
230
483 mm2 ACSR 45/l
345
Ruling span, m
483 mm2 ACSR 4517
duplex
Maximum conductor tension,’ newtons per conductor
Conductor sag at 15.5 oc, mm
a15 500
values-NE,!%7 medium loading (metric) Insulator string length, mm
Conductor swing 0.43-kPa wind l/3 low point Degrees m
305
bll300
a19 100
4033 7521 3111
305
b21300 a26700
6947 4 111
869 869 1219 1219 1372
305
305 305 366 427 305 366
b28500 a267OO b28500 b37400 b36900 b36400 b37400 b36900
1655 4 111 7655 8948 12 821 17525 8948 12 821
1372 1676 1676 2286 2286 2286 3658 3658
50038' 50°38' 50°38' 50°38' 50°38'
11.6850 15.3174
427
b36400
17525
3658
50°38'
16.3782
213 213
r 69 through 161 kV are H-frame wood-pole construction; 2 Maximum conductor tensions are limited by:
65O19’ 65O19’
3 At 1006-m elevation, and at 15.5 OC with a 0.43-kPa wind. 4 At 1006-m elevation, and rounded off to next highest meter.
3.048 3.048
4.4531
7.6291
3.048 3.048 3.658
63OO2'
1.2185 4.6062
3.658 4.267
7.5835 4.8616
4.267 5.182 5.182 7.620 7.620 7.620
230 and 345 kV are steel tower construction.
a 25 percent ultimate strength at -29 OC final, no load. b 18 percent ultimate strength at 15.5 OC fmal, no load.
Minimum horizontal clearance to buildings,3 m
63OO2'
57009’ 57009’ 57009’ 57009’
4.4542
Outside phase to structure centerline, m
7.8389 8.6859
9.7467 12.7458
9.144 9.144 9.144
3.249 3.249 3.389 3.389
Right-of-way ,4 m
z %
22 28
g
5;
ul
i:
3.532 3532
3:
P 1 z
3.956 3.956 3.956
41 41
0 E
:48
5
4.666 4.666
54
4.666
61
m
5 z r
Table 33.-Right-of-way
kV’
Conductor
69
No. 4/O AWG ACSR 6/l
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 2417
161
477 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 4517 duplex
Ruling span, ft 700 1000 700 1000 700 1000 700 1000 1000 1200 1400 1000 1200 1400
Maximum conductor tension,2 pounds per conductor
Conductor sag at 60 OF, ft
a3500 b3900 a4300 b4800 a6000 b6400 a6000 b6400 b8400 b8300 b8200 b8400 b8300 b8200
’ 69 through 161 kV are H-frame wood-pole construction; ’ Maximum conductor tensions are limited by:
values-NESCmedium
13.16 24.63 12.37 22.75 13.49 25.15 13.49 25.15 29.38 42.07 57.38 29.38 42.07 57.38
Insulator string length, ft 2.5 2.5 4.0 4.0 4.5 4.5 5.5 5.5 7.5 7.5 7.5 12.0 12.0 12.0
loading (U.S. customary) Conductor swing 9-lb/ft2 wind l/3 low point Degrees ft 6S019’ 65O19’ 63OO2’ 63OO2’ 57009’ 57009’ 57009’ 57OO9’ 50°38’ 50°38’ 50°38’ 50’38’ 50°38’ 50°38’
230 and 345 kV are steel tower construction.
a 25 percent ultimate strength at -20 OF final, no load. b 18 percent ultimate strength at 60 OF final, no load. ’ At 3300-ft elevation, and at 60 OF with a 9-lb/ft’ wind 4 At 3300-ft elevation, and rounded off to next highest 5’f&.
14.23 24.65 14.59 23.84 15.11 24.91 15.95 25.75 28.51 38.33 50.16 31.99 41.81 53.64
Outside phase to structure centerline, ft
Minimum horizontal clearance to buildings,3 ft
10 10 12 12 14 14 17 17 25 25 25 30 30 30
10.00 10.00 10.66 10.66 11.12 11.12 11.59 11.59 12.98 12.98 12.98 15.31 15.31 15.31
Right-of-way,4 ft
70 90 ;: 85 100 1?8 135 155 180 155 175 200
II TJ -F ZJ a =I 5 z g 2
Table 34.-Right-of-way
values-NESC heavy loading (metric)
84 mm2 ACSR 6/l
213
Maximum conductor tension,? newtons per conductor a18 200
115
135 mm2 ACSR 26/l
305 213
a182OO b24400
12530 4452
869 1219
65O19' 63OO2'
12.1751 5.0547
3.048 3.658
3.048 3.249
138
242
305
9524 4665 8 101 4 665 8 101 8 954 12 844
1219 1372
2286 2286
63OO2' 57009' 57009' 57009' 57009' 50°38' 50°38'
9.5755 5.0716 1.9582 5.3270 8.2186 8.6905 11.6982
3.658 4.267 4.267 5.182 5.182 7.620 7.620
3.249 3.389 3.389 3.532 3.532 3.956 3.956
34 41 41
Rulins span,
Conductor
kV’ 69
m
230
345
Insulator string length, mm
Conductor swing 0.43kPa wind l/3 low point Degrees m
5194
869
65O19'
Outside phase to structure centerline, m
Minimum horizontal clearance to buildIngs,3 m
6.0544
3.048
3.048
25
is
31 24
f
;z
$
239”
r z
Rightof-way,4 m i
242 mm2 ACSR 24/l
213
483 mm2 ACSR 4517
305 305 366
a24900 b33300 a382OO b33 300 a38200 c51 100 c50700
421
c50 300
11515
2286
50°38'
15.3097
7.620
3.956
54
305 366 421
c51100 c50700 c50 300
128954 844 17515
3658 3658
50'38' 50°38' 50°38'
12.7590 9.7513 16.3705
9.144 9.144
4.666 4.666
54 48 61
mm2ACSR
24/l
213
305 161
Conductor sag at 15.5 oc, mm
483 mm2 ACSR 45/l duplex
: 69 through Maximum
161 kV are H-frame wood-pole conductor
construction;
1372 1676
1676
230 and 345 kV are steel tower construction.
tensions are limited by:
a 50 percent ultimate strength at -18 OC initial, full load. b 33-l/3 percent ultimate strength at -40 OC initial, RO load. c 18 percent ultimate strength at 15.5 OC final, no load. 3 At 1006-m elevation, and at 15.5 OC with a OA3kPa wind. 4 At 1006-m elevation, and rounded off to next highest meter.
m
0 FJ s 5 f
r
Table
Conductor
kV’
35 .-Right-of-way
values-NESC heavy loading (U.S. customary)
Ruhng spa% ft
Maximum conductor tension,2 pounds per conductor
Conductor sag at 60 OF, ft
Insulator string length, ft
a4 100 a4 100
18.95 41.00
2.5 2.5
65O19’ 65O19’
19.49 39.53
10 10
10.00 10.00
80 120
12 12 14 14 17
10.66 10.66 11.12 11.12 11.59 11.59 12.98
80 110 85 105 95 115 135
12.98 12.98
155 180
: =i 6 z
Conductor swing 9-lb/ft’ wind l/3 low point Degrees ft
Outside phase to structure centerline, ft
Minimum horizontal clearance to buildings,’ ft
Rightof-way,4 ft
69
No. 4/O AWG ACSR 6/l
700 1000
115
266.8 kcmil ACSR 26/7
700 1000 700 1000 700 1000 1000
b5 a5 b7 a8 b7 a8 cl1
500 600 500 600 500 600 500
14.57 31.23 15.47 26.54 15.47 26.54 29.35
4.0 4.0 4.5 4.5 5.5 5.5 7.5
63OO2’ 63OO2’ 57009’ 57009’ 57OO9’ 57009’ 50°38’
16.55 31.40 16.78 26.08 17.62 26.92 28.49
1200 1400
c11 400 cl1 300
42.13 57.51
7.5 7.5
50°38’ 50°38’
38.37 50.26
1000 1200
c11 400 500 cl1
29.35 42.13
12.0
50°38’
31.97 41.85
ii 30
15.31
155 175
57.51 12.0 50°38’ 1400 c11 300 t 69 through 161 kV are H-frame wood-pole construction; 230 and 345 kV are steel tower construction. 2 Maximum conductor tensions are limited by:
53.74
30
15.31
200
138’
477 kcmil ACSR 2417
161
477 kcmfl ACSR 2417
230
954 kcmil ACSR 4517
345
954duplex kcmil ACSR 4517
a 50 percent ultimate strength at 0 OF initial, full load. b 33-l/3 percent ultimate strength at -40 OF initial, no load. ’ 18 percent ultimate strength at 60 OF final, no load. ’ At 3300-ft elevation, and at 60 OF with a g-lb/f? wind. 4 At 3300-ft elevation, and rounded off to next highest 5 feet.
:: 25
? D : Y 5
.
: 2
282
TRANSMISSION
28.
Armor
Rods
of vibrations may
and
produced
well
result
by very
turbulence
steady
on the leeward
1 to possibly
millimeters aeolian
the
hertz,
reinforced
induces
vibrations
of an inch
the
aluminum
on a clear, conductor
cold
the conductor support, which and
The
The
a few
light
Therefore, dampers,
effect on vibration value is through
range
and
to 200
amplitudes nodes,
of
tension
force per unit length. On short spans, by the humming sound produced-like and
is usually
this type or both.
strung
to fairly
of conductor
requires
and reduce the amplitude from the reinforcing of the conductor
some protection to the conductor due to flashovers. Armor rods
for
high special
10 to 20 percent; at the point of
against vibration, the armor aluminum conductors are
to a stranded cable of larger diameter-thereby region of maximum bending stress.
A set of 7 to 13 rods, depending length of the rods vary with
are eddy
frequencies
between
and consist of a spiral layer of short, round rods surrounding conductor to its support is made in the middle of the armored
equivalent is in the
which varying
millimeters
frequencies distance
and
morning.
is comparatively
rods have some damping their greatest protective
frequencies
from
types
conductor
periodically
the excitation.
length,
and other
in the
natural
It is the
range
or more. span
to aeolian
stresses
of the
and the conductor and is evident only
Armor however,
to offering from burns
those
produces
velocity,
so it is quite susceptible to vibration. by the use of armor rods, vibration
maximum stress. In addition rods protect the conductor
are subject bending
normally
inches),
wind
of the conductor, small amplitude lines
that
to several
of the
MANUAL
(1 to 30 mi/h).
amplitudes
tensions, protection
made of aluminum attachment of the
are
of 1 to 48 km/h and
are functions
singing of telephone Steel
repeated
Aeolian
winds
in the conductor, diameter the vibration is of extremely the
conductors
which
side of the conductor
100
(a fraction vibrations
Dampers.-All
wind,
in its failure.
stimulated from
Vibration
by
LINE DESIGN
the conductor. length. This
strengthening
The makes
it at the
on conductor size, is required to armor a conductor. The size the size of the conductor. Generally, because of the ease of
application, and for both
and removal if necessary, preformed armor rods are used for all sizes of ACSR conductors steel and Alumoweld overhead ground wires. Formed rods are manufactured with a spiral
shape
the
to fit
diameter
of the
conductor
on which
they
are to be used.
The
ends
of each
rod
are
discharge of armor
or parrot-billed to reduce the chance of abraiding the conductor and the tendency for corona at these points. Clips or clamps are not required on this type of armor rod. Older types rods, now seldom used by the Bureau, include the straight rod and the tapered-rod types.
Straight
armor
rounded
rods,
having
a constant
diameter
sizes of 15 to 62 mm2 (No. 6 AWG to No. with long tapered ends and are used for straight at the
and tapered types time of installation
for their
full
length,
of rods are furnished using special armor
straight and the spiral rod wrenches. These
on the conductor by the installation of armor rod clips or clamps been formed. Normally, armor rod clamps are used on transmission and higher, and armor mostly to the possibility Through experience, effective device against
are used
l/O AWG), inclusive. Tapered 79 mm2 (No. 2/O AWG) and
has found and, when
damper will greatly reduce vibration. We use both armor rods and vibration
dampers
the Stockbridge-type properly installed,
for ACSR
conductor
rods are straight rods conductors. Both the
is formed around the conductor types of rods are held in place at each end after the spiral has lines for voltages of 115 kilovolts
rod clips are used for voltages of 69 kilovolts of corona loss off the sharper edges of the the Bureau vibration
armor larger
the
on our transmission
suspension points may be eliminated if sized clamps are used for the be an almost perfect fit, with extremely small tolerance, to provide strand breakage at this stress point.
and clips. vibration latest lines.
lower.
This
choice
is due
damper to be a very models of this type of Armor
conductor. the desired
rods
at conductor
These clamps must protection against
Each
construction
application,
contractor
and
transmission field office
location
in the
to furnish
DATA
the
dampers
vibration
middle
of the
of possible
A damper
the
problem loop
centerline
could
formed
frequencies
effective,
however, absolutely
from
of the
should
be handled
in the is almost
are
be located
conductor
to be furnished
must
be located
in the
middle
suspension
regardless
of size, span
simply.
and
the
midpoint point
A vibration
problem
third
another
of a loop
would becomes
of a loop for
and
are transmitted dampers. The
so the problem
at the
the midpoint could be a node no effect (see fig. 112).
recommendations
conductor
quite
unlimited
283
manufacturer’s
that
or compression dead end. vibrated at the same frequency
the
to be most wind; have
is required
of the‘ vibration
distance
of a strain clamp If all conductors
number
V-ADDITIONAL
line. The data are checked and, if found satisfactory, as the criteria to use for installation of the vibration
at a prescribed
velocity,
CHAPTER
created frequency,
to be effective.
for size,
installed
on the
to the appropriate dampers are installed
clamp
or from
length,
tension,
damper
could
he solved. more
the
and Studies
and
wind
be placed
However,
complex.
in the
mouth
conductor the
the
A damper, by the
damper should
would be made
so that a damper installed at the chosen location will be effective on as many probable frequencies as possible. Numerous laboratory studies have been made by manufacturers of dampers over the years. The new, more sophisticated dampers have been developed through these laboratory studies and should be applied as recommended by the manufacturer. Formulas for computing the frequency and loop length and the basic theory of vibration can be found in most physics books. Two such formulas are:
For frequency :
Metric
U.S. Customary
Hz 51.4534 km/h
Hz 3.26 mi/h
mm
in
f&l d
where f = frequency k= a constant (for air) V= velocity of wind d= outside diameter of conductor For loop length:
where L = loop length f= frequency T= tension in conductor g = acceleration due to gravity W= force of conductor
A standing but
of opposite Reduction
wave,
such
direction of span
as the vibration
loop,
mm Hz N 9.8066 m/s* N/m
is the result
of two
traveling
of motion. length
and
tension
reduces
the
severity
of vibration.
in Hz lb 32.2 ft/s* lb/ft
waves
equal
in magnitude
TRANSMISSION
284
LINE DESIGN
MANUAL
Midpoint of loop f
(Vibration waves are exaggerated vertically for illustmtion) Figure
Galloping
or dancing
112.-Schematic
conductors
by strong gusty winds blowing of eliminating this phenomenon melt
it off
as quickly
value.
Corona
are large-amplitude,
after
it forms
loss on a transmission of conductors when the
occurs
when
waves in a conductor.
low-frequency
vibrations.
Galloping
the
potential
and
before
damage
occurs
(see sec.
line is the result of the ionization electric stress (or voltage gradient)
of a conductor
in air
is raised
conductors
will
result.
There
is always
a power
When and where will corona occur on a given be? What can be done to reduce or eliminate investigators have studied over the years. Three Rockwell Peterson
[ 161, and Peterson formulas have been
to such
used for calculating of obtaining good
the expected data is to take
This
true
of the
Recent available
corona the data
loss for these from the line
extra-high-voltage
lines,
so care
study
based
In fair conductor.
up to a voltage near voltage is an indicator
surface For
the
of a given same
a smooth will
increase
size of the
conductor
diameter,
conductor.
approaches a stranded
Any
corona-and conductors
distortion their
the
spacings
line
cylinder,
is good
to the surface
the higher and
a smooth
conductor
voltage,
also
the
corona.
country. region,
The below
Carroll-Rockwell 3.1 kilowatt
higher voltages. Actually, the being studied after it has been
a published
is small disruptive
that
and per phase
work has been directed toward corona loss in the information for this range should be explored and
and the method of calculation from to that which you propose using. weather, corona The calculated
a value
tufts or streamers the odor of ozone. enough, corrosion
transmission line ? How much power loss will there it? These are some of the questions that many methods of calculation by Peek [15], Carroll and
[ 171 are in general use in this the most accurate in the low-loss
kilometer (5 kilowatt per phase mile). extra-high-voltage range, and the latest
is especially
loss with
14).
process which takes exceeds a certain
dielectric strength of the surrounding air is exceeded. Corona is visible as bluish around the conductor; the visible discharge is accompanied by a hissing sound and In the presence of moisture, nitrous acid is produced and, if the corona is heavy of the
is caused
across irregularly ice-covered conductors. The only known methods are to either prevent the ice from forming on the conductor, or to
as possible
29. Corona.-Corona place on the surface
of vibration
have
the
be exercised
to select line
the disruptive voltage of corona-performance. the
for
of the
must
on transmission
higher
about
considerable
the critical
80 to 85 percent
conductor more
(raised
critical effect
these
best method constructed.
strands,
data
test
very
data
similar
for a particular The closer the disruptive
voltage.
of the
voltage
burrs,
scratches)
of
rough spots become. The
on corona
loss. Fair
weather,
CHAPTER rain,
snow,
hoarfrost,
corona loss. rain produces the
same
loss is observed line
to know
In earlier When
rates
of rainfall
behavior.
Corona
can and
and
dimension
instead
between
text
reduce
overvoltage surge. for
figures
of the
were
illustrations,
from
we have
are
present,
open-circuited
loss to be expected an entire
lines,
transmission
because become corona and
in a
be necessary line.
of energy
more can
affect
it will
loss.
important. system
attenuate
both
corona
reference
chosen
along
studying
The presence of voltage at which
do so, it would
has probably
expected
SI metric
To
when
factor. of the
was avoided-strictly
of corona
the
be considered
of corona
simultaneously
on long
taken
value
switching)
calculating
preferred
peak
corona
aspect
(lightning,
switching
related and
transmission,
must
to determine.
exist
285
than any other single as low as 65 percent
The
could
DATA
temperature
impossible,
influence
voltages
is a procedure
procedure
weather.
that
radio
high
voltage
Following
the
and
loss more at voltages
if not
of high-voltage
years,
abnormally
lightning
fair
difficult,
years
recent
during
is very
all of the
more
pressure,
Rain probably affects corona corona loss on a conductor
transmission
In
atmospheric
V-ADDITIONAL
loss on a transmission line. is reference used centimeters Th
[18].
dimension
of millimeters.
To
to present
the
in centimeters:
procedure
ensure
This as a
compatibility
Nomenclature: Pk =
corona
loss,
kW/km
P,
=
corona
loss,
kW/mi
E
=
average
surface
critical
visual
Eo= =
line
to ground
>
=
line
frequency,
6
=
air
n
=
number
r
=
conductor
=
spacing
g
=
mean
g,,
=
surface
;=
density
at 50 Hz at 60 Hz
voltage corona
(per
phase)
(per
3-phase)
gradient gradient
voltage,
kV
Hz factor
of conductors radius,
in bundle
cm
of conductors
equivalent
phase
between
spacing, average
voltage
m = conductor
in bundle, cm and
gradient
surface
cm
factor
maximum
surface
gradient,
at which
corona
starts,
(assumed
0.88,
average
kV/cm
kV/cm weathered
conductor)
Assume: 345-kV
transmission
483-mm2 457-mm 10.06-m The
basic
line
(954-kcmil) (18~in) (33-ft)
formula
for
at 1829-m
ACSR,45/7
spacing on conductor flat phase spacing reading
the
corona
(6000-ft) conductor
elevation (duplex)
e =
199.2
r
1.48
=
cm
s = 45.72 cm
bundle
D = loss from
kV
the
curves
shown
on figures
1005.84 113
cm and
114
is:
286
TRANSMISSION
LINE DESIGN
MANUAL
pk
g is analogous to E so, y22 g,
= F A. 0go
0
For a duplex conductor, l+$ (
g=
e )
(2r) log, A+For a single conductor,
g=
e r log, f
g=
(1 +~)WW
(2) (1.48) log,
Calculateg, Results
from
for air density the two-thirds
a high-altitude
test
205.65 == 14.45 kV/cm 14.23
(1 ;;;;k8p72, . fromg,
project
= 21.1 m 6%
at Leadville,
Colo.
0.301 1+ fi > ( [19]
8 varies as the one-half power in lieu of the first power power as indicated by Peterson’s investigations [17].
concluded
that
as suggested
the
= 20.72 kV/cm Calculate
g/go
and
read
corresponding
value
for
14.45 g -z-z go 20.72 From
figure
113,
-&
curve
Pk /n
2 r2 at 50 Hz
from
figure
o 7. ’
A :
= 0.04 Pk = 0.04(2)2 (1.48)2 = 0.2368 kW/km at 50 Hz (per phase)
correction
by Peek
113:
[15]
or
CHAPTER
V-ADDITIONAL
287
DATA
‘k n2r2
0.4
0.6
Figure 113.-Corona
As read test.
from
Because
should multiplying
1.0
1.2
0.3
loss curves for (A) fair weather,
figures
113
the corona
be multiplied
by the
in kilowatts
per
for
~7
QS
(B) rainfall,(C)
for
a 60-Hz
factors, three
phases
The
0.3 OA Q5 Q6 Q7 0.9 09 1.0 I.1 1.2 13
and(D)
value
phases,
should
60-Hz
snow. 104-D-1116.
From [18].
for each phase from a 50-Hz the value read from the chart
kilometer
for all three
for
---
per kilometer to frequency,
system.
the figure
1.1
hoarfrost,
Pk is in kilowatts is in direct proportion
if the loss is desired
three
mile
~5
114,
60/50
and
Combining
and
loss factor
by 1.6093,
by three. value
0.9
may the
be changed
answer
be multiplied
should
by 5.79
to
mile
by
be multiplied to obtain
a loss
systems:
Pk = 0.2368 kW/km at 50 Hz (per phase) PC = 5.79 (0.2368) = 1.371 kW/mi at 60 Hz (per 3-phase)
When curve the
rainfall
two,
three,
100 percent. give
is to be considered,
B. Similarly,
the
for hoarfrost or four
Taking
expected
(whichever the assigned
corona
loss for
the
or snow,
corona
is applicable) percentages the
line
loss due
losses are obtained values times ‘in question.
for
to rain
must
from corona
the corresponding
be read
curves
Cor
loss must
from
figure
ZI, respectively. be apportioned
losses and
summing
113 using Then, to make these
will
288
TRANSMISSION
LINE DESIGN
MANUAL
1.0 0.8
0.6
0.1
0.08 0.06
0.01
0.5
0.6
0.7
0.8
0.9
1.0
I.1
Figure 114.-Average values of corona loss under fair weather with different conductor bundles. (1) single conductor (2) two-conductor bundle (3) three-conductor bundle (4) four-conductor bundle (5) average curve. 104-D-1117. From [18].
CHAPTER
V-ADDITIONAL
DATA
289
Example: Assume
that
is fair,
the
line
5 percent
previously
of the
used
time
is located
it rains,
and
such
that
10 percent
85 percent
of the
time
of the
time
it snows-all
the
during
weather a period
of a year.
pk
-
= 0.04 for fair weather (curve A, fig. 113)
n2 Y2
Pk = 0.04(2)2 (1 .4Q2 = 0.2368 kW/km at 50 Hz (per phase) PC = 5.79(0.2368) ‘k
-
= 1.37 1 kW/mi at 60 Hz (per 3-phase)
= 0.90 for rainfall (curve B, fig. 113)
n2 r2
Pk = 0.90(2j2(
= 7.885 kW/km at 50 Hz (per phase)
1 .48)2
PC = 5.79(7.885) = 45.654 kW/mi at 60 Hz (per 3-phase) pk n2 r2
for snow (curve D, fig. 113)
= 0.15
Pk = 0.1 5(2)2 (1 .48)2 = 1.3 14 kW/km at 50 Hz (per phase) PC = 5.79(1.314) = 7.608 kW/mi at 60 Hz (Per 3-phase)
Summation of losses times percentages: (0.85)(1.371)
+ (0.05)(45.654)
+ 0.10 (7.608) = 4.21 kW/mi at 60 Hz (per 3-phase)
This is the average corona loss for the year. Although justified
this
method
for practical
due to weather conductor. decrease Factors
conditions.
New
rapidly
Fair
weather lines
with
various
for
As indicated
transmission
rather for
of calculation
purposes.
corona
loss is only
in the example, corona
tend
there
loss depends
to have
higher
an approximation,
mostly
losses;
on the
however,
changes surface
these
conductors
weather
conditions
conductor
in fog,
mist,
Weathered
conductor
in fair
weather
Corona
loss curves and
computed
by the
for
ACSR
higher
of the
values
will
are:
in rain
Weathered
elevations
in the losses
condition
time.
Range All
it is apparently
are substantial
different conductor
Carroll-Rockwell
and
voltages sizes-from method
snow
are shown which for
fair
0.47
to 0.60
0.54
0.60
to 0.80
0.70
0.80
to 0.95
0.88
on figure may
A verage value
115.
Curves
be determined
the
weather
are shown estimated
at 25 o C (77 o F).
for corona
different loss as
TRANSMISSION
290
a 0
LINE DESIGN MANUAL
CHAPTER
V-ADDITIONAL
DATA
291
TRANSMISSION
292 30.
Stringing
Sag
furnished
for stringing
sag data the
sag and
studies,
tension
data
determination
electrical For
field
results
installation
for
spans
than
sag table ruling
conductor
for
to cover length
a range
increments,
and
from
are not
the
without
high
become
On
free
suspension from
the
tensions,
and
if the stringing
sags
and
are usually
loading
a temperature
form
lengths
in 5-m
elevation,
range
Spans.-When
conductors
spans.
If the
if the
terrain
however,
sag and
loading
is
use and
F in 10’
are
increments,
above
-18
if
conductor
in field
from
tension
conditions
if the
to 50 percent
should
at a lower
the
ruling
to 49 ‘C
in 5’
increments.
Offset Data for Inclined low
below
tables
unloaded
0 to 120’
span.
Stringing
for the preparation
conditions
from
span.
generally
for convenience
range the
but
on initial
loading
in table
sag tables
on the ruling
required
are the
are based
on final
listed
data
to furnish of each
lengths,
basic spans
values
50 percent
strings
span
and
of sag in that sheaves
conductor
hanging
terrain
is not
is quite
conductor
supports
in stringing
sheaves
very
this
steep,
to hang put span
to obtain
dead
intermediate
ends
to the
conductor. the
steep,
the
proper
dead
dead
should
tend
problem sagging
on adjacent to run
downhill
can be handled of the
one
to isolate
be such as to minimize sag and offset dead end (the last structure clipped
the
steep
conductor
see figure
is clipped
a way
that
the amount
the
in, slack
conductors
of slack
in a given
span
the sag while
has been
clipped
dead
ends,
must
be sagged the
For
either
sagged
structure from
in one
conductor
purposes
tension
permanent
ahead, during the
the
the suspension between
the
the
clip-in
comparatively
the conductor
the
the
distance
it is necessary temporary clamp
dead
sections
dead
will
end
operation. level
for
since
Where
in one operation,
where
of
is changed,
in. Calculations
operation.
the
be taken
or temporary,
of calculation,
For
components
to change
conductor
116. must
horizontal
it is necessary
of line being
to maintain
be equal;
the
sagging ends.
be at least
is snubbed, ends,
ends
T2 must
in such
Whenever
between
to permit
the
span
sag after dead
in the section
There
conductor
temporary
great
temporary
be the last structure
where
between
is too
after
upper
correct
of spans
of conductor
establish
the
is also changed-so
the
in a series
between
vertically
into
Tl and
tensions
HI and Hz are equal.
tension
length
these
suspension
These
units,
insulator
are made
shall
level
about
sheaves,
the amount
entire
sags and
based
length
span
The
from
running
the conductor
offsets
on exact line.
metric
concern;
on
line
and
lengths
the individual
For
the
the
directly
including
it is necessary
of span
lengths
into
final
right,
If
based
complex.
lower
is in the
upon
are also based
conductor.
wires,
range
of span
at the same
spans
much
may
ground
based
as to cover
Sag and Insulator
(b)
for
important.
are not
design
he exactly
increments.
span
extremely
wires
calculations will
the entire
is unstressed,
an extent
in lo-ft
structures
the
sag values
to such
span
cover
approximately for
the
strengths,
separately
to be installed
and
complete
calculations
and overhead
which
to a substation
span
Stringing
expanded
line,
used on the rest of the transmission
of a stringing
prestressed.
ground
he disastrous.
spans
values the
of the
are
overhead
of the
sizes and
None
sag data
and
design
of conductors
spans
that
at the
the
are computed
for approach
Tables-Stringing
conductors
for
may
suspension
Dead-ended tension
used
is wrong.
far off-the
prepared
Sag the
of structure
clearances
are too
data
Data.-(u)
LINE DESIGN MANUAL
be clipped
and
The
to end
the point
selection
of line,
calculations. The insulator string ofthe in) must be held in a vertical position
last previous temporary while the next section
The tension in the conductor while after the suspension clamp is clipped
in the stringing to the conductor,
or lower than the tension insulator string clipped
in may
the
line
is brought
swing
to the
towards
proper
or away
of
should of
sag.
from
new
section
sheaves may be higher so the last suspension of line
being
brought
to sag if the
insulator
is
CHAPTER
V-ADDITdONAL
DATA
293
Figure 116.-Conductor tensions running stringing sheaves.
not properly held sagging and clipping to sheave a reference string clamp for
sag by mark
in a vertical position. in of the conductor
is equal
to the
and
sag correction
at any point
in a conductor
length
of the
ordinate
data
is given
of uniform of the
curve
in the
error in the is brought
sag plus correction) of several spans, under the point where each insulator
following
cross section at the
using free
vertical, a serious After the conductor
Clipping in is then started at any structure by placing offset distance and direction from the reference mark.
offset
Procedure The tension
is not held could occur.
checking the corrected sag (stringing chart should be placed on the conductor directly
is supported. at the proper
calculating
If the insulator in the new section
when
given
the center of the suspension An explanation of a method paragraphs.
suspended point
in the form times
the
unit
of a catenary force
conductor. At
support
A on figure
117:
Directrix 2
+”
1
Figure 117.-Dimensions required for calculating stringing operations. 104-D-1 119.
insulator
offset
and sag correction
data during
of the
294
TRANSMISSION
LINE DESIGN MANUAL
T, = WYA in span 1
+Y, - Y,)inspan2
T, =W(YA
T, - T, = W(Y, - Y,)
where : W = force of conductor in newtons per meter (pounds per foot) T, and T, = conductor tensions in newtons (pounds)
= difference in elevation between the directrices of the two cantenaries, which is also the difference in elevation between the low points of sag in the two spans, in meters (feet)
y2 - Yl
A table with the following column headings should be made: Column 1: Station number. This shows the survey station 2: Span length L, in meters (feet) 3: Yz- Yt in meters (feet). This value
Column Column
the low points at the stringing be essentially sheets. Column
4:
of sags in spans adjacent temperature; however, the
same
at any
W(
yZ- Y,),
given
( W)
(col.
shows
the
where
each
difference
structure
in elevation
is located. Yz- Yl between
to each structure. These sags should be the initial sags because the difference between sags in the two spans will Ys- Yr may be measured on the plan-profile temperature, 3),
in newtons
(pounds).
This
value
shows
the
Tz-Tl, on the two sides of the structure. between the conductor tensions, Column 5: Assumed tension Hin newtons (pounds). This value shows an assumed component Hof the tension (called horizontal tension for convenience) in the conductor in the stringing at the stringing
sheaves. For temperature
this assumption, use the initial horizontal as shown on the sag-tension calculation
difference horizontal as it hangs
tension of the conductor form. Assume this tension
to be in a certain span (generally, it is best to use one of the longer spans) and compute the tensions in other spans by adding or subtracting increments from column 4. (pounds). This value shows the difference between Column 6: H,H, (& -col. S), in newtons the horizontal
H
in each Column
tension span with 7: Offset
in the the Kin
conductor
conductor millimeters
at the
ruling
K= lOOOW2 L3 mm/N 12H,,3 This value in tension. slack per Column in slack in this
shows the change The sum of the
column
span
corresponding
is the overall
or K=-
change
and
w2 L3
in slack in a span corresponding values in this column gives the
pound) change in the tension 8: Trial offset, (col. 6) (col. for each
Ho
span
the assumed
horizontal
tension
hanging in the stringing sheaves. per newton (inches per pound).
for the complete 7), in millimeters
to the of slack
unbalanced
Hl13
in/lb
to a one-newton (one-pound) change total change in slack per newton (or section of line (inches). This
tensions.
for the complete
The
section
being value
considered. shows the
algebraic of line,
based
sum of the
change values
on the assumed
CHAPTER tensions. sum the
This
is a positive line.
The
sum
must
he zero
value,
If the
sum
should
sum
of column
be applied
that
to the
Ho-H
9:
Column
10:
Column
11: Modulus
by
Corrected
offset,
of column
(col.
295
has been
he subtracted
sum
he added
to the
7 is the
assumed
in each
from
complete
the
complete
total
span.
section
section
correction
If the
of the
in tension
of line.
which
of line.
column
correction
must must
section
corrected,
DATA
tension
amount
the
complete
correct
of slack
that
8 divided
Column
if the
amount
is negative,
V-ADDITIONAL
6 - (2 col. 7)
(col.
8/X
col.
7), in newtons
9), in millimeters
in millimeters
(pounds).
(inches).
(inches)
1OOOL (col. 9) mm or AE
12L (col. 9) in AE
where : A = area of conductor in square millimeters (square inches) E = modulus of conductor in gigapascals (pounds per square inch) Column
12: Final
correction
in millimeters
(inches).
(Z col. 10 + x col. 11) (col. 7) z col. 7 Columns (col.
9, 10, 11, and
11) is the
in columns corrections
in length
13: Final
amount Column
the amount
of the
11 should
proportional
Column the
change
10 and
12 are used equal
of offset
(col.
required
14: Sum
of offsets,
necessary
to offset
span.
(running
sum
insulator
change
be made
in column
13),
in millimeters
string
from
the vertical.
in millimeters
modulus
The
sum
correction of the
values
in either
of these
12 to offset
these
remainders.
(inches).
This
value
shows
(inches).
This
value
shows
12), in millimeters
of col.
spans. while in sheaves
The
in tension.
is a remainder
11 + col.
in each each
of the offsets in the individual Column 15: Sag correction
must
col.
in the offsets.
with
If there
length
10 +
corrections
conductor zero.
to the span offset,
to make
This
offset
columns,
is the summation
(feet)
(3H, )(col. 10) (3H,,)(col. 10) (2W)(col. 2) mm Or (2W)(col. 2) (1/12) ft
This
column
conductors
shows
are in the
the
amount
stringing
that sheaves
will
be necessary
to obtain
to correct
the
correct
the sag in each
sag after
the
span
while
conductor
the
is clipped
in. The long rough and
offset
as the terrain accurate
and
sag correction
individual where
offset the offset
computer
data
as computed
for one span
is not
in any one span
program
should
in such in excess
in a section
be used
instead
a table
should
of 381 mm of line
of
may this
(15 in).
be sufficiently For
accurate
installations
exceed
381 mm,
simplified
method.
a more It
as
on very detailed is usually
TRANSMISSION
296 unnecessary in one
to consider
operation,
the
the
offset
and
corrections
LINE DESIGN MANUAL
sag correction
calculated
data
are within
if, in a section all three
of line
of the
following
Line conductor mm w (1) Maximum summation of offsets at any structure (2) Maximum difference between summations of offsets at adjacent structures (3) Maximum sag correction in any span
The
same
conductors
procedure should
A sample
as described
he used
problem
for
to calculate
has been
worked
out
in both
kcmil),
ACSR,
sagged
limits:
Overhead ground wire mm (id
(6)
76
(3)
76
(3)
51
(2)
305
(12)
305
(12)
the
data
is being
152
calculating
similar
that
for
offset
the
metric
and
overhead
and
U.S.
sag correction ground
customary
data
for
line
wires. units
to illustrate
this
procedure:
Example Conductor: Full
load
644 mm2 conditions:
Maximum Initial
tension tension
(1272 13-mm
under
at 15.5
(l/2-in)
full ‘C
load
(60
45/7
radial conditions
“F)
(Bittern)
ice with =
is 26 040
a 0.19-kPa
53 378
N (5854
(4-lh/ft2)
wind
at -18
’ C (0 ’ F)
N (12 OOd lb)
lb) widh
a korresponding
sag of 12 485
mm
(40.96 ft). Area
of conductor
A =
Initial
modulus
of conductor
689 mm2
AE = 32 162 542 N H,, = T- Ws = 26 040 -
Initial
E
(1.068 =
(7 230
46.678
Figures shows
in the
118 and 119 the stationing,
procedure
is shown
GPa
(6.77~10~
lb/in2)
=
N
360 lb)
(20.9277)(12.485)
= 5854 - (1.434)(40.96)
120
in2)
25 778
= 5795 lb
show the sag and tension calculations elevations, and span lengths for the in tables
36 and
37.
for the given conductor, and figure sample problem. The table described
CHAPTER
OCm-678
V-ADDITIONAL
DATA
297
(3-78)
:":nT:"L' SAGCALCULATIONS
Ml
2 CONDUCTORst'jmm R/7%7"
//3Sf
.4547
LOADING&
Code Nams
Linear Force Fnclor:
@3
Rated Breaking Strength/q Diameter .A
N
Dead Load Force (W’) i?t&d!
Permanenr set 0.00 Qa. CreepO.OOQ
*s
Tenston Llmlt*tions: Initial.-
%.Ai-K-
Final.!.
;;;“y+f$-
N 25
8g9
N
o.ow
Exp.: jc
A=
Initial
+!ZZt// Final AE
OzL&perOC
Dare ~
Initial */977
T~cp-/UNSTRESSEG LENGTN
LOADING Ice
HEX.
./
N/l? Modulus. (E) Final &.c&&-
Temp. Coeff. of Linear
%-
Computed by
yd,
sqj
Total O.CQd6?
Area (A)amd
-N
Final .- 15.5% .-
,“;
(W”‘)
Resultant:
% -N
Loaded.~oC.5oW
/dn?m
N/m
mm
jb.
GPa
/,,79
44I//9
GPa
009
AE .&
,”
x=d3782
SAG, mfn
1 SAGFACTOR /
3 '; I SPAN LENGTH(S
1
SW,N
1
TENSION, N
NO Ice. No Wind (W’)
Figure
DC-578
118.Sag
and tension
calculation
form for example
problem
on insulator
offset
and sag correction
(metric).
(3.73)
!;,p CONDUCTOR&J
7
Code Nams
Riftcrn
Rated Breaking Diameter Tenston
LOADING k'eavv
14, Load
J!!.?+
Weight Factors: ,?
,
/ofi
Dead Weight
lb + ‘/Lin.
inch
Llmltatlons: o
lb
Final *OF*%-
Compuled by -
LOADING
IbItt 3,gy
0
Wind Resultant:
lb OFa%-
(W’) ./,
Ice (W”)
&lb
Initial ,OF&s. Loaded, Final. *OF-
SAGCALCULATIONS
jb
Area (A) /,& in2 Temo. Coeff. of Linear Exp.:
lb
Total
0.000 0 a
jc
TEMP.. oF UNSTRESSED LFJGTH
i!
per “F
1
Modulus. (E) Final 51.36 Initial mx
f=o.3/
x 103 lb/i&? 105 lb/in2
NE% lzl
k=O.&7 SAGFACTOR 1
Y
0.00~~.
:iIi:
?R/977
% -lb Date
7
Creep o.ooni2f-
78/T
3.‘0073
(W”‘)
Permanent Set O.OOti?
Ib/ft
SAG.fl
A”,’ +z?z?-
1
SW,Ib
:,”
1 TENSION,Ib
SPAN LENGTH(S) -FEET
No Ice. No Wind (W) 120
Figure 119.~Sag customary).
I/,nn3
and tension
922 IO. d/l/3 a & 7 lo. QQ&&@
calculation
form
/ I / 1
for example
I
problem
I
on insulator
i/hi/9. JL49.
offset
/
I
/
I
and sag correction
(U.S.
298
TRANSMISSION
LINE DESIGN MANUAL
365.76 (1200)
457.2
-I
335.28
(1500)
426.72
(1400)
396.24
(1300)
(1100)
g + E 03
\
fcr; .l”.J.
j 7c I ”
fImn\ \trvv,
-. -.38 (1225)
304.8 (IqOO)
*.
381 (1250)
\x L
335.28
(D g
I
(1100)
\ylooo~
A 2 243.84 ZOO)
I
Y-1
213.36 (700)
182.88 (600:
1 All values shown are in meters (feet) 152.4 (500) Figure
120.-Profile
of spans for example
problem
on insulator
offset and sag correction.
104-D-1120.
Table 36.-Data from example problem on insulator offset and sag correction (metric) 1
Station
2
SP k@h L.
3
4
y, - y, . In
m
WY2 - Yt) W(3), N
5
Asrunltd H, N
6
7
Ho-H. H,
- (5).
N
20+72.64 365.760 24+38.40
28642 -50.597
27583 -41.148
-861
-45.110
-944
-1805
.08030
-944
(6) _ z
(8)
(7)(9),
2:0’N
-
13
Fhul mnectlon
lOOOL(9)
[Z(lO) + Z(11#7)
AE’ mm
Z(7)
15
14
FiMl
sum of
ofr33t
ofY3et3
(lo)+ (ll)+ (12). “E). '
mm
.% cofr3ction whikln
SiHwus 3Ho
(10)
2wo’ mm
mm 0
-299
-2445
-255
-28
0
-283
-43.5%
-912
-52.121
-1091
358.140
-13%
-145
-111
-14
0
-1288
-125
-612
.11091
-105
-525
-58
-6
0
-287
-64 -472
25778
365.760 38+93.82
0.104 26
-2864
(6) (7).
Corrected Corrected Moduhu Ho-H offat correction
12
-408 26722
381.000 35+28.06
1000 3Ls 3 128s , mm/N
Trill OffwA
11
-283
373.380 31+47.06
K
10
9
-1059
335.280 27+73.68
8
othet pr Newton
0
,117
84
0
419
49
5
0
238
54 -418
24 866
912
.I0426
95
1331
139
15
0
154
2003
.09788
196
2422
237
27
0
264
702 -264
23775
42+51.%
1223 0
Tot&
0.615
45
-258
l1
-
-1
Numbers in parentheses are column numbers.
Table 37.-Data from example problem on insulator offset and sag correction (U.S. customary) 1
2
3
4
W(Y,-Y,) W(3).
lb
5
A33llmd H, lh
6
7
8
Ho-H.
0ff33t po:d
Ho - (5).
K
lb
W2L3
Trial off3et (6);)~
10
9
cofaected fim
offmt
Ho-H (6)-z,
11 Modulur
12 FillsI
13 FiMl
14 Sumof
whikhl
(7) (9h
3heavel
la
Ho3.
lb
in
3Ho
1200 8o+oo
91+00 103+25
1100 1225 1250
115+75
6439 -lag
2W(2)
ft
-194
-148
-212
-171 1175
-549.6
-10.04
.014 06
-5.725
-311.6
-4.38
-117.6
-2.28
26
-1.09
0 0.0017
-11.13
-0.57
.0013
-4.95
6201
-4%
6007
-212
.01942
-4.113
5795
0
.02064
0
-0.24
.0018
-2.52
55%
205
.01826
5345
450
.01714
94.4
1.95
0.20
.cm19
2.15
3.751
299.4
5.47
0.60
.0017
6.07
7.695
544.4
9.33
1.06
.0016
10.39
-205
1200 127+75
-11.785
0.018
-238
-135
-143
-644
-245
139+50
TOti Numbers in parentheses are column numbers.
-0.107
-78
(10)
-
in
in/lb 68+00
15 SW w ‘II
-10.177
+a05
-0.04
-11.1 -16.1 -18.6 -16.4
-4.2 -2.0 -0.9 0.8 2.3
-10.4 0
4.0
-1 0 12 ,
300
TRANSMISSION
31.
Transmission
Line Equations.-If
and there are no later reroutes; in numerical notation and there start
work
on the
equation
will
Assume crew
the line,
also
that
starts
same result
two
from
4752
2370+66.4
while
second
this point is Sta. 2370+ 66.4Bk belongs to the part of the line that station in the two other
crews
(fig.
121).
is surveyed
from
one end to the other,
he one
of a line ends
meet
or more
after
of a line station
equations
a survey
and which
at a common
toward
is the point
crew
designates
it as Sta.
2374+31.2.
in the
has been
work
on the
line,
the
The
200+364.8 If the station and the length If the
length
ahead line
These
is greater
is shortened
One
length they
will
common
equation
of each
point
as
to identify
= Sta. 2374 + 31.2Ah. The Bk means backand indicates that station behind the common point. Similarly, Ah means ahead and indicates
lengths
may
of the common point. will be 475 200-364.8 be in meters
or feet,
There is a difference of 364.8 = 474 835.2 if there are no depending
= 475 564.8 if there are no other equations (fig. 122). back is greater than the station ahead, then there is an overlap of the line is increased by the amount of overlap (fig. 123).
station of the
An
other.
on the
units
Assume the crew which started at the beginning of the line determines that the meeting Sta. 2374+31:2, and the crew starting at the end of the line says the point is Sta. 2370+66.4. equation will then read Sta. 2374+ 31.2Bk = Sta. 2370+66.4Ah, and the line length will 475
line.
completed.
each
approximate
point, but the values will be different. at the beginning of the line designates
belongs to the section of line ahead designations, and the length of line
equations
will
at an assumed
the two
that common which started the
there
at opposite
other
line
equally spaced stations will increase uniformly in the line. However, if two or more survey crews
of a portion
start
the
+ 00. When
have a station value for Assume that the crew Sta.
and
points,
a reroute
crews
0 +00
a transmission
then all successive, will he no equations
at different
survey
at Sta.
say Sta.
line
LINE DESIGN MANUAL
than by
the
the
station
value
back,
of the
length
then
there of the
of station
is a gap in the gap
(fig.
124).
used. point
is The then be
designations
stationing
and
the
2360+002360+00 -
2370+00 2370+00-
on 2374+31.2Bk
EQUATION on 2370+66.4Ah
-1
:--I
.J
r ---I Station
2370+66.4Bk-
EQUATION St&ion
2374+31.2Ah
1
I 1 I L
---me
I
1--1
2380+00-
2380+00-
TRANSMISSION
302
Figure 123.Station ahead
Figure
124.-Station
LINE DESIGN
designations
designations
when station
when station
MANUAL
back is greater than station
ahead is greater
than station
back.
<< Bibliography [l]
“Rules
for
Public [2]
Overhead Utilities
“National
Electrical
Electrical [3]
and
“National
and
Martin,
Ehrenhurg, D. pp. 719-728,
[6]
“Copperweld
[7]
Rodee,
H.
[8]
Bissiri,
[9]
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750 Third
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TRANSMISSION
304 “Stress-Strain-Creep
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750
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Pa.
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vol.
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Tension,
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and Wire
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<
A
A METHOD FOR COMPUTING TRANSMISSION LINE SAGS AND TENSIONS IN SPANS ADJACENT TO A BROKEN CONDUCTOR A thesis by G. R. Wiszneauckas’ I-INTRODUCTION Description
of the Problem.-The
determination
of sag and
conductor or cable under various conditions of temperature the mechanical design of a transmission line. It is of equal of sag and tension from the simple cases of symmetrical nonsymmetrical to a broken
and special spans, none conductor. The determination
special case for the reason such as railroad, highway, national
and/or
Purpose of the
local
conductor
thesis
which
methods
now
date, several methods or techniques have problem; however, in many of the methods
Study
of Initial
in this
case all such
in of
adjacent in this
is to develop
a technique
been proposed rather severe
for the solution limitations have
assumed for any particular problem without making Another somewhat undesirable aspect common to procedures. These factors set forth the purpose
or method
by which
the
sags and
while accounting in essence the
tensions
to some trial-and-error
in a series
degree for the aspects of
in use.
II-DEVELOPMENT OF A TECHNIQUE STRESSES DUE TO A BROKEN
that is before the tensions, and span
any
of structure heights necessary at critical points or power line crossings in order to comply with
of spans adjacent to a broken conductor can be computed asymmetries present in any particular case and eliminating the
for
codes.
been imposed in that level, equal spans have been corrections to account for existing asymmetries. most methods is the time consuming trial-and-error of this
tension
least of which is the case of a series of spans of sags and corresponding tensions is important
that it assures the designer waterway, telephone line,
safety
of Thesis.-To
broken
the
corresponding
and loading is of basic importance importance to extend this determination spans to the more complicated cases
and Final
Conditions
.-In
the
broken
conductor breaks, is one of static lengths known. The final condition quantities
are unknown.
The
307
This
conductor
equilibrium is likewise
diagrams
’ Former Electrical Engineer with Bureau of Reclamation. Science from the University of Colorado in 1949.
FOR ANALYZING CONDUCTOR
shown
method
problem
the
initial
condition,
with all quantities such as sags, one of static equilibrium; however, in figures
1 and
2 have
been
given
was his thesis for the degree of Master
of
308
TRANSMISSION
to illustrate in general these initial and final insulator strings and their deflections have other elements of the spans shown in order consideration. A study of figure 2 reveals the complexity in order to maintain static equilibrium after a method for treating this problem by not been made temporarily: (a) (b) (c) (d) (e) (f)
LINE DESIGN
MANUAL
conditions. In figures 1 and 2, as in those following, the been shown somewhat exaggerated as compared to the to present a more readable picture of the features under of the conditions which must be satisfied simultaneously the conductor breaks. To facilitate the development of complicating it further, the following assumptions have
Level, equal spans exist before the conductor breaks. Conductor breaks at mid-span. No deflection of supporting structure as a result of the conductor breaking. No slipp in g o f conductor in its clamps as a result of the conductor breaking. The changes in elevation of the conductor after the conductor breaks are negligible. The insulator acts as a rigid body.
After a procedure has been established for dealing with the problem under the above assumptions, criteria will be presented by which assumptions (a), (b), an d (c) can be removed entirely. For most cases the assumption made under assumption (d) is valid; however, conductor clamps are sometimes set to slip at a predetermined tension, in which case this assumption may not be in order. The assumptions made under assumptions (e) and (f) are reasonable for all but very special cases. Further study of figure 2 shows that the forces acting as a result of a conductor breaking can be resolved into two opposing horizontal forces. Herein lies the basis for the technique which has been developed. Study of the P Force.-Referring again to figure 2, the horizontal force designated P is the force which retards or damps the effects of the broken conductor and may be considered as the equal and opposite of the force required to deflect an insulator string by any angle 0 while a vertical load is acting. The relation between this force, P, and the vertical load can be developed from figure 3. Again, assuming that the insulator string acts as a rigid body and also that its gravity axis is midway between the conductor and the attachment hinge, the following relations can be written: For equilibrium at any angle 8, Wd = P ‘v or P ‘= Wd/v. Also, cos 8 = v/i and tan 8 =’ d/v = P/W from which P = Wd/v ; therefore, P = P : Also, P = Wd/i cos 8, which is a form more convenient for calculation. Insofar as the broken conductor problem is concerned, this relation should be interpreted as: P is the horizontal force which resists the movement of an insulator string of length i from the vertical to any angle 8 while a vertical load W is acting. Study of the H Force.-The horizontal force designated H in figure 2 is the horizontal component of tension acting in the conductor or cable. Insofar as the broken conductor problem is concerned, the relation between this force and a change in span length, such as might be caused by the deflection of an insulator string, is of primary importance and can be developed from figure 4 as follows: The length of conductor in the initial span is:
I =*fJo 0-
W
WLO
sinh -
*HO
APPENDIX The
length
of conductor
in the
span
after
a change
309
A of 4 is:
I, =-24 sinh w(L, -#I W
The
change
from
Ho
in conductor
HI
to
length
24
due to the elastic
properties
of the conductor
in changing
the tension
is:
U-4,- H,) U,) AE Then,
barring
temperature
conductor length length is increased
By substituting
and/or
plus or minus or decreased,
the
values
loading
changes,
the
change
in the
II
le,
the elastic i.e.
found
above
for
and
final
conductor
conductor
length
must
depending
equal
on whether
the the
initial span
2Hl sinh W
w(Lo _ @) or sinh
2H,
=
HI
and solving for Cp: k. $=L,
By way of interpretation, 4, the horizontal tension
The forces
Relations become
of which will figure 11. Consider which also
Between
the aids
from
P in the
a simple
+, Hoi:J
SinhO’
this means that when in the cable changes
invaluable progress
- ‘G
sirthzi(l
and
H
solution special
a span from
of length to
Ho
Forces.-The of the
L e is HI.
changed
relations broken
case as shown
as developed
conductor in figure
first the case of a conductor breaking in a span adjacent outlines the conditions to be satisfied simultaneously
in length
problem, 5 to a general
by an amount
for the
the
P
and
H
development
case as shown
in
to a dead end as shown in figure in order to maintain equilibrium.
5,
TRANSMISSION
310 Although
these
common presented:
conditions
are
trial-and-error
If the
P
and
simple
procedures
H
relations,
and
LINE DESIGN few,
considerable
to evaluate
previously
MANUAL
them.
developed,
effort
In
could
contrast,
are plotted
the
with
be expanded following
a common
in using
solution system
of coordinates
as shown in figure 6, the resulting curves will intersect at some point which, upon examination, prove to be the only point in the system which could possibly satisfy simultaneously all necessary
and
sufficient
to demonstrate lies,
for
this
instance,
conditions
solution above
which
the
point
must compare
The and
value of d will be less than likewise, will be greater than
there
with
are any Pand
Hcurve.
the
number
value
of points
H curve-which
d which
trial-and-error procedure
Compute Knowing
the
to the
value
value
this
of
6 has been
given
Hcurve
which
of the
be apparent
of Hat
to a value
Figure
any point
should
or conditions for which P= also the other necessary
point,
P which
that note
the
the
equals
the
solution
value
of 4
value
of
H
H, there condition
is only that
one-the
intersection
d = $.
of this more or less special case, consider next the case of a conductor dead end as shown in figure 7. In this case an additional set of
commonly
(1) Referring to figure which would be HI. Also, of P1. (2) (3)
by studying Pcurve-it
corresponds
to maintain equilibrium. Pand Hcurves no longer
case; however, these required conditions.
procedures are as follows:
solution.
will of the
the value of 4 for every point so selected above the intersection, do for every point below the intersection. Note then, that although
must be satisfied in order the intersection of the basic
as in the previous satisfy all of the
the
it is the
satisfies
As a step in the generalization breaking two spans away from conditions seen that
with
Corresponding of
hence,
can be substantiated
intersection
and
of the
lie on the
for equilibrium;
the
has been
of
to figure 8, it can easily be all of the required conditions
basic curves can be manipulated A method for this manipulation used
in other
7, assume a value for based on the assumed
Hz, compute
Referring satisfies
methods.
essentials
of such
which from
will the
a trial-and-error
d 1 and compute the corresponding new tension value for d 1, compute the corresponding value
Hz by subtracting the
The
to obtain values can be derived
corresponding
PI from value
HI.
of 4s.
(4) From this value of $2, the value of dz can be determined by the relation: dz = $2 + d 1. (5) Pz can now be evaluated since it is a function of dz. If this value for Pz is equal to the value computed for H 2, the initial assumption for the value of d 1 is correct and all other values computed are correct; however, if this is not the case, then a new value must be selected for
dl and the entire
procedure
repeated.
value of d 1 which can then be found for HI, Hz, and d 2 can be computed.
Usually, by
three
interpolation,
Based on this procedure, a straightforward graphical possible values for dl were assumed, then all possible from which all possible values of Hz could be found.
or four
trials
and
corresponding
the
will
bracket
the correct
correct values
analysis can be developed as follows: if all values for HI and PI could be determined This can be accomplished very easily by
subtracting graphically, point by point, the abscissa values of the basic Pcurve from those of the basic Hcurve. The resulting curve then represents the locus of all possible values for Hz with respect to d 1. In similar manner, the graphical addition of the ordinates of the newly formed Hz curve, which represents represents all possible all possible
also the locus of all possible all possible values of 42, will values values
values of d 1 to the ordinates result in forming a new curve
of d2 and also represents all possible for Hz with respect to corresponding
values values
of the basic H curve, which which represents the locus of
of Hz with respect of dl and d2 have
to dz. Now been defined,
that all
APPENDIX that
remains
to be done
conditions.
Referring
is to determine
again
to figure
which
A
311
of the
8, it should
possible
be evident
values
that
some
will point
satisfy
the
on the
newly
ds curve will satisfy the conditions required in the conductor. As in the previous case,
at the insulator it will be found
string immediately adjacent that there are any number
this
condition
ds =
curve
which
seen that which
the
can satisfy
to the break. can
will
b, note
The
next
step
necessary
simple
Hz in the
and
for this required
case that only in the previous
for
bon
of the
away from to the two
the
4s
equilibrium
+
dl.
at the
first
Hcurve
at the
second
would
the
only
insulator
string.
be
point
adjacent
point
which
In
regard
from
point
down
H curve.
basic
be to add
only
string
to be the vertically
to intersect
it can
u) is the
insulator
formed
to the break of points on
inspection,
(point
it is determined-project problem
By
ds curve
the basic
horizontally
generalization
nature in which the is moved away from
and
for equilibrium
in which
thence
that
Pcurve point
conditions
make the dead end three spans interest to note the similarities and interrelated conductor breaks
prove
manner
curve
basic
conditions
will
necessary
the
the
necessary of the
inspection
all of the
a to intersect
the point
all of the
Further
satisfy
to point
satisfy
intersection
required
another
span
in the
series
to
the break as shown in figure 9. In this case it will be of previous cases. Of special importance is the progressive
requirements the dead end.
for equilibrium By comparing
occur as the span in which the these requirements, it will be seen
one set of conditions is needed to maintain equilibrium in addition case in which the conductor breaks two spans away from the dead
to those end. Also,
though it may not be immediately apparent, the graphical analysis as developed for the previous case can be utilized in its entirety and requires only an additional step to account for the additional requirements for equilibrium in order to provide the complete solution. This additional step is one which of the
is in continuation possible
values
values
H3 with
of
of those
graphically, point of the dz curve
found respect
for to
taken
d 2, the
in the
previous
corresponding
case,
and
possible
dz can be determined.
This
consists
value can
and
Based
can
be substantiated
on these
can be outlined
special
from
which
all
all possible
by
subtracting
from the corresponding all possible values of
corresponding values of da can be determined by adding graphically, ordinates of the basic Hcurve-thus of the H3 curve to the corresponding which represents the locus of all possible values of H3 with respect
case
from
be accomplished
by point, the abscissa values of the basic Pcurve thus forming a new curve, Ha. Then, knowing
manipulations have been shown in figure 10. Also indicated points a, 6, and c. These points were obtained in a manner
of determining
of Ps
values the
Hs,
point
by point, the ordinates forming a new curve, df, to da. The results of these
is the solution which is represented by similar to that given for the previous
likewise. cases,
a procedure
for
solving
a general
case
as represented
by figure
11
as follows:
(I) Compute and plot values for the basic P and H curves as shown in figure 12. (2) Subtract graphically, point by point, the abscissa values of the basic Pcurve from the abscissa values of the basic H curve to form a new curve, Hz. (3) Add graphically, point by point, the ordinate values of the new Hz curve to the ordinate of the basic H curve Subtract graphically,
values (4) abscissa (5) values (6)
values
of the
new
to form a new point by point,
dz curve
curve, dt. the abscissa
to form
a new
curve,
values
of the
basic
Pcurve
from
the
HS.
Add graphically, point by point, the ordinate values of the new H3 curve to the ordinate of the basic H curve to form a new curve, d 3. Continue this composition process of subtracting abscissa values of the basic Pcurve
from
those
these
new
of each Hcurves
succeeding
d curve
successively
to the ordinate
to form
new values
H curves,
and
of the basic
add
Hcurve
the
ordinate
to form
values new
dcurves
of
TRANSMISSION
312 until
the
d,, and
be represented
H,, curves
in which
the
indicates
point
(-)
(7) The the d,,curve adjacent
are established.
symbolically H-
p=H2
+H=d, point
point
to the
conductor
to the
curve
and
to the
dn-z
across Each
intersection
insulator
span
insulator of each
by point
which
. . .H,
as described
above
can
+H=d,
of abscissa
ordinate
string
which
and
values
values
of curves,
and
the
(+)
of curves.
tension to the
and
of the
converging
by the
above
horizontal and
curve
across
down
corresponds
is identified
as described
the
H,, curve
and the tension in each span and the corresponding
procedure
+H=d,
subtraction
of the
break
break,
the
procedure
solution is then found graphically by stairstepping down from the intersection with the basic P curve, which defines the deflection of the insulator immediately
conductor
of the
composition
- P=H,
addition
to the
is reached.
The
as:
indicates by
LINE DESIGN MANUAL
to the
H n-z
stairstep
to the
same
in the dn-l
with
down
etc.
until
the
a d curve
of the
Having
immediately and
curve,
subscript
subscript.
span
curve
curve
established
defines
of
adjacent to the
basic
Hn+
Hcurve
the
deflection
the
tension
and
also
the
deflections
in
of each
span from the conductor break to the dead end, the length sag can he computed by any standard method. The stairstep
can
be represented
symbolically
as:
0d,, in which vertical
d,, X P indicates projection down
horizontal
projection,
left
the intersection from one curve to right,
from
of d,, and to another, one curve
P curves, the vertical and the horizontal
to another.
The
circles
arrows arrows indicate
indicate indicate
a a
intersection
points of the stairstep with d curves, which points describe insulator deflections and conductor tensions. From the procedure as outlined to this point, a question as to the physical possibility of constructing all of the indicated number of curves for a case in which the nearest dead end is a very great number immediately
of spans away from suggests trying to find
the the
conductor limiting
break might logically be raised. Such locus of the d, and H, curves. Fortunately,
be done with a fair degree of accuracy. By following the procedure six d and corresponding H curves have been constructed, a tendency regarding the space relations of the intersection points of the dcurves examining will very
these space relations closely, it will be found that a geometric closely describe this tendency. Then, it is but a simple
convergence point of the
and find d,, curve.
its sum which, The location
a question this can
as outlined above until five or of convergence can be noted with the basic Pcurve. Upon series matter
can be arranged which to test the series for
if existent, will describe the space relations of the intersection can be established by drawing a curve through this point and
the Ho point such that it appears to be a member of the family of curves thus far established. many cases, this will be a straight line for practical purposes. From the d,, curve, the H, curve easily established by subtracting abscissa values of the basic Pcurve, point by point, from those the
d,, curve.
By stairstepping
with the basic Pcurve to the on the d,, curve, the insulator
down
between
Ho point, deflection
these
curves
from
the intersection
and noting the intersection points and tension value for each span
point
of the
of the converging progressing away
In is of
d,, curve stairstep from the
conductor break will be defined. These points present an interesting relation in that regardless of the distance to the nearest dead, end, the effects of a conductor breaking will be damped out for practical purposes in a very few spans. This is in agreement with statements made by other authors on this
subject.
Figure
16 illustrates
in detail
a solution
for
a typical
problem
by
this
procedure.
APPENDIX To substantiate Since
the validity
d, and
the
of stairstepping
H,, curves
represent
curves, it should be evident that for practical purposes one could
d n-1000 Hn-2,
curve.
Likewise,
curve.
be equally
Therefore,
number of curves in the family purposes, to operating between
appear
academic
encountered from
in practice
the
break
in the
Pcurve far
and
force
to ensure
scale.
This
be attained cross-section cases. Criteria adjusting
as the
since
it can represent
for
the
the
case in which
the
H,,
the
H,, curves previously this aspect
majority
Hn-l,
the
end
the
to represent given of the
such
reduces, analysis
of preliminary
dead
of
together that d,,-2, or even the
for may
problems
is beyond
a few
spans
conductor. feature inspection
that
feature
of this entire in a manner
is approached and not some other the question of accuracy. As with the other curves drawn offer sufficient
Assumptions .-The far to accommodate
following problems
spans,
it should
than the exception, and that any method which does not recognize this fact and the problem.
be realized
for dealing offers some
that
point on the horizontal methods, accuracy can
on a standard llaccuracy for all but
by 15-inch very special
is an outline of procedures for with asymmetries, such as unequal
and with other variables, such as deflections break which were initially assumed constant.
nonsymmetrical
the results can easily be shown in figures 4, 6, 8,
the d, intersection point with the basic is, reversing the process of composition)
Ho point
the
prompts
spans, conductor
procedure is that such as has been
should be taken to check by resolving them (that
for Removing Initial the method developed thus
and
for
as follows: number
close
between
d, and
the
reason
of an unlimited
to be so indescribably the d,, , the dn-l,
solution
any
H, curves,
positions
to distinguish
to any degree desired. With this method, sheet as shown in figures 16 or 17, should
and nonsymmetrical the point of the unequal
will have between
d, and
the
that the stairstep formula the d, and H, curves. While
it serves
connection, care d,, and H, curves
the
enough
limiting
difficult
actually
Another interesting and useful checked either graphically or by 10 or 12. In this
only
the
it is possible
a great practical
only,
between
in theory
these curves not distinquish
it would
Hn-looo
or the
313
A
such
in supporting In dealing
a series
of spans
structures and with a series of is the
rule rather
with problems regarding such a series of spans means to account for it-is not doing justice to
Two criteria can be used to adjust the method developed thus far to account for such asymmetries and variables. One offers an approximate correction at the expense of very little additional work and is suitable for use in making preliminary studies and estimates. The other offers a comparatively exact solution
but
requires
much
more
a high degree of accuracy. The approximate correction any series of random-length symmetrical
spans
same distance problem, the in a conductor
which
will
work
and
is suitable
for
use in connection
is based on the Ruling Span Theory which symmetrical spans, there can be found have
the
as the random-length implications are then, and the nearest dead
same
horizontal
tension,
the
same
with
problems
requiring
states, in effect, that a series of equal-length
for
total
the
slack,
and
cover
series of spans. Applying this theory to the broken conductor that for any series of spans which might exist between a break end, there will exist one series of equal-length symmetrical spans
which will best describe the characteristics of the existing series of spans. If such-an equivalent series of spans can be established, the method, as developed, can be applied. In order to establish the equivalent series of spans, a means for determining the equivalent level or symmetrical span for any inclined or nonsymmetrical and is given by a relation * Numbers
in brackets
span as:
will
be required.
refer to items in the Bibliography,
Such
a means
section VI.
has been
developed
by Martin[8]*
TRANSMISSION
314 Equivalent
level
20 percent This and
relation leaves
spans.
span
=
2 (inclined
span
makes
possible
one
can
the
condition
be done
conversion
yet
of any
The
ruling
The
the more
- (horizontal
span
by using
length
solution
a relation
is then
the
of a typical
exact
correction
series
to be fulfilled-that
span
length).
(Safe
limit
=
by
into
a series
of symmetrical
an equivalent
series
spans
of equal
length
of spans.
Figure
Still[6].
length
problem
of spans
of finding
given
Ruling span length =
16 gives
length)
slope)
only
This
length
LINE DESIGN MANUAL
of each by
this
is accomplished
span
in the
approximate
equivalent
series
method.
by recognizing
asymmetries
as they
actually
exist
and
treating them as such without recourse to equivalent arrangements. Treatment of a problem on this basis requires a separate basic Pand H curve for each span involved, and while possible, undue difficulties would be experienced in computing the basic Hcurves for nonsymmetrical spans. In order to alleviate
these
difficulties,
on the equivalent H curve relations previously outlined;
but
with
little
or no sacrifice
level span of each nonsymmetrical as previously derived. The basic however, for nonsymmetrical
in accuracy,
H curves
the
insulator must be taken as equal to the weight of conductor from low point to low can be measured on the plan-profile sheets describing the series of spans under given
to illustrate
a typical
to account only of the conductor
conductor the basic
break
occurs at midspan of the insulator
for the actual length of conductor from in the adjacent span. In this connection,
curves into
Represented steps
involved
above
structure deflection and the horizontal deflecting curve similar in aspect to the basic Pcurve can
the ordinates of this curve to the basic Pcurve effects of insulator and structure deflections will as the P incorporated
are. By a similar the basic Pcurves.
in figure in this
procedure,
14 is a solution procedure
can
by this be outlined
into
a basic span.
H Curve
for
each
the
span weight
horizontal
the basic
to the low that if the
were inclined so or uplift would position
Pcurves
which
if the
is
relation
force is known to the extent that a be drawn. By adding, point by point,
of each span, new curves describing the combined be formed and can be used in the procedure exactly the criteria
effects
of “hinged”
for the
typical
crossarms case shown
may in figure
also
be
13. The
as follows:
(1) Compute a basic P curve for each insulator string conductor weights as determined from low-point distances such as structure deflections, hinged crossarms, etc. (2) Compute for each actual
This distance Figure 13 is
the assumed break point it is interesting to note
string and if the adjacent of the span, a negative
act on the insulator string which could cause it to deflect generally considered the limiting position. The effects of structure deflection can also be incorporated the
point. study.
can be generalized under this immediately adjacent to the
P curve
conductor is assumed to break next to an insulator that its low point would fall sufficiently far outside
between descriptive
be based
problem.
The initial assumption that the correction procedure by adjusting break point
can
span thereby making possible the use of the P curves required can be computed exactly as spans, the weight of conductor acting on each
span
involved,
to be considered, based on actual and based on other considerations based
on the
equivalent
level
span
APPENDIX (3)
Plot
(4)
Manipulate
these
curves
in the
same
these
curves
graphically
coordinate
H, - pl =H,‘+H, (5)
The
solution
is given
by
0d, The
justification
general
case
concerns
the handling
break. out
for
the
of a problem
practical
depending
purposes
on the
nature
One
the
same
reasoning
as given
could
end is a great
are all that
=d,
0d,
which
the
formula:
formula:
the effects
so that
problem,
symbolic
4 Hz’-,
question
cases considered,
of the
0d,
the dead
spans
following
stairstep
follows
11.
in which
in a few
the
=d, - Pz +H3’+H3 symbolic
solution
in figure
In this case, as in previous for
the
315
system.
by
X P3 4 H,‘+
above
as represented
A
previously
be raised
distance
away
of the broken
from
6, 8, or 10 spans
need
be considered.
will
away
the
connection
the conductor
conductor
first
for
in this
be damped
from
the
break,
III-SUMMARY To
summarize,
catenary
relations
the
discussion
for
determining
presented insulator
outlines
a general
and/or
structure
method
or procedure
deflections
and
based
on special
conductor
tensions
in
spans adjacent to a broken conductor. Knowing these deflections and tensions, the corresponding conductor sags can be computed by the use of standard catenary relations. The method, while graphical in nature, is capable of a high degree of accuracy and is straightforward; that is, it does not
involve
conductor method
the
usual
problem with those
The Solution conductor to facilitate selected. tension By
trial-and-error
procedures.
In
appendix
has been worked out and a comparison as obtained by another method.
of a Typical
Broken
problem has been worked a comparison of results,
The details of the problem in span A if the conductor
A-l made
IV-APPENDIX
A-l
Conductor
Problem.-In
which
follows,
a typical
of the
results
as obtained
the
following,
a typical
out to illustrate the techniques the typical problem used by
broken by
this
broken
presented. For this purpose and Bissiri and Landau[4] has been
are given in figure 15. The requirement breaks next to insulator No. 6.
is to find
the
sag and
the approximate method the procedure is as follows: (1) Using the nomograph given in figure 18, convert the series of given spans into a series of level spans. Since all equivalent level span lengths are less than 2 feet more than the horizontal span lengths (2) Using spans into series. (3) of 4.
a series
Using These
shown, all spans the Ruling Span
the values
of level
equal
will be assumed level without correction. Computation Chart given in figure 18, convert spans.
Take
H
force formula, assume are given in table A.
(4) Using the P f orce formula; P. These values are given in table
assume B.
970
feet
as the
values
for
HI
values
of
d and
span
length
and
compute
compute
the
series
for the equal corresponding corresponding
of level
level
span values
values
of
TRANSMISSION
316 (5)
Plot
curves
the
computed
according
to the
values
Since
the
dead (6)
by Bissiri
the
end
he assumed,
For
dead
will
the
the
dead
dead
end
04 The By
16 and
manipulate
the
resulting
Pand
- P=H, and
. . .H,, +H=d,
Landau) first,
does
a great
not
state
distance
away
the
location and,
of the
second,
nearest
at insulator
end
a great
results
distance
away,
XPJ-H,,+
at insulator
No.
0d,
XP+H,+
are tabulated
in table
the
solution
is given
by the
symbolic
formula:
@H/@...H,, d 1, the
solution
0d,
J-&-,
is given
by
0d,
rH,+
the
$Hp
symbolic
formula:
0d,
E.
the more exact method, the procedure is as follows: (1) Compute an Hcurve for each span. Assume that span E is dead ended at insulator No. 1 and that all spans are level spans without correction since the correction is less than 2 feet for each span. These (2) Compute
values are given in table C. a P curve for each suspension
table D. (3) Plot the according to the
H
HE-P,
The
The
results
Discussion between
and symbolic
P
curves formula:
as shown
+HE)+HD =d3- P3 =HD’+Hc=d,-
(4)
the typical
solution
are tabulated
by the
in table
of Results.-Considering
problem, the
is given
methods
the results
check
lies in the
insulator
in figure
string. 1’7 and
P., =Hc’+H,=d,
following
symbolic
values
manipulate
are
them
-Ps =HB”HA
given
graphically
=d6 -Ph =HA’
E.
made
by
armor rods, vibration dampers, etc., were acting. Since several times that of a conductor, the effects of such relative
magnitudes
of the
tension
in
formula:
the inherent differences each other as well as could
assumption
These
Bissiri
between the methods used to solve he expected. The principal difference
and
Landau-
that
the
conductor
length
in the span adjacent to a break is increased by the length of the insulator string immediately adjacent to the break. Theoretically, this would be true only if the weight distribution over the insulator string were the same as that over the conductor, and if no concentrated loads such as holddown weights,
on the
H
E.
0d, For
+H=d,
(as given
1 in span
in figure
MANUAL
formula:
program
end,
No.
as shown
symbolic
H- p=H2
LINE DESIGN
in the
system
the unit weight a discontinuity to the
total
of an insulator string of weight distribution weight
of conductor,
is usually depend insulators,
APPENDIX and
concentrated
has a varying low
loads effect,
comprising
being
more
the
system.
correct
for
A
Hence,
long
317
the
spans
assumption
with
high
made
tensions
by Bissiri
than
and
for short
Landau
spans
with
tensions.
V-APPENDIX To Chart
facilitate and
are given Figure conductor several
certain
a Sag and on the
following
20 shows can specific
computations Tension
a typical
be facilitated. ruling
span
such
Computation pages
lengths
Chart
as figures
set of data The
as made
by
by the
in Appendix
have
18 and
span-tension
A-2
which
A-l,
devised.
a Ruling These
Span
Computation
are self-explanatory
and
19, respectively. preliminary
curves
approximate
been
have method
studies been
of the
plotted as presented
from
effects data herein.
of a broken computed
for
W E
Table A.-H curve computation
H,, = 4400 lb; L, = 970 ft; w = 1.57 lb/ft; 1 Hl
2 Ho&h-
3 WLO
l--
Ho-H,
765.2528 765.2528 765.2528 765.2528
5
6
(4)
(2) (3)
AE
WO
2300 2500 3000 4000
4
AE = 6,635,672
slnh-’
7 (5)
H,
0.999638 .999713 .999789 .999939
765.0106 765.0331 765.0913 765.2066
0.33261 .30601 .25500 .19130
0.3268 .3015 .2524 .1902
8
9
4 5
Wl -r
(6) (7)
2929.936 3184.713 3821.650 5095.540
957.503 959.880 964.584 969.171
Lo - (8) 12.5 10.12 5.42 0.83
zi z
E Z
m
Numbers in parenthesis are column numbers.
Table B.-P curve computation Wd
p=-
ic0sll W = 1655 lb; i = 12.58 ft = 150.96 in d
d
A i
case
ii
0.1987 .3975
0.4803 .9178
0.2027 .4331
335.5 716.8
90 120 130
.5962 .7949 .8611
.8028 .6074 so90
.7426 1.3086 1.6910
1229.0 2165.7 2798.6
ic0se
P
Table C . -2 curve computations
Ho = 4400 lb; w = 1.57 lb/ft; AB = 6,635,672 Lo = 880,910,980, and 1050 ft 1
880
2
3
4
5
(2) (3)
H,
(4)
6
7
slnh-’ (5)
8
16) (7)
9
Lo -
(‘3) D
869.350
10.6
: s 0 z
2200 2500 3000 4000
693.6416 693.6416 693.6416 693.6416
0.999668 .999714 .999789 .999939
693.4116 693.4429 693.4951 693.5996
0.3152 .2774 .2309 .1734
0.3102 .2739 .2289 .1725
2802.548 3184.710 3821.660 5095.540
872.292 874.777 878.981
;:‘2
910
2200 2500 3000 4000
717.4822 711.4822 717.4822 711.4822
.999668 .999714 .999789 .999939
717.2443 717.2768 717.3308 717.4384
.3260 .2869 .2389 .1794
.3205 .2831 .2366 .1783
2802.548 3184.710 3821.660 5095.540
898.216 901.591 904.205 908.980
11.8 8.4 5.8 1.02
980
2300 2500 3000 4000
773.2210 773.2210 773.2210 773.2210
.999683 .999714 .999789 .999939
772.9763 772.9996 773.0579 773.1744
.3361 .3092 .2574 .1933
.3300 .3044 .2547 .1921
2929.936 3184.710 3821.660 5095.540
996.879 969.426 973.377 978.853
13.12 10.6 6.62 1.15
1050
2500 3000 4000
829.0365 829.0365 829.0365
.999714 .999789 .999939
828.7991 828.8616 828.9865
.3315 .2760 .2072
.3258 .2727 .2058
3184.710 3821.660 5095.540
1037.597 1042.166 1048.662
12.4 7.83 1.34
'
Numbers in parenthesis are column numbers.
1.02
D
Table D.-P Curve computations
p=wd i cosd i = 12.58 ft = 150.96 in d
i8 90 120 130 140 142 144 146
-d i
me
0.1987 .3975 .5962 .7949 .8611 .9274 .9406 .9539 .9671
0.9803 .9178 .8028 .6074 .5090 .3740 .3394 .3002 .2542
d
p2
p3
p4
ps
i cost9
w = 1750
W = 1546
W = 1609
W = 1766
0.2027 0.4331 0.7426 1.3086 1.6910 2.4790 2.7710 3.1770 3.8050
354.7 757.9 1299.6 2290.1 2959.3
313.4 669.6 1148.1 2023.1 2614.3
326.1 696.9 1194.8 2105.5 2720.2
357.9 764.9 1311.4 2310.9 2986.3
Table E.-Tab& Approximate Dead end a great dist. from break
Item
Tension (lb)-A -B -C -D -E Insulator deflection
2920 3590 3930 4120 4230 (in)-6 -5
-2 2 Sag (ft)-A
tion of results
method Dead end at insuIat01 No. 1 2900 3550 3870 4050 4120
Exact method
2710 3620 3950 4120 4220
131.2 58.0 31.2 18.0 10.8
131.1 57.8 30.0 16.0 6.9
145.8 67.4 32.8 17.0 7.5
53.0
53.5
57.0
Bissiri and Landau ’
2625
59.0
’ For a final result, Bissiri and Landau give only an interpolated catenary parameter value for the span adjacent to the break. From this, Tension A = (1670)(1.57) = 2625 lb. 2 Sag values determined by use of Computing Chart given in figure 19.
‘6
w=730 174.9 316.2 542.1 955.3 1234.4 1809.7 2022.8 2319.2 2777.6
INITIAL
3
Lo
= _
Lo
CONDITIONS - Before
_) “0 LO
LO
FIGURE
c-c----------
G
b-2 LO
LO
Conditions
Break
--
for
equilibrium:
-
b-3
b-3
b-4
--lLO
LO
C.f
Ln-4
b-3
h-2
dn-1
dn
in conductor
I
CONDITIONS - After
h-I
LO
LO
= Horizontal tension = Span length
FINAL
Break
---LO
0= Change In span length.
Pn = Hn ; Pn-1 + Hn = “n-1 ; Pn-2 + “n-1 = “n-2 ; Pn-3 + “n-2 = “n-3;
On = dn- dn-1; an-1 = dn-1 -dn-2 ; (dn-2=dn-2 Ln = Lo-0n;
Ln-2 = Lo -0n-2 Ln-1 =Lo -0n-1; FIGURE 2 104.D-1121
etc. -dn-4
-dn-3 ; On-3 =dn-3 , Ln-3 = Lo - 0n-3 ; etc.
; etc.
TRANSMISSION
322
di v eWIW2-
WPP’ -
LINE DESIGN MANUAL
Horizontal displacement of insulator string. Length of insulator string. Vertical displacement of insulator string. Angle of deflection of insulator string. Weight of insulator string. Weight of conductor acting on insulator string. Total vertical load = % + w2. Horizontal force caused by w when the insulator string is deflected by an angle 8, Horizontal force required to deflect the insulator string by an angle 8 when a load w is acting. FIGURE
3
Initial span length. Change in span length. Final span length. k ‘0 - Initial conductor length. ‘I - Conductor length after a change of 8 in span length. Initial horizontal tension in conductor. HOafter a change of 8 “,- Horizontal tension in conductor in span length. WUnit weight of conductor. Product of Modulus of elasticity and cross section area. AE-
LO-
0-
FIGURE 104-D-1122
4
APPENDIX
Conductor
Break
323
A
in a Span Adjacent
to a Dead End
4 // -ijoJ4
LI
_
Conditions for equilibrium after P,=H,; 0, = d, ; L, = ~~-0, FIGURE 5
Force
*
c HO
FIGURE 104-D-1123
conductor
Relations
Horizontal P, & H,
c
LO
d
P&H
-w--e-
6
breaks:
324
TRANSMISSION
Conductor
LINE DESIGN
MANUAL
Break Two Spans Removed From Dead End
,, / ----L,
L2 4
_ d2
LO
LO
Conditions for equilibrium after conductor breaks: P,=H,; P,+H,=H,; 0,=d,-d,; 0,=d,; L,= Lo-Q12; L,=L,-0, FIGURE 7 P & H Force
Horizontal .
Force
p2 &
H2
I
H,
.
Relations
-4 HO -I
FIGURE 104-D-1124
8
c
APPENDIX
Conductor
Conditions P3= Hg 8, =d,;
Break
for
Three
Spans
conductor 0,=d3-d,;
P,+Hz=H,; L,=L,-8,; FIGURE
P&H
_
Removed From Dead End
equi Ii brium after
P2+ H,=Hz; L,=L,-8,;
f
325
A
Horizontal
breaks: 02=d2-d,;
L, =~~-a,
9
Force Relations
Force
P,&H,
_ p2 H2
PI HI HO FIGURE 104-D-1125
4 IO
II P
-A
\to=
APPENDIX A
Conditions for equilibrium after conductor P3 = H;; P + H’,=H;; P, + H;= Hi; 0,=d,-d,; L$= L,-0,; L’,=L,-0, 8, = d,; Lf,=L,-03; FIGURE 13
104-D-1127
327
breaks: 0*=4-d,;
1030’ El. difrb;oq.80’
900’ _ 940’ w: El. diffT7.89’ El. d~~o~l.50’ d-P-
1040’ _ El. diff=,l8.92’ 980
Normal horizontal tension ___________H, Conductor weight per ft ____________w AE= cond. area x modulus __________ Insulator length _-----___________ i Insulator weight----------------------For other details see Reference C4l FIGURE 15 104-D-1128
380’
El. dif8f=$.07’
= = = = = -
4400 lb 1.57 lb 6,635,672 12.58 ft 265 lb Bibliography
5m
APPENDIX
A
329
gkTT
The determination
of a geometric
the space reloiiars of the ‘II’ curve intersections with the ‘P’curve : dtstance d2to dx-4e units
I
Avp mtio=0.277 Since mtio
I
t
i
i
Requirements for I equihbrlum: “‘Y-Ho’% ‘k”C’% . . . . . . . . . +4-4 . . . . . . . . . Ld- La+,
i
I “cb+h #&-4
Y-Y’S ~4,-d,
Hl’ps k4-4
L,+LO-&
L&LO-b
L;&-h
Lg - 970’ 1
-
I
Horizontal FIGURE
Force - Pounds 16
104-D-1 129
I
TRANSMISSION
LINE DESIGN
MANUAL
Horizontol Force - Pounds FIGURE 104-D-1130
I7
APPENDIX
A
331
VI-BIBLIOGRAPHY Technical [1] [2] [3] [4]
Technical [5] [6] [7] [8]
Journals
Brown, R. S., “Stresses Produced in a Transmission Line by Breaking of a Conductor,” Electrical World, vol. 61, No. 13, pp. 673-676, March 29, 1913. September, Healy, E. S., and Wright, A. J., “Unbalanced Conductor Tensions,” Trans. of AIEE, pp. 1064-1070, 1926. Den Hartog, J. P., “Calculation of Sags in a Transmission Line With a Broken Conductor,” The Electric Journal, vol. XXV, pp. 24-26, January, 1928. Effect on Sags in Suspension Spans,” Trans. of AIEE, vol, 66, pp. Bissiri, A., and Landau, M., “Broken Conductor 1181-1188, 1947.
Books
Painton, E. T., “Mechanical Design of Overhead Electrical Transmission Lines,” D. Van Nostrand Co., New York, pp. 265-269, 1925. Third Edition, McGraw-Hill Book Co., New York, pp. 137-138, 1927. Still, A., “Electric Power Transmission,” Engineers Handbook-Electric Power,” Third Edition, Pender, H., Del Mar, W. A., and McIlwain, K., “Electrical Section 14, pp. 71-73, 1936. Martin, J. S., “Sag Calculations by the Use of Martin’s Tables,” Copperweld Steel Co., Glassport, Pa., pp. 39-40, 1942.
332
TRANSMISSION
LINE DESIGN MANUAL
EOUIVALENT
HORIZONTAL
SPAN
NOMOGRAPH
NOTES These charts are designed to facilitate the computation of the ruling span length for any series of suspension spans. The procedure for computing the ruling span length is OS follows: I. Compute the Equivalent Horizontol Spon (He) for each span in the series being considered by using the nomograph which is based on J.S. Martin’s formula: He=ZI-H. (Use only for spans of 20% slope or less.) 2. The Ruling Span Length by using the relation: the solution of which is facilitated by using the Ruling Span Computation Chart.
900 600 5. no-c 8
20
600--
-
500--
z g
400--
G
z
30 40 50
E :: = .u + k
5 t ki 100 k
i3 =
s
300--
200
>
200 300
Z He- 2700:
400 i
EXAMPLE:
Horizontol span (H) Vertical span (V) Correction K) Equiv. horiz. span
ZHe’ 0.27 x IO’ line. 4. Project vertlcolly down from this point to the Hrs scale ond read the ruling span length of 910 ft.
500 I
= 1000’ -100’
= IO’ -1010’
FIGURE (Sheet
ZH,‘-22.5~10’
3. Enter the auxiliary bias lines at the value corresponding to ZHeL 22.5~ IO’ and read down the bias line to the intersection of the horizontal
300
200--
IOO-
EXAMPLE Fmd the ruling span length for a SerieS of level spans of lengths, He=800, 900. 6 1000 ft. Solution: (Using the Ruling Span Chart), I. Enter the equivalent horizontal stole at the span lengths given and read the corresponding He3 values. 2. Add the Hd& He values:
Problem:
18
2 of 2)
334
NMS
s
LINE DESIGN MANUAL
NI H19N31
TRANSMISSION
133d
EXPLANATION The purpose of this chart is to focilitote the computation of tronsmission line conductor sags and tensions when any three of the elements-span length, unit weight, sag, or tension ore known and when accuracy beyond the first decimal place is not required. This chart is based on the cotenory functions OS derived by J.S. Martin and given in the pamphlet “Sog Colculotions By The Use Of Mortin’s Tables” published by the Copperweld Steel Compony, Glossport. PO. The procedure for computing o sag value when the span length, unit weight, and tension ore known is OS follows:
3. Project horizontally from this point to the right or left to intersect the sag ratio curve. 4. From this potnt project vertically upward to intersect the Bose Spon Aux. Bios Line. 5. Thence, project horizontally -right or left- to intersect the bias line correspondtng to the span length used in step (I) obove. 6. from this point project vertically downward to intersect the sag scale ond read the corresponding sag value in feet. As on exomple, the followmg problem has been worked through: Find the sag for o conductor which weighs 1.1 lb. per ft when the span length is II00 ft. and the tension is 7000 lb. Answer by chart: 23.9 ft. Answer by more exact computation: 23.871 ft
I. Enter the span length scale at o point corresponding to the equivalent level span length of the span under consideration ond project horizontally to the right to intersect the bias line which corresponds to the unit weight of the conductor. 2. Project vertically -up or down- from this point to intersect the bias line which corresponds to the tension in tne conductor:
FIGURE I9 (Sheet
2 of 2)
D : 1 0 Z D
336
TRANSMISSION
LINE DESIGN MANUAL
1000
RULING
1. P. 3. 4. 5. 6.
7.
I200
SPAN LENGTH
- F 1.
Dead-end in first span adjacent Deod- end in second won odjocrnt hod-end in third spon odjocmt Dood-end in fourth spon odjocent Dead-end in fifth spon odjocrnt Dead-•d o great distoncr from Tonsion brforr brook.
FIGURE
20 2)
(Sheet I of 104-D-1133
to brook. to brook. to brook. to brook. to brook. break.
1400
APPENDIX
Theso curves ot crossings ore
bosed
ore to be use’?1 which worront on the following: Conductor Looding Insulators
A
NOTES in moking preliminary determinations compliance with titionol o&/or
337
of conductor h6ights Loco/ sofety codes ond
- 195,000 C. M. MS. R. 6617 stronding. 130°F. tinol no load with mox. lood = 7500 Ibs. Q 25% ond #*wind. - lb, &“x lOWsuspension units.
The following l xomple is given to illustrate the use of the curves shown to the left. PROBLEM: Determine conductor heights ot crossing shown below, moking provisions for required cleoronce under broken conductor conditions.
PROCEDURE: FIRSTFrom pertinent SECOND - Determine
safety cod6s determine required cleoronce over crossing. the ruling spon from crossing spon to neorest deod-end by: level spons, where the l quivolent Note: L,, Le, etc. ore l quivolent l?S=jy:*. level spon = 2 (Inclined spon) - octuol spon. THIRD - ;nter?he curves ot the value of the ruling spon OS determined obove ond using the curve which best describes the location of the neorest deod-end reod For deod-ends more thon 5 spons the corresponding value of horizontol tension. from breok use curve No.6. FOURTH - Determine brok6n conductor sog and/or profile OS required.
In applying conductor pro file to transmission line profil6, the shift in the spon due to the conductor breoC need be consider6d only for vrry short spans. FIFTH - For o I6vel crossing spon, conductor height = required clr. + broken cond. $09. For on inclined spon, us6 height osindicohd by intercepts of the broken cond. prOfil6 on the StruCtur6 center lines.
FIGURE 20 (Sheet 2 of 2)
<
USEFUL
FIGURES
339
AND TABLES
B
TRANSMISSION
340
t= II 36 I ---
LINE DESIGN
MANUAL
6 Miles
I I
line 3’
l
I
32
j
I 5 I
35
33 3
4
1
2
36
j 31 -----
I
E --.--
6 _--
7
8
9
IO
II
12
i I2 cr---
7 ---
XL I3
I8
I6
I7
I5
I4
I3
I8 _--
3L 3r
24
19
20
23
22
21
u a .2 u
I9
24
---7
--25
30
29
28
27
26
25
31
32
33
34
35
36
--36
2 30 = Q, F --cz 31 _----
I
6
1
5
I
!
4
3
f
j
2
j
Townshi; I ine J Figure
B-l.-Typical
township
showing
section
numbering.
104-D-1134.
I
/6
APPENDIX
B
341
I Mile /FN
\
$ car.
---
‘NW car. Sec.15 /t/6\’ co, ‘% senter NW$ 9\’
VEcar:Sec.15’
(Center NE { i 0 -;
ai J r w
t Center SE i
SECOT. Set 15.
---
Typical Section of Land Showing Corner Designations
---
-
---l---NW ) of NW;
NE ; of NW;
SW $ of NW)
SE 4’ of NW $ . 15---I I I
Typical $ Section Figure B-2.-Typical
land section
showing
corner and l/16
designations.
104-D-1135.
tmnsmission line olwoys runs from left to right on o key mop or on o plon-profile drawing. The direction (beoring) of o line, OS indicated on the plan-profile drawing, is related to the directions given on on azimuth chart. Examples ore: N8803O’OO”E
S 62” 36’47” E
+l E a Indicates the angle .. turned, and the arrow In head indicates the 5 direction of the new segment of the line i in relation to the segment just before the angle point. S 71“15’00” W /
S48’09’OO”W
& The letters PI (point of intersection) are += 5 8 used OS a prefix to CD’D a station to denote eP on angle and to q indicate the exact ;a location of the angle point. Figure B-3.-Azimuth
chart.
104-D-1136.
APPENDIX
B
343
Consider pole as a simple beam where f = M= S= J = Y= r = C =
stress in outer fiber maximum moment section modulus moment of inertia distance from center of gravity to outer fiber radius of pole cross section circumference of pole cross section
N/mm* N-mm mm3 mm4 mm mm mm
(Ib/in* ) (lb-in) (in3) (in4) (in) iin) (in)
axis of moments through center
then b = 4 7 r rrd _ rr 4 J =w-7 ;Ay3 S = $a$. =f ! M = fS=f (y3) C = 27r r CL 27T
r3= c3 87r3
M = f ($)($)
=fL-$=0.003
166fc3
If f is in N/mm* and c is in mm, M is in N.mm. Dividing by 1000, M iS in N-m. M =3.166 x 10+fC3 N-m. If f is in lb/in* and c is in inches, M is in lb-in. Dividing by 12, M is in lb-ft. M=2.638 xIOe4fc3 lb-ft.
Figure B-4.-Development
of formula
for maximum
moment
of resistance
on wood poles. 104-D-1137.
344
TRANSMISSION
LINE DESIGN
MANUAL
APPENDIX Table B-l .-Maximum
Metric:
345
moment of resistance for pole circumferences at ground line- USBR standard
M,. = 3.166 x 10s6fc3 (c in mm)
Pole Circumference
B
U.S. customary:
Western Red Cedar
Pole Diameter
f= 38.610 88 MPa
M,. = 2.638 x 10w4fc3 (c in inches) Douglas Fir and Southern Yellow Pine
f= 5600 lb/in2
fz51.021
52 MPa
f= 7400 lb/in2
C
mm
in
mm
in
N-m
lb.ft
N.m
lb-ft
508 521 533 546 559
20.0 20.5 21.0 21.5 22.0
162 166 170 114 178
6.37 6.53 6.68 6.84 7.00
16025 17 287 18509 19 891 21 352
11 12 13 14 15
818 726 681 681 730
21176 22 844 24459 26293 28 216
15 616 16817 18 078 19 400 20186
512 584 597 610 622
22.5 23.0 23.5 24.0 24.5
182 186 190 194 198
7.16 7.32 7.48 1.64 7.80
22871 24 341 26 010 27 746 29416
16 821 17 914 19 171 20421 21125
30230 32173 34 370 36665 38 871
22235 23 751 25 334 26986 28708
635 648 660 673 686
25.0 25.5 26.0 26.5 27.0
202 206 210 214 218
7.96 8.12 8.28 8.44 8.59
31299 33261 35 144 37261 39463
23082 24495 25 964 21491 29 071
41360 43953 46440 49239 52147
30501 32368 34 310 36328 38423
699 711 124 737 749
27.5 28.0 28.5 29.0 29.5
222 226 230 235 238
8.75 8.91 9.07 9.23 9.39
41149 43936 46 391 48935 51364
30122 32429 34 191 36029 37925
55 169 58059 61302 64 664 67 874
40597 42852 45 189 41610 50115
162 115 787 800 813
30.0 30.5 31.0 31.5 32.0
242 247 250 255 259
9.55 9.71 9.87 10.03 10.19
54086 56 901 59586 62587 65 688
39886 41914 44009 46173 48407
71470 15 191 78738 82705 86803
52707 55 386 58155 61015 63967
826 838 851 864 876
32.5 33.0 33.5 34.0 34.5
263 267 271 275 219
10.35 10.50 10.66 10.82 10.98
68890 71937 75 337 78842 82017
50712 53089 55538 58063 60662
91034 95059 99552 104185 108586
67012 70153 73 390 76726 80161
889 902 914 921 940
35.0 35.5 36.0 36.5 37.0
283 287 291 295 299
llJ4 11.30 11.46 11.62 11.78
85 89 93 97 101
886 709 338 377 532
63338 66 091 68923 71835 74 828
113493 118545 123 339 128677 134 167
83691 87 335 91078 94925 98880
953 965 978 991 1003
31.5 38.0 38.5 39.0 39.5
303 307 311 315 319
11.94 12.10 12.25 12.41 13.57
105 109 114 118 123
803 850 350 971 345
17903 81 061 84 303 87 630 91044
139 811 145 159 151105 157 211 162992
102943 107 116 111400 115 797 120 308
1016 1029 1041 1054 1067
40.0 40.5 41.0 41.5 42.0
323 328 331 336 340
12.73 12.89 13.05 13.21 13.37
128 133 137 143 148
204 188 902 133 495
94545 98135 101 815 105 586 109 448
169412 175 999 182228 189141 196226
124 129 134 139 144
935 679 542 524 628
TRANSMISSION
LINE DESIGN MANUAL
Table B-l .-Maximum moment of resistance for pole circumferences at ground line-USBR standard-Continued Pole Circumference
Western Red Cedar
Pole Diameter
f= 38.610 88 MPa
C
N.m
Douglas Fir and Southern Yellow Pine
f=5600
lb/in2
f= 51.02152
MPa
f = 7400 lb/in2
mm
in
mm
in
1080 1092 1105 1118 1130
42.5 43.0 43.5 44.0 44.5
344 348 352 356 360
13.53 13.69 13.85 14.01 14.16
153 159 164 170 176
989 180 932 822 382
113 117 121 125 130
404 454 599 840 179
203 210 217 225 233
486 345 947 730 077
149 155 160 166 172
855 207 684 289 023
1143 1156 1168 1181 1194
45.0 45.5 46.0 46.5 47.0
364 368 372 376 380
14.32 14.48 14.64 14.80 14.96
182 188 194 201 208
540 840 782 358 081
134 139 143 148 153
617 154 792 532 375
241 249 257 266 274
214 538 390 081 964
177 183 190 196 202
886 882 011 275 674
1207 1219 1232 1245 1257
47.5 48.0 48.5 49.0 49.5
384 388 392 396 400
15.12 15.28 15.44 15.60 15.76
214 952 221427 228 587 235 900 242 787
158 163 168 173 179
322 375 534 800 175
284 292 302 311 320
044 600 062 725 826
209 215 222 229 236
212 888 705 664 767
1270 1283 1295 1308 1321
50.0 50.5 51.0 51.5 52.0
404 408 412 416 420
15.92 16.07 16.23 16.39 16.55
250 258 265 273 281
398 166 478 554 792
184 190 195 201 207
660 255 962 782 717
330 883 341 149 350 811 361482 372 368
244 015 251408 258 950 266 641 274 483
1334 1346 1359 1372 1384
52.5 53.0 53.5 54.0 54.5
425 428 433 437 440
16.71 16.87 17.03 17.19 17.35
290 298 306 315 324
193 095 816 706 062
213 219 226 232 239
767 933 216 618 140
383 393 405 417 428
470 912 436 183 225
282 290 298 307 316
477 625 928 388 006
1397 1410 1422 1435 1448
55.0 55.5 56.0 56.5 57.0
445 449 453 457 461
17.51 17.67 17.83 17.98 18.14
333 280 342 671 351495 361 223 371 130
245 252 259 266 273
782 546 434 445 581
440 452 464 477 490
406 815 475 331 422
324 333 342 352 361
783 722 823 088 518
1461 1473 1486 1499 1511
57.5 58.0 58.5 59.0 59.5
465 469 473 477 481
18.30 18.46 18.62 18.78 18.94
381 390 401 411 421
216 686 122 742 710
280 288 295 303 311
844 235 753 402 181
503 516 530 544 557
749 264 054 088 259
371 380 390 400 411
116 882 817 924 204
1524 1537 1549 1562 1575
60.0 60.5 61.0 61.5 62.0
485 489 493 497 501
19.10 19.26 19.42 19.58 19.74
432 443 454 465 477
688 856 333 868 597
319 327 335 343 352
092 136 314 627 077
571 586 600 615 631
767 524 369 612 111
421 432 443 454 465
657 287 094 079 244
1588 1600 1613 1626 1638
62.5 63.0 63.5 64.0 64.5
506 509 513 518 521
19.89 20.05 20.21 20.37 20.53
489 500 513 525 537
521 703 007 511 232
360 369 378 387 396
664 389 254 260 407
646 661 677 694 709
868 643 902 425 914
476 488 499 511 523
591 121 836 736 824
lb-ft
N-m
lb*ft
APPENDIX
347
B
Table B-l .-Maximum moment of resistance for pole circumferences at ground line-USBR standard-Continued Pole Circumference
Douglas Fir and Southern Yellow Pine
Western Red Cedar
Pole Diameter
f= 38.610 88 MPa
f= 5600 lb/in2
f=5’1.02152
MPa
f = 7400 lb/in2
C
mm
N.m
lb-ft
N-m
lb-ft
in
mm
in
1651 1664 1676 1689 1702
65.0 65.5 66.0 66.5 67.0
526 530 534 538 542
20.69 20.85 21.01 21.17 21.33
550 563 575 588 602
125 223 496 992 697
405 415 424 434 444
698 132 712 437 311
726 744 760 778 796
951 259 477 311 421
536 548 561 574 587
100 567 226 078 125
1715 1727 1740 1753 1765
67.5 68.0 68.5 69.0 69.5
546 550 554 558 562
21.49 21.65 21.80 21.96 22.12
6i6 629 643 658 672
613 647 974 516 132
454 464 474 485 495
332 504 826 299 926
814 832 850 870 888
810 034 965 181 174
600 613 627 641 655
368 808 448 288 331
1778 1791 1803 1816 1829
70.0 70.5 71.0 71.5 72.0
566 570 574 578 582
22.28 22.44 22.60 22.76 22.92
687 702 716 732 747
093 275 486 096 931
506 517 528 539 551
707 642 734 984 391
907 928 946 967 988
945 006 785 412 337
669 684 698 713 728
577 027 685 550 624
1842 1854 1867 1880 1892
72.5 73.0 73.5 74.0 74.5
586 590 594 598 602
23.08 23.24 23.40 23.55 23.71
763 779 795 812 827
993 022 524 258 911
562 574 586 598 610
959 687 576 629 845
1009 1 029 1051 1073 1094
562 422 228 341 026
743 759 775 791 807
910 407 119 045 189
1905 1918 1930 1943 1956
75.0 75.5 76.0 76.5 77.0
606 610 614 618 623
23.87 24.03 24.19 24.35 24.51
845 862 878 896 914
095 514 805 683 802
623 635 648 661 674
227 775 490 374 427
1 116 1139 1 161 1184 1 208
732 751 278 902 845
823 840 856 873 891
550 131 933 958 207
TRANSMISSION
348
LINE DESIGN
MANUAL
Table B-2.-Maximum moment of resistance for pole circumferences at ground line-ANSI standard Mr=2.64x
10-4fc3 Western Larch
Pole diameter,
20.0 20.5 21.0 21.5 22.0
6.37 6.53 6.68 6.84 7.00
12612 13646 14669 15142 16866
16896 18 195 19 559 20990 22488
17 741 19 105 20537 22039 23613
22.5 23.0 23.5 24.0 24.5
7.16 7.32 7.48 7.64 7.80
18042 19 212 20566 21 897 23294
24057 25 696 21409 29 196 31 059
25 259 26 981 28779 30656 32612
25.0 25.5 26.0 26.5 27.0
7.96 8.12 8.28 8.44 8.59
24750 26264 21840 29477 31177
33000 35 019 37 120 39303 41570
34 650 36170 38976 41268 43649
21.5 28.0 28.5 29.0 29.5
8.75 8.91 9.07 9.23 9.39
32942 34 771 36668 38632 40665
43923 46 362 48890 51509 54220
46 119 48680 51335 54085 56 931
30.0 30.5 31.0 31.5 32.0
9.55 9.71 9.87 10.03 10.19
42768 44942 47188 49 509 51904
57 024 59 922 62 918 66012 69 206
59875 62 919 66064 69313 72666
32.5 33.0 33.5 34.0 34.5
10.35 10.50 10.66 10.82 10.98
54 315 56924 59551 62251 65044
72501 75 898 79401 83 010 86726
76126 79 693 83 371 87160 91 062
35.0 35.5 36.0 36.5 37.0
11.14 11.30 11.46 11.62 11.78
67 914 70866 73903 77025 80234
90552 94488 98531 102700 106979
95 079 99212 103464 107 835 112328
37.5 38.0 38.5 39.0 39.5
11.94 12.10 12.26 12 41 12.57
83531 86 917 90 393 93 961 97 621
111315 115 889 120 524 125 281 130 162
116943 121684 126550 131545 136670
40.0 40.5 41.0 41.5 42.0
12.73 12.89 13.05 13.21 13.37
135 168 140300 145 561 150 951 156 413
141926 147 315 152 839 158 499 164 297
in
f
Western Red Cedar = 6000 lb/in2, lb*ft
Southern Yellow Pine f = 8000 lb/in2, lb*ft
Pole circumference c, in
101 105 109 113 117
376 225 170 213 355
f= 8400 Ib/in2, lb-ft
APPENDIX
6
Table B-2.-Maximum moment of resistance for pole circumferences at ground line-ANSIstandard-Continued Pole Circumference c, in
Pole Diameter,
42.5 43.0 43.5 44.0 44.5
13.53 13.69 13.85 14.01 14.17
121 125 130 134 139
596 939 383 931 583
162 167 173 179 186
129 918 844 908 111
170 176 182 188 195
235 314 537 904 417
45.0 45.5 46.0 46.5 47.0
14.32 14.48 14.64 14.80 14.96
144 149 154 159 164
342 201 180 262 455
192 198 205 212 219
456 942 573 350 274
202 208 215 222 230
078 889 852 961 237
47.5 48.0 48.5 49.0 49.5
15.12 15.28 15.44 15.60 15.76
169 175 180 186 192
760 177 709 356 119
226 233 240 248 256
347 570 945 474 158
237 245 252 260 268
664 248 992 898 966
50.0 50.5 51.0 51.5 52.0
15.92 16.08 16.23 16.39 16.55
198 203 210 216 222
000 999 119 359 723
264 271 280 288 296
000 999 158 479 964
277 200 285 599 294 166 302 903 311812
52.5 53.0 53.5 54.0 54.5
16.71 16.87 17.03 17.19 17.35
229 235 242 249 256
209 821 558 422 415
305 314 323 332 341
613 428 411 563 887
320 330 339 349 358
893 149 581 192 982
55.0 55.5 56.0 56.5 57.0
17.51 17.67 17.83 17.99 18.14
263 270 278 285 293
538 790 175 693 345
351 361 370 380 391
384 054 900 924 127
368 379 389 399 310
953 107 466 971 683
57.5 58.0 58.5 59.0 59.5
18.30 18.46 18.62 18.78 18.94
301 309 317 325 333
133 057 119 320 661
401511 412 076 422 825 433 760 444 881
421 432 443 455 467
586 680 967 448 126
60.0 60.5 61.0 61.5 62.0
19.10 19.26 19.42 19.58 19.74
342 350 359 368 377
144 769 537 451 511
456 467 479 491 503
192 692 383 268 348
479 491 503 515 528
001 076 353 832 516
62.5 63.0 63.5 64.0 64.5
19.90 20.05 20.21 20.37 20.53
386 396 405 415 425
718 074 579 236 044
515 528 540 553 566
625 099 713 648 725
541 554 567 581 595
506 504 811 330 062
in
f
Western Red Cedar = 6000 lb/in2 lb*ft
f
Southern Yellow Pine = 8000 lb/in2 lb*ft
Western Larch = 8400 lb/in2
f
lb-ft
TRANSMISSION
LINE DESIGN MANUAL
Table B-2.-Maximum
moment of resistance for pole circumferences at ground line-ANSI standard-continued Western Larch
Pole Diameter,
65.0 65.5 66.0 66.5 67.0
20.69 20.84 21.00 21.16 21.32
435 445 455 465 476
006 122 393 822 408
580 008 593 496 607 191 621096 635 211
609 623 637 652 666
008 170 551 150 972
67.5 68.0 68.5 69.0 69.5
21.48 21.64 21.80 21.96 22.12
487 498 509 520 531
154 060 127 358 752
649 664 678 693 709
539 080 837 811 003
682 697 712 728 744
015 284 779 501 453
70.0 70.5 71.0 71.5 72.0
22.28 22.44 22.60 22.75 22.91
543 555 566 578 591
312 037 931 992 224
724 740 755 771 788
416 050 908 990 299
760 777 793 810 827
636 052 703 590 714
72.5 73.0 73.5 74.0 74.5
23.07 23.23 23.39 23.55 23.71
603 616 628 641 654
627 202 95 1 874 973
804 821 838 855 873
837 603 602 833 298
845 862 880 898 916
078 684 532 624 963
75.0 75.5 76.0 76.5 77.0
23.87 24.03 24.19 24.35 24.50
668 681 695 709 723
250 704 337 152 148
891 908 927 945 964
000 939 117 536 197
935 954 973 992 1012
550 386 473 813 407
77.5 78.0 78.5 79.0 79.5
24.66 24.82 24.98 25.14 25.30
737 751 766 780 795
327 690 238 973 896
983 1002 1021 1041 1061
103 253 651 298 195
1032 1052 1072 1 093 1114
258 366 734 363 255
80.0 80.5 81.0 81.5 82.0
25.46 25.62 25.78 25.94 26.10
811 826 841 857 873
008 309 802 487 366
1081 1 101 1 122 1 143 1 164
344 746 403 317 489
1 1 1 1 1
135 156 178 200 222
411 833 523 483 713
82.5 83.0 83.5 84.0 84.5
26.26 26.41 26.57 26.73 26.89
889 905 922 938 955
440 710 177 843 708
1185 1 207 1 229 1 251 1 274
921 614 570 790 277
1245 1 267 1 291 1 314 1337
217 994 048 380 991
85.0 85.5
27.05 27.21
972 774 990 041
in
f
Western Red Cedar = 6000 lb/in2 lb*ft
Southern Yellow Pine = 8000 lb/in2 lb-ft
Pole Circumference c, in
f
1 297 032 1 320 055
f = 8400 lb/in2 lb-ft
1 361 883 1 386 058
APPENDIX Table B-3.-Pole SOUTHERN
YELLOW
PINE AND DOUGLAS FIR DISTANCE CLASS I FROM TOP CIRC. FEET INCHES
2 3 4 5 6 7 8 9 10
30 CLASS CIRC. INCHES
CLASS CIRC. INCHES
2
3
CLASS CIRC. INCHES
TOP 1 2 3 4 5 6 7 8 9 10
27.00 27.40 27.79 20.19 28.58 28.98 29.38 29.77 30.17 30.56 30.96
25.00 25.38 25.75 26.13 26.50 26.68 27.25 27.63 28.00 28.38 28.75
23.00 23.38 23.75 24.13 24.50 24.89 25.25 25.63 26.00 26.38 26.75
21 .oo 21.33 21 .67 22.00 22.33 22.67 23.00 23.33 23.67 24.00 24.33
I 1 12 13 14 15 16 17 18 19 20
31.35 31.75 32.15 32.54 32.94 33.33 33.73 34.12 34.52 34.92
29.13 29.50 29.00 30.25 30.63 31 .oo 31.38 31.75 32.13 32.50
27.13 27.50 27.68 28.25 28.63 29.00 29.36 29.75 30.13 30.50
24.67 25.00 25.33 25.67 26.00 26.33 26.67 27.00 27.33 27.61
25 26 27 28 29 30
TOP
351
circumferences for Douglas fir and southern yellow pine
21 22 23 24
SOUTHERN YELLOW DISTANCE FROM TOP FEET
6
35.31 35.71 36.10 36.50 GROUND 36.90 37.29 37.69 38.08 38.48 38.87
L.INE
PINE AND DOUGLAS FIR CLASS H-2 CLASS H-l CIRC. CIRC. INCHES INCHES 31 .oo 31.43 31.86 32.29 32.72 33.16 33.59 34.02 34.45 34.88 35.31
29.00 29.43 29.86 30.29 30.72 31.16 31.59 32.02 32.45 32.88 33.31
32.88 33.25 33.63 34.00 (5 FEE1 34.38 34.75 35.13 35.50 35.88 36.25
30.88 31 .25 31 .63 32.00 6 INCHESl------32.38 32.75 33.13 33.50 33.68 34.25
CLASS CIRC. INCHES 27 27 27 28 28 29 29 29 30 30 31
00 41 83 24 66 07 48 90 31 72 14
1
CLASS CIRC. INCHES 25.00 25.40 25.79 26.19 26.59 26.98 27.38 27.78 28.17 28.57 28.97
2
FOOT
POLE
4
28.00 28.33 28.67 29.00 29.33 29.67 30.00 30.33 30.67 31 .oo
CLASS CIRC. INCHES 23.00 23.38 23.76 24.14 24.52 24.90 25.28 25.66 26.03 26.41 26.79
35 FOOT CLASS 4 CIRC. INCHES
3
_
21 .oo 21 .36 21 .72 22.09 22.45 22.81 23.17 23.53 23.90 24.26 24.62
POLE
TRANSMISSION
352
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
I I 12 13 14
CLASS CIRC.
1
CLASS CIRC.
INCHES
CLASS CIRC.
INCHES
INCHES
5
FOOT POLE-COII. CLASS 4 CIRC. INCHES
17 18 19 20
33.74 34.17 34.60 35 03 35 47 35 90 36 33 36 76 37 19 37 62
31.55 31.97 32.38 32 79 33 21 33 62 34 03 34 45 34 86 35 28
29.36 29.76 30.16 30.55 30.95 31.34 31.74 32.14 32.53 32.93
27.17 27.55 27.93 28.31 28.69 29.07 29.45 29.83 30.21 30.59
24.98 25.34 25.71 26.07 26.43 26.79 27.16 27.52 27.88 28.24
21 22 23 24 25 26 27 28 29
40.05 40.48 40.91 41.34 41 .78 42.21 42.64 43.07 43.50
38 38 38 39 39 40 40 41 41
35 36 36 36 37 37 38 38 39
69 10 52 93 34 76 17 59 00
33.33 33.72 34.12 34.52 34.91 35.31 35.71 36.10 36.50
30.97 31.34 31 .72 32.10 32.48 32.86 33.24 33.62 34.00 --------------34.38
28.60 28.97 29.33 29.69 30.05 30.41 30.78 31.14 31.50
34.76 35.14 35.52 35.90 36.28
32.22 32.59 32.95 33.31 33.67
-----------------GROUND
05 48 91 34 78 21 64 07 50 LINE
(6
FEET
30
43.93
41.93
39.4
31 32 33 34 35
44.36 44.79 45.22 45.66 46.09
42.36 42.79 43.22 43.66 44.09
39 40 40 41 41
YELLOW CLASS
PINE H-3
CIRC. INCHES
AND DOUGLAS CLASS H-2
CIRC. INCHES
0
INCHES)36.90
83 24 66 07 48
37.29 37.69 38.09 38.48 38.88
FIR CLASS
H-l
CIRC. INCHES
CLASS CIRC. 1 NCHES
33.00 33.46 33.91 34.37 34.82 35.28 35.74 36.19 36.65 37.10 37.56
31 00 31 44 31 88 32 32 32 76 33.21 33.65 34 09 34 53 34 97 35 41
29 29 29 30 30 31 31 31 32 32 33
00
1 2 3 4 5 6 7 8 9 10
43 85 28 71 13 56 99 41 84 26
27 27 27 28 28 29 29 29 30 30 31
82 24 65 06 47 88 29 71 12
11 12 13 14 15 16 17 18 19 20
38.01 38.47 38.93 39.38 39.84 40.29 40.75 41.21 41.66 42.12
35 36 36 37 37 38 38 38 39 39
33 34 34 34 35 35 36 36 37 37
69 12 54 97 40 82 25 68 10 53
31 31 32 32 33 33 34 34 34 35
53 94 35 76 18 59 00 41 82 24
TOP
2
35.74 36.17 36.60 37.03 37.47 37.90 38.33 38.76 39.19 39.62
15 16
SOUTHERN DISTANCE FROM TOP FEET
35
PINE AND DOUGLAS FIR CLASS H-2 CLASS H-l CIRC. CIRC. INCHES INCHES
85 29 74 18 62 06 50 94 38 82
00 41
1
CLASS
2
CLASS
31.86
40 FOOT POLE 3 CLASS 4
CIRC. INCHES
CIRC. INCHES
CIRC. INCHES
25.00 25.40 25.79 26.19 26.59 26.99 27.38 27.78 28.18 28.57 28.97
23.00 23.38 23.76 24.15 24.53 24.91 25.29 25.68 26.06 26.44 26.82
21.37 21.74 22.10 22.47 22.84 23.21 23.57 23.94 24.31 24.68
29.37 29.76
27.21 27.59 27.97 28.35 28.74 29.12 29.50 29.88 30.26 30.65
25.04 25.41 25.78 26.15 26.51 26.88 27.25 27.62 27.99 28.35
30.16 30.56 30.96 31.35 31.75 32.15 32.54 32.94
21 .oo
APPENDIX
353
6
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET 21 22 23 24 25 26 27 28 29 30 31 32 33 --------34 35 36 31 38 39 40
SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES
42.57 43.03 43.49 43.94 44.40 44.85 45.31 45.76 46.22 46.68
40 40 41 41 42 42 42 43 43 44
47.13 47.59 48.04 ---------------GROUND 48.50 48.96 49.41 49.87 50.32 50.78 51 .24
YELLOW PINE CLASS H-3 CIRC. INCHES
FIR
26 71 15 59 03 47 91 35 79 24
46.00 46.44 46.88 41.32 47.76 48.21 48.65
37.96 38.38 38.81 39.24 39.66 40.09 40.51 40.94 41.37 41.79
35.65 36.06 36.47 36.88 37.29 37.71 38.12 38.53 38.94 39.35
33 33 34 34 34 35 35 36 36 36
34 74 13 53 93 32 72 12 51 91
31.03 31.41 31.79 32.18 32.56 32.94 33.32 33.71 34.09 34.47
28 72 29 09 29 46 29.82 30.19 30 56 30 93 31 29 31 66 32 03
39.76 40.18 40.59 0 INCHES)--41 .oo 41.41 41 .82 42.24 42.65 43.06 43.47
37 37 38
31 71 10
34.85 35.24 35.62
32 32 33
40 76 13
38 38 39 39 40 40 40
50 90 29 69 09 49 88
36.00 36.38 36.76 37.15 37.53 37.91 38.29
33 33 34 34 34 35 35
50 87 24 60 97 34 71
AND DOUGLAS CLASS H-2 CIRC. INCHES
FEET
CLASS CIRC. INCHES
2
POLE-con. CLASS CIRC. INCHES
CLASS CIRC. INCHES
42.22 42.65 43.07 LINE (6 43.50 43.93 44.35 44.78 45.21 45.63 46.06
44.68 45.12 45.56
1
40 FOOT CLASS 3 CIRC. INCHES
CLASS H-l CIRC. INCHES
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
45 FOOT POLE 3 CLASS 4 CIRC. INCHES
3 4 5 6 7 8 9 10
33.00 33.46 33.92 34.38 34.85 35.31 35.71 36.23 36.69 37.15 37.62
31 .oo 31.45 31.90 32.35 32.79 33.24 33.69 34.14 34.59 35.04 35.49
29.00 29.42 29.85 30.27 30.69 31.12 31.54 31 .96 32.38 32.81 33.23
27.00 27.41 27.82 28.23 28.64 29.05 29.46 29.87 30.28 30.69 31.10
25 25 25 26 26 26 21 27 28 28 28
00 40 19 19 59 99 38 78 18 58 97
23.00 23.37 23.14 24. 12 24.49 24.86 25.23 25.60 25.97 26.35 26.72
21 21 21 22 22 22 23 23 23 24 24
00 36 72 08 44 79 15 51 87 23 59
I I 12 13 14 15 16 17 18 19 20
38.08 38.54 39.00 39.46 39.92 40.38 40.85 41.31 41.77 42.23
35 36 36 37 37 38 38 39 39 39
33.65 34.08 34.50 34.92 35.35 35.77 36.19 36.62 37.04 37.46
31.51 31.92 32.33 32.74 33.15 33.56 33.97 34.38 34.79 35.21
29 29 30 30 30 31 31 32 32 32
37 77 17 56 96 36 76 15 55 95
27.09 27.46 27.83 28.21 28.58 28.95 29.32 29.69 3Q. 06 30.44
24 25 25 26 26 26 27 27 27 28
95 31 67 03 38 74 10 46 82 18
TOP
2
94 38 83 28 73 18 63 08 53 97
4
354
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
21 22 23 24 25 26 27 28 29 30
42.69 43.15 43.62 44.08 44.54 45.00 45.46 45.92 46.38 46.85
31 32 33 34 35 36 37 38 --------------.
47.31 47.77 48.23 48.69 49.15 49.62 50.08 50.54
39 40
51 .oo 51 .46
41 42 43 44 45
51.92 52.38 52.85 53.31 53.77
SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES 40 40 41 41 42 42 43 43 44 44
FIR
42 a7 32 77 22 67 12 56 01 46
44.91 45.36 45.81 46.26 46.71 47.15 47.60 48.05 ---GROUND 48.50 48.95 49.40 49.85 50.29 50.74 51.19
AND DOUGLAS CLASS H-2 CIRC. INCHES
2
45 FOOT CLASS 3 CIRC. INCHES
POLE-con. CLASS CIRC. INCHES
CLASS CIRC. INCHES
37.88 38.31 38.73 39.15 39.58 40.00 40.42 40.85 41 .27 41 .69
35.62 36.03 36.44 36.85 37.26 37.67 38.08 38.49 38.90 39.31
33 33 34 34 34 35 35 36 36 36
35 74 14 54 94 33 73 13 53 92
30.81 31.18 31.55 31.92 32.29 32.67 33.04 33.41 33.78 34.15
28.54 28.90 29.26 29.62 29.97 30.33 30.69 31.05 31.41 31 .I7
39.72 40.13 40.54 40.95 41 .36 41 .I7 42.18 42.59 6 INCHES)--43.00 43.41
37 37 38 38 38 39 39 40
32 72 12 51 91 31 71 10
34.53 34.90 35.27 35.. 64 36.01 36.38 36.76 37.13
32.13 32.49 32.85 33.21 33.56 33.92 34.28 34.64
40 40
50 90
37.50 37.87
35.00 35.36
46.35 46.77 47.19 47.62 48.04
43.82 44.23 44.64 45.05 45.46
41.29 41 .69 42.09 42.49 42.88
38.24 38.62 38.99 39.36 39.73
35.72 36.08 36.44 36.79 37.15
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
42.12 42.54 42.96 43.38 43.81 44.23 44.65 45.08 LINE (6 45.50 45.92
FEET,
1
CLASS CIRC. INCHES
CLASS H-l CIRC. INCHES
FIR 1
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
50 3
4
FOOT POLE CLASS 4 CIRC. INCHES
TOP 1 2 3 4 5 6 7 a 9 10
33.00 33.45 33.91 34.36 34.82 35.27 35.73 36.18 36.64 37.09 37.55
31 .oo 31.44 31 .a9 32.33 32.77 33.22 33.66 34.10 34.55 34.99 35.43
29.00 29.42 29.84 30.26 30.68 31.10 31 .52 31.94 32.36 32.78 33.20
27.00 27.41 27.82 28.23 28.64 29.05 29.45 29.86 30.27 30.68 31.09
25.00 25.39 25.77 26.16 26.55 26.93 27.32 27.70 28.09 28.48 28.86
23.00 23.36 23.73 24.09 24.45 24.82 25.18 25.55 25.91 26.27 26.64
21 .oo 21.35 21.70 22.06 22.41 22.76 23.11 23.47 23.82 24.17 24.52
11 12 13 14 15 16 17 18 19 20
38.00 38.45 38.91 39.36 39.82 40.27 40.73 41.18 41 .64 42.09
35.88 36.32 36.76 37.20 37.65 38.09 38.53 38.98 39.42 39.86
33.63 34.05 34.47 34.89 35.31 35.73 36.15 36.57 36.99 37.41
31.50 31.91 32.32 32.73 33.14 33.55 33.95 34.36 34.77 35.18
29.25 29.64 30.02 30.41 30.80 31.18 31.57 31.95 32.34 32.73
27.00 27.36 27.73 28.09 28.45 28.82 29.18 29.55 29.91 30.27
24.87 25.23 25.58 25.93 26.28 26.64 26.99 27.34 27.69 28.05
APPENDIX
355
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC.
INCHES
AND DOUGLAS CLASS H-2 CIRC.
FIR CLASS H-l CIRC. INCHES
INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
50 FOOT CLASS 3 CIRC.
INCHES
POLE-con. CLASS CIRC. INCHES
42.55 43.00 43.45 43.91 44.36 44.82 45.27 45.73 46.18 46.64
40.31
40.75 41.19 41 .64 42.08 42.52 42.97 43.41 43.85 44.30
37.83 38.25 38.67 39.09 39.51 39.93 40.35 40.77 41.19 41 .61
35.59
22 23 24 25 26 27 28 29 30
36.00 36.41 36.82 37.23 37.64 38.05 38.45 38.86 39.27
33.11 33.50 33.89 34.27 34.66 35.05 35.43 35.82 36.20 36.59
30.64 31 .oo 31 .36 31.73 32.09 32.45 32.82 33.18 33.55 33.91
28.40 28.75 29.10 29.45 29.81 30.16 30.51 30.86 31.22 31.57
31 32 33 34 35 36 37 38 39 40
47.09 47.55 48.00 48.45 48.91 49.36 49.82 50.27 50.73 51.18
44.74 45.18 45.62 46.07 46.51 46.95 47.40 47.84 48.28 48.73
42.03 42.45 42.87 43.30 43.72 44.14 44.56 44.98 45.40 45.82
39.68 40.09 40.50 40.91 41 .32 41.73 42.14 42.55 42.95 43.36
36.98 37.36 37.75 38.14 38.52 38.91 39.30 39.68 40.07 40.45
34.27 34.64 35.00 35.36 35.73 36.09 36.45 36.82 37.18 37.55
31.92 32.27 32.62 32.98 33.33 33.68 34.03 34.39 34.74 35.09
41
42
51 .64 52.09
49.17 49.61
46.24 46.66
43.77 44.18
40.84 41 .23
35.44 35.80
43 44 45 46 47 48 49 50
52.55 53.00 53.45 53.91 54.36 54.82 55.27 55.73
37.91 38.27 --------------38.64 39.00 39.36 39.73 40.09 40.45 40.82 41.18
21
---GROUND
SOUTHERN DISTANCE FROM TOP FEET TOP 1
2 3 4 5 6 7 8 9 10
YELLOW PINE CLASS H-3 CIRC. INCHES
33.00 33.45 33.90 34.35 34.80 35.24 35.69 36. 14 36.59 37.04 37.49
LINE
50.06 50.50 50.94 51.39 51 .83 52.27 52.72 53.16
AND DOUGLAS CLASS H-2 CIRC. INCHES
31 .oo 31.43 31.86 32.29 32.71 33.14 33.57 34.00 34.43 34.86 35.29
(7
FEET
47.08 47.50 47.92 48.34 48.76 49.18 49.60 50.02
0 INCHES)------44.59 41 .61
45.00 45.41 45.82 46.23 46.64 47.05 47.45
42.00 42.39 42.77 43.16 43.55 43.93 44.32
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. 1 NCHES
29.00 29.42 29.84
27.00 27.40 27.80 28.19 28.59 28.99 29.39 29.79 30.18 30.58 30.98
30.26 30.67 31.09 31.51 31.93 32.35 32.77 33.18
1
CLASS CIRC. INCHES
25 25 25 26 26 26 27 27 28 28 28
00
38 76 13 51 89 27 64 02 40 78
2
4
36.15 36.50 36.85 37.20 37.56 37.91 38.26 38.61
55 FOOT POLE 3 CLASS 4 CIRC. INCHES 1 NCHES
CLASS CIRC.
23.00 23.36 23.71 24.07 24.43 24.79 25.14 25.50 25.86 26,21 26.57
21 00 21 35 21 69 22 04 22 39 22 73 23 08 23 43 23 78 24 12 24 47
356
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
I I 12 13 14 15 16 17 18 19 20
37.94 38.39 38.84 39.29 39.13 40.18 40.63 41 .08 41.53 41 .98
21 22 23 24 25 26 27 28 29 30
AND DOUGLAS CLASS H-2 CIRC. INCHES
.
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
CLASS CIRC. INCHES
2
55 FOOT CLASS 3 CIRC. INCHES
POLE-con. CLASS CIRC. INCHES
35.71 36. 14 36.57 37.00 37.43 37.86 38.29 38.71 39.14 39.57
33 34 34 34 35 35 36 36 36 37
60 02 44 86 28 69 11 53 95 37
31 .38 31 .78 32.17 32.57 32.97 33.37 33.77 34.16 34.56 34.96
29.15 29.53 29.91 30.29 30.66 31.04 31 .42 31 .80 32.17 32.55
26.93 27.29 27.64 28.00 28.36 28.71 29.07 29.43 29.79 30.14
24.82 25.16 25.51 25.86 26.20 26.55 26.90 27.24 27.59 27.94
42.43 42.88 43.33 43.78 44.22 44.67 45.12 45.57 46.02 46.47
40.00 40.43 40.86 41 .29 41.71 42.14 42.57 43.00 43.43 43.86
37 38 38 39 39 39 40 40 41 41
79 20 62 04 46 88 30 71 13 55
35.36 35.76 36.15 36.55 36.95 37.35 37.74 38. 14 38.54 38.94
32.93 33.31 33.68 34.06 34.44 34.82 35.19 35.51 35.95 36.33
30.50 30.86 31.21 31.57 31.93 32.29 32.64 33.00 33.36 33.71
28.29 28.63 28.98 29.33 29.67 30.02 30.37 30.71 31 .06 31.41
31 32 33 34 35 36 37 38 39 40
46.92 47.37 47.82 48.27 48.71 49.16 49.61 50.06 50.51 50.96
44.29 44.71 45.14 45.57 46.00 46.43 46.86 47.29 47.71 48.14
41 42 42 43 43 44 44 44 45 45
97 39 81 22 64 06 48 90 32 73
39.34 39.73 40.13 40.53 40.93 41.33 41 .72 42.12 42.52 42.92
36.70 37.08 37.46 37.84 38.21 38.59 38.97 39.35 39.72 40.10
34.07 34.43 34.79 35.14 35.50 35.86 36.21 36.57 36.93 37.29
31 .76 32.10 32.45 32.80 33.14 33.49 33.84 34.18 34.53 34.88
41 42 43 44 45 46 47
51.41 51.86 52.31 52.76 53.20 53.65 54.10
48.57 49.00 49.43 49.86 50.29 50.71 51.14
46 46 46 47 47 48 48
37.64 38.00 38.36 38.71 39.07 39.43 39.79
35.22 35.57 35.92 36.27 36.61 36.96 37.31 ------
54.55 55.00 55.45
51.57 52.00 52.43
49 49.50 49.92
43.32 43.71 44.11 44.51 44.91 45.31 45.70 6 INCHES)------46.10 46.50 46.90
40.48 40.86 41 .23 41 .61 41.99 42.37 42.74
48 49 50
15 57 99 41 83 24 66 7 FEET, 08
43.12 43.50 43.88
40.14 40.50 40.86
37.65 38.00 38.35
51 52 53 54 55
55.90 56.35 56.80 57.24 57.69
52.86 53.29 53.71 54.14 54.57
50 50 51 51 52
34 76 17 59 01
47.30 47.69 48.09 48.49 48.89
44.26 44.63 45.01 45.39 45.77
41.21 41.57 41.93 42.29 42.64
38.69 39.04 39.39 39.13 40.08
-----------------------GROUND
LINE
4
APPENDIX
357
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
60 3
FOOT POLE CLASS 4 CIRC. INCHES
33.00 33.44 33.89 34.33 34.78 35.22 35.61 36.11 36.56 37.00 37.44
31 .oo 31.43 31.85 32.28 32.70 33.13 33.56 33.98 34.41 34.83 35.26
29.00 29.41 29.81 30.22 30.63 31.04 31.44 31 .85 32.26 32.67 33.07
27.00 27.39 27.78 28.17 28.56 28.94 29.33 29.72 30.11 30.50 30.89
25.00 25.37 25.74 26.11 26.48 26.85 27.22 27.59 27.96 28.33 28.70
23.00 23.35 23.70 24.06 24.41 24.76 25.11 25.46 25.81 26.17 26.52
21 .oo 21.33 21 .67 22.00 22.33 22.67 23.00 23.33 23.67 24.00 24.33
11 12 13 14 I5 16 17 18 19 20
37.89 38.33 38.78 39.22 39.67 40.11 40.56 41 .oo 41.44 41 .89
35.69 36.11 36.54 36.96 37.39 37.81 38.24 38.61 39.09 39.52
33.48 33.89 34.30 34.70 35.11 35.52 35.93 36.33 36.74 31.15
31 .28 31 .67 32.06 32.44 32.83 33.22 33.61 34.00 34.39 34.78
29.07 29.44 29.81 30.19 30.56 30.93 31.30 31 .67 32.04 32.41
26.87 27.22 27.57 27.93 28.28 28.63 28.98 29.33 29.69 30.04
24.67 25.00 25.33 25.67 26.00 26.33 26.67 27.00 27.33 27.67
21 22 23 24 25 26 27 28 29 30
42.33 42.78 43.22 43.67 44.11 44.56 45.00 45.44 45.89 46.33
39.94 40.37 40.80 41.22 41 .65 42.07 42.50 42.93 43.35 43.78
37.56 37.96 38.37 38.78 39.19 39.59 40.00 40.41 40.81 41.22
35.17 35.56 35.94 36.33 36.72 31.11 37.50 37.89 38.28 38.67
32.78 33.15 33.52 33.89 34.26 34.63 35.00 35.37 35.74 36.11
30.39 30.74 31.09 31.44 31 .80 32.15 32.50 32.85 33.20 33.56
28.00 28.33 28.67 29.00 29.33 29.67 30.00 30.33 30.67 31 .oo
31 32 33 34 35 36 37 38 39 40
46.78 47.22 47.67 48.11 48.56 49.00 49.44 49.89 50.33 50.78
44.20 44.63 45.06 45.48 45.91 46.33 46.76 47.19 47.61 48.04
41 .63 42.04 42.44 42.85 43.26 43.67 44.07 44.48 44.89 45.30
39.06 39.44 39.83 40.22 40.61 41 .oo 41.39 41 .78 42.17 42.56
36.48 36.85 37.22 37.59 37.96 38.33 38.70 39.07 39.44 39.81
33.91 34.26 34.61 34.96 35.31 35.67 36.02 36.37 36.72 37.07
31.33 31 .67 32.00 32.33 32.67 33.00 33.33 33.67 34.00 34.33
Ltl 42 43 44 45 46 47 48 49 50
51.22 51 .67 52.11 52.56 53.00 53.44 53.89 54.33 54.78 55.22
48.46 48.89 49.31 49.74 50.17 50.59 51.02 51.44 51 .87 52.30
45.70 46.11 46.52 46.93 47.33 47.74 48.15 48.56 48.96 49.37
42.94 43.33 43.72 44.11 44.50 44.89 45.28 45.67 46.06 46.44
40.19 40.56 40.93 41.30 41 .67 42.04 42.41 42.78 43.15 43.52
37.43 37.78 38.13 38.48 38.83 39.19 39.54 39.89 40.24 40.59
34.67 35.00 35.33 35.67 36.00 36.33 36.67 37.00 37.33 37.67
TOP 1 2 3 4 5 6 I 8 9 10
TRANSMISSION
358
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET 51 52 53 54 55 56 57 58 59 60
SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES 55.67 56.11 56.56 57.00 57.44 57.89 58.33 58.78 59.22 59.67
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES 52.72 ---GROUND 53.15 53.57 54.00 54.43 54.85 55.28 55.70 56.13 56.56
AND DOUGLAS CLASS H-2 CIRC. INCHES
FIR CLASS H-l CIRC. 1 NCHES 49.78 Ll INE (8 FEET, 50.19 50.59 51 .oo 51.41 51.81 52.22 52.63 53.04 53.44
CLASS CIRC. INCHES 46 0 47 47 48 48 48 49 49 49 50
1
83 NCHES 22 61 00 39 78 17 56 94 33
CLASS CIRC. INCHES
2
60 FOOT CLASS 3 CIRC. INCHES
43.89
40.94
44.26 44.63 45.00 45.37 45.74 46.11 46.48 46.85 47.22
91 41 42 42 42 43 43 43 44
CLASS CIRC. INCHES
1
38.00 30 65 00 35 70 06 41 76 11
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
38.33 36.67 39.00 39.33 39.67 40.00 40.33 40.67 41 .oo
65 FOOT POLE 3 CLASS 4 CIRC. INCHES
33.00 33.43 33.86 34.30 34.73 35.16 35.59 36.03 36.46 36.89 37.32
31 31 31 32 32 33 33 33 34 34 35
00 42 83 25 66 08 49 91 32 74 15
29.00 29.40 29.80 30.19 30.59 30.99 31.39 31 .I9 32.19 32.58 32.98
27.00 27.38 27.76 28.14 28.53 28.91 29.29 29.67 30.05 30.43 30.81
25.00 25.36 25.73 26.09 26.46 26.82 27.19 27.55 27.92 28.28 20.64
23.00 23.35 23.69 24.04 24.39 24.74 25.08 25.43 25.78 26.13 26.47
21 .oo 21.33 21.66 21.99 22.32 22.65 22.98 23.31 23.64 23.97 24.31
11 12 13 14 15 16 17 18 19 20
37.75 38.19 38.62 39.05 39.48 39.92 40.35 40.78 41.21 41 .64
35 35 36 36 37 37 38 38 30 39
57 98 40 81 23 64 06 47 89 31
33.38 33.78 34.18 34.58 34.97 35.37 35.77 36.17 36.57 36.97
31.19 31.58 31 .96 32.34 32.72 33.10 33.48 33.86 34.25 34.63
29.0 1 29.37 29.74 30.10 30.47 30.83 31.19 31 .56 31.92 32.29
26.82 27.17 27.52 27.86 28.21 28.56 28.91 29.25 29.60 29.95
24.64 24.97 25.30 25.63 25.96 26.29 26.62 26.95 27.28 27.61
21 22 23 24 25 26 27 28 29 30
42.08 42.51 42.94 43.37 43.81 44.24 44.67 45.10 45.53 45.97
39 40 40 40 41 41 42 42 43 43
72 14 55 97 38 80 21 63 04 46
37.36 37.76 30.16 30.56 30.96 39.36 39.75 40.15 40.55 40.95
35.01 35.39 35.77 36.15 36.53 36.92 37.30 37.68 38.06 38.44
32.65 33.02 33.38 33.75 34.11 34.47 34.84 35.20 35.57 35.93
30.30 30.64 30.99 31.34 31 .69 32.03 32.38 32.73 33.08 33.42
27.94 28.27 28.60 28.93 29.26 29.59 29.92 30.25 30.58 30.92
TOP 1 2 3 4 5 6 7 8 9 10
4
1
FIR CLASS H-l CIRC. INCHES
POLE-con. CLASS CIRC. INCHES
APPENDIX
359
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS 2 CIRC. 1 NCHES
65 FOOT CLASS 3 CIRC. INCHES
POLE-Con. CLASS CIRC. INCHES
31 32 33 34 35 36 31 38 39 40
46.40 46.83 47.26 47.69 48.13 40.56 48.99 49.42 49.86 50.29
43.87 44.29 44.70 45.12 45.53 45.95 46.36 46.78 47.19 47.61
41.35 41.75 42.14 42.54 42.94 43.34 43.74 44.14 44.53 44.93
38.82 39.20 39.50 39.97 40.35 40.73 41.11 41.49 41.87 42.25
36.30 36.66 37.03 37.39 37.75 38.12 38.48 38.85 39.21 39.58
33.77 34.12 34.47 34.81 35.16 35.51 35.86 36.20 36.55 36.90
31.25 31.58 31.91 32.24 32.57 32.90 33.23 33.56 33.89 34.22
41 42 43 44 45 46 47 48 49 50
50.72 51.15 51.58 52.02 52.45 52.88 53.31 53.75 54.16 54.61
48.03 48.44 48.86 49.27 49.69 50.10 50.52 50.93 51.35 51 .76
45.33 45.73 46.13 46.53 46.92 47.32 47.72 48.12 48.52 48.92
42.64 43.02 43.40 43.78 44.16 44.54 44.92 45.31 45.69 46.07
39.94 40.31 40.67 41.03 41.40 41 .76 42.13 42.49 42.86 43.22
37.25 37.59 37.94 38.29 38.64 38.98 39.33 39.68 40.03 40.37
34.55 34.88 35.21 35.54 35.87 36.20 36.53 36.86 37.19 37.53
51 52 53 54 55 56 --
55.04 55.41 55.91 56.34 56.77 57.20
40.72 41.07 41 .42 41 .76 42.11 42.46
37.86 38.19 38.52 38.85 39.18 39.51
57.64 58.07 58.50 58.93
46.45 46.83 47.21 47.59 47.97 48.36 6 INCHES)------48.74 49.12 49.50 49.88
43.58 43.95 44.31 44.68 45.04 45.41
57 58 59 60
52.18 52.59 53.01 53.42 53.84 54.25 ---GROUND 54.67 55.08 55.50 55.92
45.77 46.14 46.50 46.86
42.81 43.15 43.50 43.85
39.84 40.17 40.50 40.83
61 62 63 64 65
59.36 59.80 60.23 60.66 61 .09
53.30 53.69 54.09 54.49 54.89
50.26 50.64 51.03 51.41 51.79
47.23 47.59 47.96 48.32 48.69
44.19 44.54 44.89 45.24 45.58
41.16 41.49 41.82 42.15 42.48
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
29.00 29.39 29.78 30.17 30.56 30.95 31.34 31.73 32.13 32.52 32.91
27.00 27.38 27.75 28.13 28.50 28.88 29.25 29.63 30.00 30.38 30.75
SOUTHERN DISTANCE FROM TOP FEET TOP 2 3 4 5 6 7 8 9 10
YELLOW PINE CLASS H-3 CIRC. INCHES 33 33 33 34 34 35 35 36 36 36 37
00 43 86 29 72 15 58 01 44 87 30
49.31 49.71 50.11 50.51 50.91 51.31 LINE (6 51.70 52.10 52.50 52.90
56.33 56.75 57.16 57.58 57.99
AND DOUGLAS CLASS H-2 CIRC. INCHES 31 .oo 31.41 31 .I31 32.22 32.63 33.03 33.44 33.84 34.25 34.66 35.06
FEET
FIR 1
CLASS CIRC. INCHES 25 25 25 26 26 26 27 27 27 28 28
00 36 72 08 44 80 16 52 88 23 59
2
CLASS CIRC. INCHES
70 3
23.00 23.34 23.69 24.03 24: 38 24.72 25.06 25.41 25.75 26.09 26.44
4
FOOT POLE CLASS 4 CIRC. INCHES 21 21 21 21 22 22 22 23 23 23 24
00 32 64 96 28 60 92 24 56 88 20
360
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow @e-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES
FIR CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
CLASS CIRC. INCHES
2
70 FOOT CLASS 3 CIRC. INCHES
POLE-con. CLASS CIRC. INCHES
I I 12 13 14 15 16 17 18 19 20
37.73 38.16 38.59 39.02 39.45 39.88 40.30 40.73 41.16 41.59
35.47 35.88 36.28 36.69 37.09 37.50 37.91 38.31 38.72 39.13
33.30 33.69 34.08 34.47 34.86 35.25 35.64 36.03 36.42 36.81
31.13 31.50 31 .aa 32.25 32.63 33.00 33.38 33.75 34.13 34.50
28.95 29.31 29.67 30.03 30.39 30.75 31.11 31.47 31 .a3 32.19
26.78 27.13 27.47 27.81 28.16 28.50 28.84 29.19 29.53 29.88
24.52 24.84 25.16 25.48 25.80 26.13 26.45 26.71 27.09 27.41
21 22 23 24 25 26 27 28 29 30
42.02 42.45 42.88 43.31 43.74 44.17 44.60 45.03 45.46 45.89
39.53 39.94 40.34 40.75 41.16 41 .56 41.97 42.38 42.78 43.19
37.20 37.59 37.98 38.38 38.77 39.16 39.55 39.94 40.33 40.72
34.88 35.25 35.63 36.00 36.38 36.75 37.13 37.50 37.88 38.25
32.55 32.91 33.27 33.63 33.98 34.34 34.70 35.06 35.42 35.78
30.22 30.56 30.91 31 .25 31.59 31.94 32.28 32.63 32.97 33.31
27.73 28.05 28.37 28.69 29.01 29.33 29.65 29.97 30.29 30.61
31 32 33 34 35 36 37 38 39 40
46.32 46.75 47.18 47.61 48.04 48.47 48.90 49.33 49.76 50.19
43.59 44.00 44.41 44.81 45.22 45.63 46.03 46.44 46.84 47.25
41.11 41.50 41 .a9 42.28 42.67 43.06 43.45 43.84 44.23 44.63
38.63 39.00 39.38 39.75 40.13 40.50 40.88 41 .25 41 .63 42.00
36. 14 36.50 36.86 37.22 37.58 37.94 38.30 38.66 39.02 39.38
33.66 34.00 34.34 34.69 35.03 35.38 35.72 36.06 36.41 36.75
30.93 31.25 31.57 31 .a9 32.21 32.53 32.85 33.17 33.49 33.81
41 42 43 44 45 46 47 48 49 50
50.62 51.05 51.48 51.91 52.34 52.77 53.20 53.63 54.05 54.48
47.66 48.06 48.47 48.88 49.28 49.69 50.09 50.50 50.91 51.31
45.02 45.41 45.80 46.19 46.58 46.97 47.36 47.75 48.14 48.53
42.38 42.15 43.13 43.50 43.88 44.25 44.63 45.00 45.38 45.75
39.73 40.09 40.45 40.81 41.17 41.53 41 .a9 42.25 42.61 42.97
37.09 37.44 37.78 38.13 38.47 38.81 39.16 39.50 39.84 40.19
34.13 34.45 34.77 35.09 35.41 35.73 36.05 36.38 36.70 37.02
51 52 53 54 55 56 57 58 59 60
54.91 55.34 55.77 56.20 56.63 57.06 57.49 57.92 58.35 58.78
51 .72 52.13 52.53 52.94 53.34 53.75 54.16 54.56 54.97 55.38
48.92 49.31 49.70 50.09 50.48 50.88 51 .27 51.66 52.05 52.44
46.13 46.50 46.88 47.25 47.63 48.00 48.38 48.75 49.13 49.50
43.33 43.69 44.05 44.41 44.77 45.13 45.48 45.84 46.20 46.56
40.53 40.88 41.22 41 .56 41.91 42.25 42.59 42.94 43.28 43.63
37.34 37.66 37.98 38.30 38.62 38.94 39.26 39.58 39.90 40.22
+
APPENDIX
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN DISTANCE FROM TOP FEET
YELLOW PINE CLASS H-3 CIRC. INCHES
AND DOUGLAS CLASS H-2 CIRC. INCHES
-----------------------GROUND 51 62 63 64 65 66 67 68 69 70
TOP 1 2 3 4 5 6
CLASS H-l CIRC. INCHES LINE
59.21 59.64 60.07 60.50 60.93 61 .36 61 .79 62.22 62.65 63.08
SOUTHERN YELLOW DISTANCE FROM TOP FEET
70
FIR
55.78 56.19 56.59 57.00 57.41 57.81 58.22 58.63 59.03 59.44
PINE AND CLASS H-3 CIRC. INCHES
(9
CLASS CIRC. INCHES
FEET.
52.83 53.22 53.61 54.00 54.39 54.76 55.17 55.56 55.95 56.34
DOUGLAS FIR CLASS H-2 CIRC. INCHES
0
1
CLASS CIRC. INCHES
2
FOOT
CLASS CIRC. INCHES
POLE-Con.
3
CLASS CIRC. INCHES
INCHES)--------------------------
49.88 50.25 50.63 51 .oo 51.38 51 .I5 52.13 52.50 52.88 53.25
46.92 47.26 47.64 48.00 48.36 48.12 49.08 49.44 49.80 50.16
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
43.97 44.31 44.66 45.00 45.34 45.69 46.03 46.38 46.72 47.06
CLASS CIRC. INCHES
2
40.54 40.86 41.18 41.50 41 .82 42.14 42.46 42.78 43.10 43.42
75 FOOT CLASS 3 CIRC. INCHES
8 9 10
33 33 33 34 34 35 35 35 36 36 37
00 42 84 26 68 10 52 94 36 78 20
31 .oo 31.41 31 .81 32.22 32.62 33.03 33.43 33.84 34.25 34.65 35.06
29.00 29.38 29.77 30.15 30.54 30.92 31.30 31 .69 32.07 32.46 32.84
27.00 27.37 27.74 28.11 28.48 28.85 29.22 29.59 29.96 30.33 30.70
25.00 25.35 25.70 26.04 26.39 26.74 27.09 27.43 27.78 28.13 28.48
23.00 23.33 23.67 24.00 24.33 24.67 25.00 25.33 25.67 26.00 26.33
11 12 13 14 15 16 17 18 19 20
37 38 38 38 39 39 40 40 40 41
62 04 46 88 30 72 14 57 99 41
35.46 35.67 36.28 36.68 37.09 37.49 37.90 38.30 38.71 39.12
33.22 33.61 33.99 34.36 34.76 35.14 35.53 35.91 36.30 36.68
31.07 31.43 31.80 32.17 32.54 32.91 33.28 33.65 34.02 34.39
28.63 29.17 29.52 29.87 30.22 30.57 30.91 31 .26 31 .61 31 .96
26.67 27.00 27.33 27.67 28.00 28.33 28.67 29.00 29.33 29.67
21 22 23 24 25 26 27 28 29 30
41 42 42 43 43 43 44 44 45 45
83 25 67 09 51 93 35 77 19 61
39.52 39.93 40.33 40.74 41. I4 41.55 41 .96 42.36 42.77 43.17
37.07 37.45 37.83 38.22 38.60 38.99 39.37 39.75 40.14 40.52
34.76 35.13 35.50 35.87 36.24 36.61 36.98 37.35 37.12 38.09
32.30 32.65 33.00 33.35 33.70 34.04 34.39 34.14 35.09 35.43
30.00 30.33 30.67 31 .oo 31.33 31 .67 32.00 32.33 32.67 33.00
POLE
4
362
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND CLASS H-3 CIRC. INCHES
DOUGLAS FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
75 FOOT CLASS 2 CIRC. INCHES
POLE-con. CLASS CIRC. INCHES
31 32 33 34 35 36 37 38 39 40
46.03 46.45 46.87 47.29 47.71 48.13 48.55 48.97 49.39 49.81
43.58 43.99 44.39 44.80 45.20 45.61 46.01 46.42 46.83 47.23
40.91 41.29 41 .67 42.06 42.44 42.83 43.21 43.59 43.98 44.36
38.46 38.83 39.20 39.57 39.93 40.30 40.67 41.04 41.41 41 .78
35.78 36.13 36.48 36.83 37.17 37.52 37.87 38.22 38.57 38.91
33.33 33.67 34.00 34.33 34.67 35.00 35.33 35.67 36.00 36.33
41 42 43 44 45 46 47 48 49 50
50.23 50.65 51.07 51.49 51.91 52.33 52.75 53.17 53.59 54.01
47.64 48.04 48.45 48.86 49.26 49.67 50.07 50.48 50.88 51.29
44.75 45.13 45.51 45.90 46.28 46.67 47.05 47.43 47.82 48.20
42.15 42.52 42.89 43.26 43.63 44.00 44.37 44.74 45.11 45.48
39.26 39.61 39.96 40.30 40.65 41 .oo 41.35 41.70 42.04 42.39
36.67 37.00 37.33 37.67 38.00 38.33 38.67 39.00 39.33 39.67
51 52 53 54 55 56 57 58 59 60
54.43 54.86 55.28 55.70 56.12 56.54 56.96 57.38 57.80 58.22
51.70 52.10 52.51 52.91 53.32 53.72 54.13 54.54 54.94 55.35
48.59 48.97 49.36 49.74 50.12 50.51 50.89 51 .28 51.66 52.04
45.85 46.22 46.59 46.96 47.33 47.70 48.07 48.43 48.80 49.17
42.74 43.09 43.43 43.78 44.13 44.48 44.83 45.17 45.52 45.87
40.00 40.33 40.67 41 .oo 41.33 41 .67 42.00 42.33 42.67 43.00
61 62 63 64 65 ---------------
58.64 59.06 59.48 59.90 60.32
43.33 43.67 44.00 44.33 44.67 -----
60.74 61.16 61 .58 62.00 62.42
49.54 49.91 50.28 50.65 51.02 INCHES) 51.39 51 .76 52.13 52.50 52.87
46.22 46.57 46.91 47.26 47.61
66 67 68 69 70
55.75 56.16 56.57 56.97 57.38 GROUND 57.78 58.19 58.59 59.00 59.41
47.96 48.30 48.65 49.00 49.35
45.00 45.33 45.67 46.00 46.33
71 72 73 74 75
62.84 63.26 63.68 64.10 64.52
53.24 53.61 53.98 54.35 54.72
49.70 50.04 50.39 50.74 51.09
46.67 47.00 47.33 47.67 48.00
59.81 60.22 60.62 61 .03 61 .43
LINE
52.43 52.81 53.20 53.58 53.96 9 FEET, 54.35 54.73 55.12 55.50 55.88 56.27 56.65 57.04 57.42 57.80
6
3
APPENDIX
363
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND DOUGLAS FIR CLASS H-2 CLASS H-3 CIRC. CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
33.00 33.41 33.82 34.24 34.65 35.06 35.47 35.89 36.30 36.71 37.12
31 .oo 31.39 31.70 32.18 32.57 32.96 33.35 33.74 34.14 34.53 34.92
29.00 29.38 29.76
16 17 18 19 20
37.53 37.95 38.36 38.77 39.18 39.59 40.01 40.42 40.83 41 .24
21 22 23 24 25 26 21 28 29 30
CLASS CIRC.
INCHES
1
CLASS CIRC.
INCHES
2
80 FOOT POLE CLASS 3 CIRC.
INCHES
30.14 30.51 30.89 31 .27 31 .65 32.03 32.41 32.78
27.00 27.36 27.73 28.09 28.46 28.82 29.19 29.55 29.92 30.28 30.65
25.00 25.34 25.69 26.03 26.38 26.72 27.07 27.41 27.76 28. IO 28.45
23.00 23.32 23.65 23.97 24.30 24.62 24.95 25.27 25.59 25.92 26.24
35.31 35.70 36.09 36.49 36.88 37.27 37.66 38.05 38.45 38.84
33.16 33.54 33.92 34.30 34.68 35.05 35.43 35.81 36.19 36.57
31 .Ol 31 .38 31.74 32.11 32.47 32.84 33.20 33.57 33.93 34.30
28.79 29.14 29.48 29.82 30.17 30.51 30.86 31.20 31.55 31 .89
26.57 26.89 27.22 27.54 27.86 28.19 28.51 28.84 29.16 29.49
41.66 42.07 42.48 42.89 43.30 43.72 44.13 44.54 44.95 45.36
39.23 39.62 40.01 40.41 40.80 41.19 41.50 41.97 42.36 42.76
36.95 37.32 37.70 38.08 38.46 38.84 39.22 39.59 39.97 40.35
34.66 35.03 35.39 35.76 36.12 36.49 36.85 37.22 37.58 37.95
32.24 32.58 32.93 33.27 33.61 33.96 34.30 34.65 34.99 35.34
29.81 30.14 30.46 30.78
32.08 32.41 32.73
31 32 33 34 35 36 37 38 39 40
45.78 46.19 46.60 47.01 47.43 47.84 48.25 48.66 49.07 49.49
43.15 43.54 43.93 44.32 44.72 45.11 45.50 45.89 46.28 46.68
40.73
42.24 42.62 43.00 43.38 43.76 44.14
38.31 38.68 39.04 39.41 39.77 40.14 40.50 40.86 41 .23 41.59
35.68 36.03 36.37 36.72 37.06 37.41 37.75 38.09 38.44 38.78
33.05 33.38 33.70 34.03 34.35 34.68 35.00 35.32 35.65 35.97
41 42 43 44 45 46 47 48 49 50
49.90 50.31 50.72 51.14 51.55 51.96 52.37 52.78 53.20 53.61
47.07 47.46 47.85 48.24 48.64 49.03 49.42 49.81 50.20 50.59
44.51 44.89 45.27 45.65 46.03 46.41 46.78 47.16 47.54 47.92
41 .96 42.32 42.69 43.05 43.42 43.78 44.15 44.51 44.88 45.24
39.13 39.47 39.82 40.16 40.51 40.85 41.20 41.54 41 .89 42.23
36.30 36.62 36.95 37.27 37.59 37.92 38.24 38.57 38.89 39.22
TOP
1 2 3 4 5 6 7 El 9 10 11 12 13
14 15
41.11 41.49 41.86
31.11 31.43 31 .76
TRANSMISSION
364
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND DOUGLAS FIR CLASS H-2 CLASS H-3 CIRC. CIRC. INCHES INCHES
51 52 53 54 55 56 57 58 59 60
54.02 54.43 54.84 55.26 55.67 56.08 56.49 56.91 57.32 57.73
61 62 63 64 65 66 67 68 69
58.14 58.55 58.91 59.38 59.79 60.20 60.61 61 .03 61 .44
70
61 .85
71 72 73 74 75 76 77 78 79 80
62.26 62.68 63.09 63.50 63.91 64.32 64.74 65.15 65.56 65.9-l
SOUTHERN YELLOW DISTANCE FROM TOP FEET TOP 2 3 4 5 6 7 8 9 10
PINE AND CLASS H-3 CIRC. INCHES 33.00 33.41 33.81 34.22 34.62 35.03 35.43 35.84 36.24 36.65 37.05
50 99 51 38 51 77 52 16 52 55 52 95 53 34 53.73 54.12 54.51 54.91 55.30 55.69 56.08 56.47 56.86 57.26 57.65 58.04 -GROUND 58.43
LINE
58.82 59.22 59.61 60.00 60.39 60.78 61.18 61 .51 61 .96 62.35
DOUGLAS FIR CLASS H-2 CIRC. INCHES 31 31 31 32 32 32 33 33 34 34 34
00 39 77 16 54 93 32 70 09 47 86
CLASS CIRC. INCHES
48.30 48.68 49.05 49.43 49.81 50.19 50.57 50.95 51 .32 51.70
45.61 45.97 46.34 46.70 47.07 47.43 47.80 48.16 48.53 48.89
42.57 42.92 43.26 43.61 43.95 44.30 44.64 44.99 45.33 45.68
39.54 39.86 40.19 40.51 40.84 41.16 41.49 41.81 42.14 42.46
49.26 49.62 49.99 50.35 50.72 51 .08 51.45 51 .81 52.18 INCHES) 52.54
46.02 46.36 46.71 47.05 47.40 47.74 48.09 48.43 48.78
42.78 43.11 43.43 43.76 44.08 44.41 44.73 45.05 45.38
49.12
45.70
55.86 56.24 56.62 57.00 57.38 57.16 58.14 58.51 58.89 59.27
52.91 53.21 53.64 54.00 54.36 54.73 55.09 55.46 55.82 56.19
49.47 49.81 50.16 50.50 50.84 51.19 51.53 51.88 52.22 52.57
46.03 46.35 46.68 47.00 47.32 41.65 47.97 48.30 48.62 48.95
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
29.00 29.37 29.75 30.12 30.49 30.87 31 .24 31 .61 31.99 32.36 32.73
27.00 27.35 27.71 28.06 28.42 28.77 29.13 29.48 29.84 30.19 30.54
52.08 52.46 52.84 53.22 53.59 53.91 54.35 54.73 55.11 (10 FEET 55.49
0
1
80 FOOT POLE-Con. CLASS 2 CLASS 3 CIRC. CIRC. INCHES INCHES
CLASS H-l CIRC. INCHES
1
CLASS CIRC. INCHES 25.00 25.34 25.67 26.01 26.34 26.68 27.01 27.35 21.68 28.02 28.35
2
85 FOOT CLASS 3 CIRC. INCHES 23.00 23.32 23.63 23.95 24.27 24.58 24.90 25.22 25.53 25.85 26.16
POLE
APPENDIX
365
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND DOUGLAS FIR CLASS H-3 CLASS H-2 CIRC. CIRC. INCHES INCHES
85 CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
FOOT
POLE-Con.
CLASS CIRC. INCHES
11 12 13 14 15 16 17 18 19 20
37.46 37.86 38.27 38.67 39.08 39.48 39.89 40.29 40.70 41.10
35.25 35.63 36.02 36.41 36.79 37.16 37.56 37.95 38.34 38.72
33.11 33.46 33.85 34.23 34.60 34.91 35.35 35.72 36.09 36.47
30.90 31.25 31.61 31.96 32.32 32.67 33.03 33.38 33.73 34.09
28.69 29.03 29.36 29.70 30.03 30.37 30.70 31.04 31.37 31.71
26.48 26.80 27.11 27.43 27.75 28.06 28.38 28.70 29.01 29.33
21 22 23 24 25 26 27 28 29 30
41.51 41.91 42.32 42.72 43.13 43.53 43.94 44.34 44.75 45.15
39.11 39.49 39.88 40.27 40.65 41.04 41.42 41.81 42.20 42.58
36.84 37.22 37.59 37.96 38.34 38.71 39.08 39.46 39.83 40.20
34.44 34.80 35.15 35.51 35.86 36.22 36.57 36.92 37.28 37.63
32.04 32.38 32.72 33.05 33.39 33.72 34.06 34.39 34.73 35.06
29.65 29.96 30.28 30.59 30.91 31.23 31.54 31.86 32.18 32.49
31 32 33 34 35 36 37 38 39 40
45.56 45.96 46.37 46.77 47.16 47.58 47.99 48.39 48.80 49.20
42.97 43.35 43.74 44.13 44.51 44.90 45.28 45.67 46.06 46.44
40.58 40.95 41.32 41.70 42.07 42.44 42.82 43.19 43.56 43.94
37.99 36.34 38.70 39.05 39.41 39.16 40.11 40.47 40.82 41.18
35.40 35.73 36.07 36.41 36.74 37.08 37.41 37.75 38.08 38.42
32.81 33.13 33.44 33.76 34.08 34.39 34.71 35.03 35.34 35.66
41 42 43 44 45 46 47 48 49 50
49.61 50.01 50.42 50.82 51.23 51.63 52.04 52.44 52.85 53.25
46.83 47.22 47.60 47.99 48.37 48.76 49.15 49.53 49.92 50.30
44.31 44.68 45.06 45.43 45.80 46.18 46.55 46.92 47.30 47.67
41.53 41.89 42.24 42.59 42.95 43.30 43.66 44.01 44.37 44.72
38.75 39.09 39.42 39.76 40.09 40.43 40.77 41.10 41.44 41.77
35.97 36.29 36.61 36.92 37.24 37.56 37.87 38.19 38.51 38.82
51 52 53 54 55 56 57 56 59 60
53.66 54.06 54.47 54.87 55.28 55.68 56.09 56.49 56.90 57.30
50.69 51.08 51.46 51.85 52.23 52.62 53.01 53.39 53.78 54.16
48.04 48.42 48.79 49.16 49.54 49.91 50.28 50.66 51.03 51.41
45.08 45.43 45.76 46.14 46.49 46.85 47.20 47.56 47.91 48.27
42.11 42.44 42.78 43.11 43.45 43.78 44.12 44.46 44.79 45.13
39.14 39.46 39.77 40.09 40.41 40.72 41.04 41.35 41.67 41.99
3
TRANSMISSION
366
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND CLASS H-3 CIRC. INCHES
61 62 63 64 65 66 67 68 69 70
57.71 58.11 58.52 58.92 59.33 59.73 60.14 60.54 60.95 61.35
71 72 73 74
61 .76 62.16 62.57 62.97
75 76 77 78 79 80
63.38 63.78 64.19 64.59 65.00 65.41
81 82 83 84 85
65.81 66.22 66.62 67.03 67.43
SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND CLASS H-3 CIRC. INCHES
85
FOOT POLE-con. CLASS 3 CIRC. INCHES
DOUGLAS FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
54 54 55 55 56 56 56 57 57 58
51 .78 52.15 52.53 52.90 53.27 53.65 54.02 54.39 54.77 55.14
48.62 48.97 49.33 49.68 50.04 50.39 50.75 51.10 51 .46 51 .81
45.46 45.80 46.13 46.47 46.80 47.14 47.47 47.81 48.15 48.48
42.30 42.62 42.94 43.25 43.57 43.89 44.20 44.52 44.84 45.15
55.51 55.89 56.26 56.63 (10 FEET, 57.01 57.38 57.75 58.13 58.50 58.87
52.16 52.52 52.87 53.23 INCHESl---53.58 53.94 54.29 54.65 55.00 55.35
48.82 49.15 49.49 49.82
45.47 45.78 46.10 46.42
50.16 50.49 50.83 51.16 51.50 51 .84
46.73 47.05 47.37 47.68 48.00 48.32
52 52 52 53 53
48.63 48.95 49.27 49.58 49.90
55 94 32 71 09 48 87 25 64 03
58 41 58 80 59 18 59 57 -GROUND LINE 59.96 60.34 60.73 61.11 61 .50 61 .89 62.27 62.66 63.04 63.43 63.82
DOUGLAS FIR CLASS H-2 CIRC. INCHES
59.25 59.62 59.99 60.37 60.74
CLASS CIRC. INCHES
6
1
55.71 56.06 56.42 56.77 57.13
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS?-CIRC. INCHES
17 51 84 18 51
CLASS CIRC. INCHES
TOP 1 2 3 4 5 6 7 8 9 10
33.00 33.40 33.80 34.20 34.60 34.99 35.39 35.79 36.19 36.59 36.99
31 .oo 31 .38 31 .76 32.14 32.52 32.90 33.29 33.67 34.05 34.43 34.81
29.00 29.36 29.73 30.09 30.45 30.82 31.18 31.54 31.90 32.27 32.63
27.00 27.35 27.69 28.04 28.38 28.73 29.07 29.42 29.76 30.11 30.45
25.00 25.33 25.67 26.00 26.33 26.67 27.00 27.33 27.67 28.00 28.33
11 12 13 14 15 16 17 18 19 20
37.39 37.79 38.18 38.58 38.98 39.38 39.78 40.18 40.58 40.98
35.19 35.57 35.95 36.33 36.71 37.10 37.48 37.86 38.24 38.62
32.99 33.36 33.72 34.08 34.45 34.81 35.17 35.54 35.90 36.26
30.80 31.14 31.49 31 .83 32.18 32.52 32.87 33.21 33.56 33.90
28 29 29 29 30 30 30 31 31 31
2
90 FOOT POLE CLASS 3 CIRC. INCHES 23.00 23.31 23.62 23.93 24.24 24.55 24.86 25.17 25.48 25.79 26.10
67 00 33 67 00 33 67 00 33 67
26.40 26.71 27.02 27.33 27.64 27.95 28.26 28.57 28.88 29.19
APPENDIX
367
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
PINE AND DOUGLAS FIR CLASS H-3 CLASS H-2 CIRC. CIRC. INCHES INCHES
21 22 23 24 25 26 21 28 29 30
41.37 41.77 42.17 42.57 42.97 43.37 43.77 44.17 44.57 44.96
31 32 33 34 35 36 37 38 39 40
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
INCHES
FOOT POLE-Con. CLASS 3 CIRC. INCHES
CLASS CIRC.
90 2
42.05 42.43
36.62 36.99 37.35 37.71 38.08 38.44 38.80 39.17 39.53 39.89
34.25 34.60 34.94 35.29 35.63 35.98 36.32 36.67 37.01 37.36
32.00 32.33 32.67 33.00 33.33 33.67 34.00 34.33 34.67 35.00
29.81 30.12 30.43 30.74 31.05 31 .36 31 .67 31 .98 32.29
45.36 45.16 46.16 46.56 46.96 47.36 47.76 48.15 48.55 48.95
42.81 43.19 43.57 43.95 44.33 44.71 45.10 45.48 45.86 46.24
40.26 40.62 40.98 41.35 41.71 42.07 42.43 42.80 43.16 43.52
37.70 38.74 39.08 39.43 39.77 40.12 40.46 40.81
35.33 35.67 36.00 36.33 36.67 37.00 37.33 37.67 38.00 38.33
32.60 32.90 33.21 33.52 33.83 34.14 34.45 34.76 35.07 35.38
41 42 43 44 45 46 47 48 49 50
49.35 49.75 50.15 50.55 50.95 51.35 51.74 52. 14 52.54 52.94
46.62 47.00 47.38 47.76 48.14 48.52 48.90 49.29 49.67 50.05
43.89 44.25 44.61 44.98 45.34 45.70 46.07 46.43 46.79 47.15
41.15 41.50 41 .85 42.19 42.54 42.88 43.23 43.57 43.92 44.26
38.67 39.00 39.33 39.67 40.00 40.33 40.67 41 .oo 41.33 41 .67
35.69 36.00 36.31 36.62 36.93 37.24 37.55 37.86 38.17 38.48
51 52 53 54 55 56 57 58 59 60
53.34 53.74 54.14 54.54 54.93 55.33 55.13 56.13 56.53 56.93
50.43 50.81 51.19 51.57 52.33 52.71 53.10 53.48 53.06
47.52 47.88 48.24 48.61 48.97 49.33 49.70 50.06 50.42 50.79
44.61 44.95 45.30 45.64 45.99 46.33 46.68 47.02 47.37 47.71
42.00 42.33 42.67 43.00 43.33 43.67 44.00 44.33 44.67 45.00
38.79 39.10 39.40 39.71 40.02 40.33 40.64 40.95 41 .26 41.57
61 62 63 64 65 66 67 68 69 70
57.33 57.73 58.12 50.52 58.92 59.32 59.72 60.12 60.52 60.92
54.24 54.62 55.00 55.30 55.76 56.14 56.52 56.90 57.29 57.67
51.15 51.51 51 .87 52.24 52.60 52.96 53.33 53.69 54.05 54.42
48.06 48.40 48.75 49.10 49.44 49.79 50.13 50.48 50.82 51.17
45.33 45.67 46.00 46.33 46.67 47.00 47.33 47.67 48.00 48.33
41.88 42.19 42.50 42.81 43.12 43.43 43.74 44.05 44.36 44.67
39.00 39.38 39.76
40.14 40.52 40.90 41.29 Ltl .67
51.95
38.05 38.39
29.50
368
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN YELLOW DISTANCE FROM TOP FEET
SOUTHERN
PINE AND CLASS H-3 CIRC. 1 NCHES
71
61 .32
72 73 74 75 76 77 78
61 .71 62. I I 62.51 62.91 63.31 63.71 64.11
79 80
64.51 64.90
81 82 83 84 85 86 87 88 89 90
65.30 65.70 66.10 66.50 66.90 67.30 67.70 68.10 68.49 68.89
YELLOW PINE DISTANCE FROM TOP FEET TOP
1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20
DOUGLAS FIR CLASS H-2 CIRC.
90 CLASS CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
58.05 58.43 58.81 59.19 59.57 59.95 60.33 60.71
51.51 51 .86 52.20 52.55 52.89 53.24 53.58 53.93
61 .48
54.78 55.14 55.51 55.87 56.23 56.60 56.96 57.32 (11 FEET, 57.68 58.05
61 .86 62.24 62.62 63.00 63.38 63.76 64.14 64.52 64.90 65.29
58.41 58.77 59.14 59.50 59.86 60.23 60.59 60.95 61 .32 61 .68
-GROUND 61.10
AND DOUGLAS CLASS H-3 CIRC. INCHES
LINE
FIR CLASS H-2 CIRC.
INCHES
0
1
CLASS CIRC. INCHES
54.27 54.62
45.60 45.90 46.21 46.52 46.83 47.14 ----47.45 47.76
54.96 55.31 55.65 56.00 56.35 56.69 57.04 57.38 57.13 58.07
52.00 52.33 52.61 53.00 53.33 53.67 54.00 54.33 54.67 55.00
48.07 48.38 48.69 49.00 49.31 49.62 49.93 50.24 50.55 50.86
CLASS CIRC. INCHES
1
44.98 45.29
CLASS
95 2
CIRC. INCHES
31 .oo 31.38 31.75 32.13 32.51 32.88 33.26 33.63 34.0 1 34.39 34.76
29.00 29.36 29.72 30.08 30.44 30.80 31.16 31 .52 31.88 32.24 32.60
27.00 27.34 27.67 28.01 2’3.35 28.69 29.02 29.36 29.70 30.03 30.37
25.00 25.33 25.65 25.98 26.30 26.63 26.96 27.28 27.61 27.93 28.26
37.26 37.65 38.04 38.43 38.81 39.20 39.59 39.98 40.37 40.75
35.14 35.52 35.89 36.27 36.65 37.02 37.40 37.78 38.15 38.53
32 33 33 34 34 34 35 35 35 36
30 31 31 31 32 32 32 33 33 33
28.58 28.91 29.24 29.56 29.89 30.21 30.54 30.87 31.19 31 .52
31 67 03 39 75 11 47 83 19
71 04 38 72 06 39 73 07 40 74
3
INCHES
33.00 33.39 33.78 34.16 34.55 34.94 35.33 35.71 36.10 36.49 36.88
96
POLE-Con.
CLASS CIRC.
48.67 49.00 49.33 49.67 50.00 50.33 50.67 51 .oo _-----51.33 51 .67
INCHES1
CLASS H-l CIRC. INCHES
FOOT
2
FOOT
POLE
APPENDIX
369
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
95 FOOT CLASS 2 CIRC. INCHES
21 22 23 24 25 26 27 26 29 30
41.14 41.53 41.92 42.30 42.69 43.08 43.47 43.85 44.24 44.63
38.90 39.28 39.66 40.03 40.41 40.79 41.16 41.54 41.92 42.29
36.55 36.91 37.27 37.63 37.99 38.35 38.71 39.07 39.43 39.79
34.08 34.42 34.75 35.09 35.43 35.76 36.10 36.44 36.76 37.1
31 32 33 34 35 36 37 38 39 40
45.02 45.40 45.79 46. I8 46.57 46.96 47.34 47.73 48.12 48.51
42.67 43.04 43.42 43.80 44.17 44.55 44.93 45.30 45.68 46.06
40.15 40.51 40.67 41.22 41.58 41.94 42.30 42.66 43.02 43.38
37.45 37.79 38.12 38.46 38.80 39.13 39.47 39.81 40.15 40.48
35. IO 35.43 35.75 36 ~08 36.40 36.73 37.06 37.36 37.71 38.03
41 42 43 44 45 46 47 48 49 50
48.89 49.28 49.67 50.06 50.44 50.83 51.22 51 .61 51.99 52.38
46.43 46.81 47.19 47.56 47.94 48.31 48.69 49.07 49.44 49.82
43.74 44. IO 44.46 44.82 45.18 45.54 45.90 46.26 46.62 46.98
40.82 41.16 41.49 41 .83 42.17 42.51 42.84 43.18 43.52 43.85
38.36 38.69 39.01 39.34 39.66 39.99 40.31 40.64 40.97 41.29
51 52 53 54 55 56 57 58 59 60
52.77 53.16 53.54 53.93 54.32 54.71 55.10 55.48 55.87 56.26
50.20 50.57 50.95 51.33 51.70 52.08 52.46 52.83 53.21 53.56
47.34 47.70 48.06 48.42 46.78 49.13 49.49 49.85 50.21 50.57
44.19 44.53 44.87 45.20 45.54 45.88 46.21 46.55 46.89 47.22
41 .62 41.94 42.27 42.60 42.92 43.25 43.57 43.90 44.22 44.55
61 62 63 64 65 66 67 68 69 70
56.65 57.03 57.42 57.81 58.20 58.58 58.97 59.36 59.75 60.13
53.96 54.34 54.71 55.09 55.47 55.84 56.22 56.60 56.97 57.35
50.93 51.29 51 .65 52.01 52.37 52.73 53.09 53.45 53.81 54.17
47.56 47.90 46.24 48.57 48.91 49.25 49.58 49.92 50.26 50.60
44.88 45.20 45.53 45.65 46.18 46.51 46.83 47.16 47.48 47.61
I
31.84 32.17 32.49 32.82 33.15 33.47 33.80 34.12 34.45 34.78
POLE-Con.
TRANSMISSION
370
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET 71
72 73 74 75 76 77 78 79 80 81 82 83
AND DOUGLAS CLASS H-3 CIRC. 1NCHES
FIR CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
61 .69 62.07 62.46 62.85 63.24 63.62 64.01
57.72 58.10 58.48 58.85 59.23 59.61 59.98 60.36 60.74 61.11
54.53 54.89 55.25 55.61 55.97 56.33 56.69 57.04 57.40 57.76
50.93 51 .27 51 .61 51.94 52.28 52.62 52.96 53.29 53.63 53.97
64.40 64.79 65.17
61 .49 61 .87 62.24
58.12 58.48 58.84
54.30 54.64 54.98
60.52 60.91 61 .30
1
95 FOOT CLASS 2 CIRC. INCHES
85 86 87 88 89 90
65.56 65.95 66.34 66.72 67.11 67.50 67.89
62.62 62.99 63.37 63.75 64.12 64.50 64.88
59.20 59.56 59.92 60.28 60.64 61 .OO 61 .36
55.31 55.65 55.99 56.33 56.66 57.00 57.34
91 92 93 94 95
68.28 68.66 69.05 69.44 69.83
65.25 65.63 66.01 66.38 66.76
61 .72 62.08 62.44 62.80 63.16
57.67 58.01 58.35 58.69 59.02
54.65 54.98 55.30 55.63 55.96
FIR CLASS H-2 CIRC.
CLASS H-l CIRC.
CLASS CIRC.
INCHES
INCHES
INCHES
INCHES
INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.38 33.77 34.15 34.53 34.91 35.30 35.68 36.06 36.45 36.83
31 .oo 31.37 31.73 32.10 32.47 32.84 33.20 33.57 33.94 34.30 34.67
29.00 29.35 29.70 30.05 30.40 30.76 31.11 31 .46 31 .81 32.16 32.51
27.00 27.34 27.67 28.01 28.34 28.68 29.01 29.35 29.68 30.02 30.35
25.00 25.32 25.64 25.96 26.28 26.60 26.91 27.23 27.55 27.87 28.19
11 12 13 14 15 16 17 18 19 20
37.21 37.60 37.98 38.36 38.74 39.13 39.51 39.89 40.28 40.66
35.04 35.40 35.77 36.14 36.51 36.87 37.24 37.61 37.97 38.34
32.86 33.21 33.56 33.91 34.27 34.62 34.97 35.32 35.67 36.02
30.69 31.02 31 .36 31.69 32.03 32.36 32.70 33.03 33.37 33.70
28.51 28.83 29.15 29.47 29.79 30.11 30.43 30.74 31 .06 31 .38
-----GROUND
YELLOW PINE DISTANCE FROM TOP FEET TOP
AND DOUGLAS CLASS H-3 CIRC.
LINE
(11
FEET,
0
POLE-con.
48.13 48.46 48.79 49.11 49.44 49.76 50.09 50.42 50.74 51.07 51.39 51 .72 52.04 -----52.37 52.70 53.02 53.35 53.67 54.00 54.33
84
SOUTHERN
CLASS CIRC.
INCHES)-----
100 1
CLASS CIRC.
2
FOOT
POLE
APPENDIX
371
6
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC.
100
INCHES
CLASS H-l CIRC. 1NCHES
CLASS CIRC.
1
FOOT CLASS 2 CIRC.
INCHES
INCHES
22 23 24 25 26 27 28 29 30
41.04 41.43 41 .81 42.19 42.57 42.96 43.34 43.72 44.11 44.49
38.71 39.07 39.44 39.81 40.18 40.54 40.91 41 .28 41 .64 42.01
36.37 36.72 37.07 37.43 37.78 38.13 38.48 38.83 39.18 39.53
34.04 34.37 34.71 35.04 35.38 35.71 36.05 36.38 36.72 37.05
31.70 32.02 32.34 32.66 32.98 33.30 33.62 33.94 34.26 34.57
31 32 33 34 35 36 37 38 39 40
44.87 45.26 45.64 46.02 46.40 46.79 47.17 47.55 47.94 48.32
42.38 42.74 43.11 43.48 43.85 44.21 44.58 44.95 45.31 45.68
39.88 40.23 40.59 40.94 41.29 41 .64 41.99 42.34 42.69 43.04
37.39 37.72 38.06 38.39 38.73 39.06 39.40 39.73 40.07 40.40
34.89 35.21 35.53 35.05 36.17 36.49 36.81 37.13 37.45 37.77
41 42 43 44 45 46 47 48 49 50
48.70 49.09 49.47 49.85 50.23 50.62 51 .oo 51 .38 51.77 52.15
46.05 46.41 46.78 47.15 47.52 47.88 48.25 48.62 48.98 49.35
43.39 43.74 44.10 44.45 44.80 45.15 45.50 45.85 46.20 46.55
40.74 41.07 41.41 41.74 42.08 42.41 42.75 43.09 43.42 43.76
38.09 38.40 38.72 39.04 39.36 39.68 40.00 40.32 40.64 40.96
51 52 53 54 55 56 57 58 59 60
52.53 52.91 53.30 53.68 54.06 54.45 54.83 55.21 55.60 55.98
49.72 50.09 50.45 50.82 51.19 51.55 51.92 52.29 52.65 53.02
46.90 47.26 47.61 47.96 48.31 48.66 49.01 49.36 49.71 50.06
44.09 44.43 44.76 45.10 45.43 45.77 46.10 46.44 46.77 47.11
41 .28 41 .60 41.91 42.23 42.55 42.87 43.19 43.51 43.83 44.15
61 62 63 64 65 66 67 68 69 70
56.36 56.74 57.13 57.51 57.89 58.28 58.66 59.04 59.43 59.81
53.39 53.76 54.12 54.49 54.86 55.22 55.59 55.96 56.32 56.69
50.41 50.77 51.12 51.47 51 .82 52.17 52.52 52.87 53.22 53.57
47.44 47.78 48.11 48.45 48.78 49.12 49.45 49.79 50.12 50.46
44.47 44.79 45.11 45.43 45.74 46.06 46.38 46.70 47; 02 47.34
21
POLE-Con.
372
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET 71 72 73 74 75 76 77 70 79 80
60.19 60.57 60.96 61 .34 61 .72 62.11 62.49 62.87 63.26 63.64
81 82 83 84 85 86 87 88
64.02 64.40 64.79 65.17 65.55 65.94 66.32 66.70 .-----GROUND 67.09 67.47
89 90 91 92 93 94 95 96 97 98 99 100
SOUTHERN
AND DOUGLAS CLASS H-3 CIRC. INCHES
YELLOW PINE DISTANCE FROM TOP FEET TOP 1 2 3 4 5 6 7 8 9 10
67.85 68.23 68.62 69.00 69.38 69.77 70.15 70.53 70.91 71.30
AND DOUGLAS CLASS H-3 CIRC. INCHES 33.00 33.38 33.76 34.14 34.52 34.89 35.27 35.65 36.03 36.41 36.79
FIR CLASS H-2 CIRC. INCHES 57.06 57.43 57.79 58.16 58.53 58.89 59.26 59.63 59.99 60.36 60.73 61.10 61 .46 61 .83 62.20 62.56 62.93 63.30 L INE (11 ‘63.66 64.03 64 64 65 65 65 66 66 66 67 67
40 77 13 50 87 23 60 97 34 70
CLASS H-l CIRC. INCHES
CLASS CIRC. 1 NCHES
1
100 FOOT CLASS 2 CIRC. INCHES
53.93 54.28 54.63 54.98 55.33 55.68 56.03 56.38 56.73 57.09
50 51 51 51 52 52 52 53 53 53
79 13 46 80 13 47 80 14 47 81
47.66 47.98 48.30 48.62 48.94 49.26 49.57 49.89 50.21 50.53
57.44 57.79 58.14 58.49 58.84 59.19 59.54 59.89 FEET, 0 60.24 60.60
54 54 54 55 55 55 56 56
14 48 81 15 48 82 15 49
50.85 51.17 51.49 51 .81 52.13 52.45 52.77 53.09
56 57
82 16
53.40 53.72
POLE-Con.
INCHES)--
60.95 61 .30 61 .65 62.00 62.35 62.70 63.05 63.40 63.76 64.11
57.49 57.83 58.16 58.50 58.84 59.17 59.51 59.84 60.18 60.51
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
31 .oo 31 .36 31.73 32.09 32.45 32.82 33.18 33.55 33.91 34.27 34.64
29.00 29.34 29.69 30.03 30.37 30.72 31 .06 31.40 31.75 32.09 32.43
27.00 27.33 27.66 27.98 28.31 28.64 28.97 29.30 29.63 29.95 30.28
54.04 54.36 54.68 55.00 55.32 55.64 55.96 56.28 56.60 56.91
1
105 CLASS 2 CIRC. INCHES 25.00 25.31 25.63 25.94 26.25 26.57 26.88 27.19 27.51 27.82 28.13
FOOT
POLE
APPENDIX
373
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
105 FOOT POLE CLASS 2 CIRC. INCHES
I I 12 13 14 15 16 17 18 19 20
37.17 37.55 37.92 38.30 38.68 39.06 39.44 39.02 40.20 40.58
35.00 35.36 35.73 36.09 36.45 36.82 37.18 31.55 37.91 38.27
32.78 33.12 33.46 33.81 34.15 34.49 34.84 35.18 35.53 35.87
30.61 30.94 31 .27 31 .60 31.92 32.25 32.58 32.91 33.24 33.57
28.44 28.76 29.07 29.38 29.70 30.01 30.32 30.64 30.95 31 .26
21 22 23 24 25 26 27 28 29 30
40.95 41.33 41.71 42.09 42.47 42.85 43.23 43.61 43.98 44.36
38.64 39.00 39.36 39.73 40.09 40.45 40.82 41.18 41.55 41.91
36.21 36.56 36.90 37.24 37.59 37.93 38.27 38.62 38.96 39.30
33.89 34.22 34.55 34.88 35.21 35.54 35.86 36. 19 36.52 36.85
31 .58 31 .89 32.20 32.52 32.83 33.14 33.45 33.77 34.08 34.39
31 32 33 34 35 36 37 38 39 40
44.74 45.12 45.50 45.88 46.26 46.64 47.02 47.39 41.71 48.15
42.27 42.64 43.00 43.36 43.73 44.09 44.45 44.82 45.18 45.55
39.65 39.99 40.33 40.68 41.02 41 .36 41.71 42.05 42.39 42.74
37.18 37.51 37.83 38.16 38.49 38.82 39.15 39.47 39.80 40.13
34.71 35.02 35.33 35.65 35.96 36.27 36.59 36.90 37.21 37.53
41 42 43 44 45 46 47 48 49 50
48.53 48.91 49.29 49.67 50.05 50.42 50.80 51.18 51 .56 51.94
45.91 46.27 46.64 47.00 47.36 47.73 48.09 48.45 48.82 49.18
43.08 43.42 43.77 44. I I 44.45 44.80 45.14 45.48 45.83 46.17
40.46 40.79 41.12 41.44 41.77 42.10 42.43 42.76 43.09 43.41
37.84 38.15 38.46 38.78 39.09 39.40 39.72 40.03 40.34 40.66
51 52 53 54 55 56 57 58 59 60
52.32 52.70 53.08 53.45 53.83 54.21 54.59 54.97 55.35 55.73
49.55 49.91 50.27 50.64 51 .oo 51 .36 51.73 52.09 52.45 52.82
46.52 46.86 47.20 47.55 47.89 48.23 48.58 48.92 49.26 49.61
43.74 44.07 44.40 44.73 45.06 45.38 45.71 46.04 46.37 46.70
40.97 41 .28 41 .60 41.91 42.22 42.54 42.85 43.16 43.. 47 43.79
-Con.
374
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. 1 NCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
105 FOOT CLASS 2 CIRC. INCHES
61 62 63 64 65 66 67 68 69 70
56.11 56.46 56.86 57.24 57.62 58.00 58.38 58.76 59.14 59.52
53.18 53.55 53.91 54.27 54.64 55.00 55.36 55.73 56.09 56.45
49.95 50.29 50.64 50.98 51 .32 51 .67 52.01 52.35 52.70 53.04
47.03 47.35 47.68 48.01 48.34 48.67 48.99 49.32 49.65 49.98
44.10 44.41 44.73 45.04 45.35 45.67 45.98 46.29 46.61 46.92
71 72 73 74 75 76 77 78 79 80
59.89 60.27 60.65 61 .03 61 .41 61 .79 62.17 62.55 62.92 63.30
56.82 57.18 57.55 57.91 56.27 56.64 59.00 59.36 59.73 60.09
53.38 53.73 54.07 54.41 54.76 55.10 55.44 55.79 56.13 56.47
50.31 50.64 50.96 51 .29 51 .62 51.95 52.28 52.61 52.93 53.26
47.23 47.55 47.86 48: 17 48.48 48.60 49.11 49.42 49.74 50.05
81 82 83 84 85 86 07 88 69 90
63.68 64.06 64.44 64.82 65.20 65.58 65.95 66.33 66.71 67.09
60.45 60.82 61.18 61 .55 61 .91 62.27 62.64 63.00 63.36 63.73
56.82 57.16 57.51 57.85 58.19 56.54 58.88 59.22 59.57 59.91
53.59 53.92 54.25 54.58 54.90 55.23 55.56 55.89 56.22 56.55
50.36 50.68 50.99 51.30 51 .62 51.93 52.24 52.56 52.87 53.18
67.47 91 92 67.85 -------------GROUND 93 68.23 94 68.61 95 68.98 96 69.36 97 69.74 98 70.12 99 70.50 100 70.88 101 102 103 104 105
71 .26 71 .64 72.02 72.39 72.77
64.09 64.45 LINE 64.62 65.18 65.55 65.91 66.27 66.64 67.00 67.36 67.73 68.09 68.45 68.82 69.18
(12
60.25 56.87 60.60 57.20 FEET, 0 INCHES)----60.94 57.53 61 .28 57.86 61 .63 58.19 61 .97 58.52 62.31 58.84 62.66 59.17 63.00 59.50 63.34 59.83 63.69 64.03 64.37 64.72 65.06
60.16 60.48 60.81 61.14 61 .47
53.49 53.81 54.12 54.43 54.75 55.06 55.37 55.69 56.00 56.31 56.63 56.94 57.25 57.57 57.88
POLE-Con.
APPENDIX
375
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET TOP
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
110 FOOT CLASS 2 CIRC. INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.37 33.74 34.11 34.48 34.85 35.22 35.59 35.96 36.33 36.70
31.00 31.36 31.71 32.07 32.42 32.78 33.13 33.49 33.85 34.20 34.56
29.00 29.34 29.68 30.02 30.37 30.71 31.05 31.39 31.73 32.07 32.41
27.00 27.32 27.64 27.97 28.29 28.61 28.93 29.25 29.58 29.90 30.22
25.00 25.31 25.62 25.92 26.23 26.54 26.85 27.15 27.46 27.77 28.08
11 12 13 14 15 16 17 18 19 20
37.07 37.44 37.81 38.18 38.55 38.92 39.29 39.66 40.03 40.40
34.91 35.27 35.62 35.98 36.34 36.69 37.05 37.40 37.76 38.12
32.75 33.10 33.44 33.78 34.12 34.46 34.80 35.14 35.49 35.83
30.54 30.87 31.19 31.51 31.83 32.15 32.48 32.80 33.12 33.44
28.38 28.69 29.00 29.31 29.62 29.92 30.23 30.54 30.85 31.15
21 22 23 24 25 26 27 28 29 30
40.77 41.14 41.51 41.88 42.25 42.62 43.00 43.37 43.74 44.11
38.47 38.83 39.18 39.54 39.89 40.25 40.61 40.96 41.32 41.67
36.17 36.51 36.85 37.19 37.53 37.87 38.22 38.56 38.90 39.24
33.76 34.09 34.41 34.73 35.05 35.37 35.70 36.02 36.34 36.66
31.46 31.77 32.08 32.38 32.69 33.00 33.31 33.62 33.92 34.23
31 32 33 34 35 36 37 38 39 40
44.48 44.85 45.22 45.59 45.96 46.33 46.70 47.07 47.44 47.81
42.03 42.38 42.74 43.10 43.45 43.81 44.16 44.52 44.87 45.23
39.58 39.92 40.26 40.61 40.95 41.29 41.63 41.97 42.31 42.65
36.99 37.31 37.63 37.95 38.27 38.60 38.92 39.24 39.56 39.88
34.54 34.65 35.15 35.46 35.77 36.08 36.38 36.69 37.00 37.31
41 42 43 44 45 46 47 48 49 50
48.18 48.55 48.92 49.29 49.66 50.03 50.40 50.77 51.14 51.51
45.59 45.94 46.30 46.65 47.01 47.37 47.72 48.08 48.43 48.79
43.00 43.34 43.68 44.02 44.36 44.70 45.04 45.38 45.73 46.07
40.21 40.53 40.85 41.17 41.50 41.82 42.14 42.46 42.78 43.11
37.62 37.92 38.23 38.54 38.85 39.15 39.46 39.77 40.08 40.38
POLE
TRANSMISSION
376
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
110 FOOT CLASS 2 CIRC. INCHES
51 52 53 54 55 56 57 58 59 60
51.88 52.25 52.62 52.99 53.36 53.73 54.10 54.47 54.84 55.21
49.14 49.50 49.86 50.21 50.57 50.92 51.28 51.63 51.99 52.35
46.41 46.75 47.09 47.43 47.77 48.12 48.46 48.80 49.14 49.48
43.43 43.75 44.07 44.39 44.72 45.04 45.36 45.68 46.00 46.33
40.69 41.00 41.31 41.62 41.92 42.23 42.54 42.85 43.15 43.46
61 62 63 64 65 66 67 68 69 70
55.56 55.95 56.32 56.69 57.06 57.43 57.80 58.17 58.54 58.91
52.70 53.06 53.41 53.77 54.12 54.48 54.84 55.19 55.55 55.90
49.82 50.16 50.50 50.85 51.19 51.53 51.87 52.21 52.55 52.89
46.65 46.97 47.29 47.62 47.94 48.26 48.58 48.90 49.23 49.55
43.77 44.08 44.38 44.69 45.00 45.31 45.62 45.92 46.23 46.54
71 72 73 74 75 76 77 78 79 80
59.28 59.65 60.02 60.39 60.76 61.13 61.50 61.87 62.25 62.62
56.26 56.62 56.97 57.33 57.60 58.04 58.39 50.75 59.11 59.46
53.24 53.58 53.92 54.26 54.60 54.94 55.28 55.62 55.97 56.31
49.87 50.19 50.51 50.84 51.16 51.48 51.80 52.12 52.45 52.77
46.85 47.15 47.46 47.77 48.08 48.38 48.69 49.00 49.31 49.62
81 82 83 84 85 86 87 88 89 90
62.99 63.36 63.73 64.10 64.47 64.84 65.21 65.58 65.95 66.32
59.82 60.17 60.53 60.88 61.24 61.60 61.95 62.31 62.66 63.02
56.65 56.99 57.33 57.67 58.01 58.36 58.70 59.04 59.38 59.72
53.09 53.41 53.74 54.06 54.38 54.70 55.02 55.35 55.67 55.99
49.92 50.23 50.54 50.05 51.15 51.46 51.77 52.08 52.38 52.69
91 66.69 67.06 92 67.43 93 67.80 94 68.17 95 68.54 96 68.91 97 -------------GROUND 98 69.28 99 69.65 100 70.02
63.37 63.73 64.09 64.44 64.80 65.15 65.51 LINE 65.67 66.22 66.58
60.06 60.40 60.75 61.09 61.43 61.77 62.11 FEET, 0 62.45 62.79 63.13
56.31 56.63 56.96 57.28 57.60 57.92 58.25
53.00 53.31 53.62 53.92 54.23 54.54 54.85
58.57 58.89 59.21
55.15 55.46 55.77
(12
INCHES)------
POLE-con.
APPENDIX
377
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SGUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
101 102 103
104 105 106 107 108 109 1 IO
;OUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. 1 NCHES
70.39 70.76 71.13 71.50 71.87 72.24 72.61 72.98 73.35 73.72
66.93 67.29 67.64 68.00 60.36 68.71 69.07 69.42 69.70
70.13
CLASS H-i CIRC.
INCHES 63 63 64 64 64 65 65 65 66 66
48
82 16 50 84 18 52 07 21 55
CLASS H-l CIRC.
INCHES
INCHES
INCHES
31 .oo 31.35 31.70 32.05 32.39 32.74 33.09 33.44 33.79 34.14 34.49
29.00
9 10
33.00 33.36 33.72 34.09 34.45 34.81 35.17 35.54 35.90 36.26 36.62
11 12 13 14 15 16
36.99 37.35 37.71 38.07 38.44 38.80
17
39.16
18 19 20
39.52 39.09 40.25
34.83 35.18 35.53 35.88 36.23 36.50 36.93 37.28 37.62 37.97
32.60 33.02 33.35 33.69 34.02 34.36 34.69 35.03 35.36 35.70
21 22 23 24 25 26 27 28 29 30
40.61 40.97 41.33 41.70 42.06 42.42 42.78 43.15
38.32 30.67 39.02 39.37 39.72 40.06 40.41 40.76 41.11 41 .46
36.03 36.37 36.70 37.04 37.37 37.71 38.04 38.38 38.71 39.05
2 3 5 6
8
43.51
43.87
CLASS CIRC.
1
INCHES 59 59
60 60 60 61 61 61 62 62
110 FOOT CLASS 2 CIRC.
53 86 18 50 82 14 47 79 11 43
29.33 29.67 30.00 30.34 30.67 31 .Ol 31.34 31 .68 32.01 32.35
CLASS CIRC.
56.08 56.38 56.69 57.00 57.31 57.62 57.92 58.23 58.54 58.05
1
CLASS CIRC.
INCHES
INCHES
27.00 27.32 27.63 27.95
25.00 25.30 25.61 25.91 26.21 26.51 26.82 27.12 27.42 27.72 28.03
28.27
28.5’3 28.90 29.22 29.53 29.85 30.17 30.48 30.80
32.06 32.38 32.70 33.01 33.33
28.33 28.63 28.94 29.24 29.54 29.84 30.15 30.45 30.75 31 .06
33.65 33.96 34.28 34.60 34.91 35.23 35.55 35.06 36.18 36.50
31 .36 31.66 31 .96 32.27 32.57 32.07 33.17 33.48 33.78 34.08
31.11 31.43 31.75
POLE-con.
INCHES
115
FIR CLASS H-2 CIRC.
TOP
AND DOUGLAS CLASS H-3 CIRC.
FIR CLASS H-2 CIRC. INCHES
2
FOOT
POLE
378
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
1 15 FOOT CLASS 2 CIRC. INCHES
31 32 33 34 35 36 37 38 39 40
44.23 44.60 44.96 45.32 45.68 46.05 46.41 46.77 47.13 47.50
41.81 42.16 42.50 42.85 43.20 43.55 43.90 44.25 44.60 44.94
39.38 39.72 40.05 40.39 40.72 41 .06 41.39 41 .72 42.06 42.39
36.81 37.13 37.44 37.76 38.08 38.39 38.71 39.03 39.34 39.66
34.39 34.69 34.99 35.29 35.60 35.90 36.20 36.50 36.81 37.11
41 42 43 44 45 46 47 48 49 50
47.96 48.22 48.58 48.94 49.31 49.67 50.03 50.39 50.76 51.12
45.29 45.64 45.99 46.34 46.69 47.04 47.39 47.73 48.08 48.43
42.73 43.06 43.40 43.73 44.07 44.40 44.74 45.07 45.41 45.74
39.98 40.29 40.61 40.93 41 .24 41 .56 41.88 42.19 42.51 42.83
37.41 37.72 38.02 38.32 30.62 38.93 39.23 39.53 39.83 40.14
51 52 53 54 55 56 57 58 59 60
51.48 51.84 52.21 52.57 52.93 53.29 53.66 54.02 54.38 54.74
48.78 49.13 49.48 49.83 50.17 50.52 50.87 51.22 51.57 51.92
46.08 46.41 46.15 47.08 47.42 47.75 48.09 48.42 48.76 49.09
43.14 43.46 43.78 44.09 44.41 44.72 45.04 45.36 45.67 45.99
40.44 40.74 41.05 41.35 41 .65 41.95 42.26 42.56 42.86 43.17
61 62 63 64 65 66 61 68 69 70
55.11 55.47 55.83 56.19 56.56 56.92 57.28 57.64 58.00 58.37
52.27 52.61 52.96 53.31 53.66 54.01 54.36 54.71 55.06 55.40
49.43 49.76 50.10 50.43 50.77 51.10 51.44 51.77 52.11 52.44
46.31 46.62 46.94 47.26 47.57 47.89 48.21 48.52 48.84 49.16
43.47 43.77 44.07 44.38 44.68 44.98 45.28 45.59 45.89 46.19
71 72 73 74 75 76 77 78 79 80
59.73 59.09 59.45 59.82 60.18 60.54 60.90 61 .27 61 .63 61 .99
55.75 56.10 56.45 56.80 57.15 57.50 57.84 58.19 58.54 58.89
52.78 53.11 53.44 53.78 54.11 54.45 54.79 55.12 55.45 55.19
49.47 49.79 50.11 50.42 50.74 51 .06 51.37 51 .69 52.00 52.32
46.50 46.80 47.10 47.40 47.71 48.01 48.31 48.61 48.92 49.22
POLE-con.
APPENDIX
379
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
FIR CLASS H-2 CIRC. INCHES
CLASS CIRC. INCHES
56.12 56.46 56.79 57.13 57.46 57.80 58.13 58.47 58.80 59.14
52.64 52.95 53.27 53.59 53.90 54.22 54.54 54.85 55.17 55.49
49.52 49.63 50.13 50.43 50.73 51.04 51.34 51.64 51.94 52.25
62.35 62.72 63.08 63.44 63.80 64.17 64.53 64.89 65.25 65.61
59 59 59 60 60 60 61 61 62 62
91 92 93 94 95 96 97 98 99 100
65.98 66.34 66.70 67.06 67.43 67.19 68.15 68.51 68.88 69.24
62.72 63.07 63.42 63.77 64.12 64.41 64.82 65.17 65.51 65.86
59.47 59.81 60.14 60.48 60.81 61.15 61.48 61.82 62.15 62.49
55.80 56.12 56.44 56.75 57.07 57.39 57.70 58.02 58.33 58.65
52.55 52.85 53.16 53.46 53.76 54.06 54.37 54.67 54.97 55.28
66.21 66.56 LINE 66.91 67.26 67.61 67.95 68.30 68.65 69.00 69.35
62.82 63.16 0 FEE T. 63.49 63.83 64.16 64.50 64.63 65.17 65.50 65.83
58.97 59.28 INCHES)---------------
55.58 55.88
59.60 59.92 60.23 60.55 60.87 61.18 61.50 61.82
56.18 56.49 56.79 57.09 57.39 57.70 58.00 58.30
66.17 66.50 66.84 67.17 67.51
62.13 62.45 62.77 63.06 63.40
58.61 58.91 59.21 59.51 59.82
.-
103 109 105 106 107 108 109 110 111 112 113 114 115
YELLOW PINE DISTANCE FROM TOP FEET TOP 2 3 4 5 6 7 8 9 10
69.60 69.96 -----GROUND 70.33 70.69 71.05 71.41 71.78 72.14 72.50 72.86 73.22 73.59 73.95 74.31 74.67
( 12
69.70 70.05 70.39 70.74 71.09
AND DOUGLAS CLASS H-3 CIRC. INCHES 33 33 33 34 34 34 35 35 35 36 36
24 59 94 28 63 98 33 60 03 38
1
1 15 FOOT CLASS 2 CIRC. INCHES
CLASS H-l CIRC. INCHES
81 82 83 84 85 06 87 88 89 90
101 102 ---
SOUTHERN
AND DOUGLAS CLASS H-3 CIRC. 1 NCHES
00 36 72 08 44 80 16 52 88 24 60
FIR CLASS H-2 CIRC. INCHES 31.00 31.34 31.60 32.03 32.37 32.71 33.05 33.39 33.74 34.08 34.42
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
29.00 29.33 29.66 29.99 30.32 30.64 30.97 31.30 31.63 31.96 32.29
27.00 27.31 27.62 27.93 28.25 28.56 28.87 29.18 29.49 29.80 30.11
1
120 CLASS 2 CIRC. INCHES 25 25 25 25 26 26 26 27 27 27 27
00 30 60 89 19 49 79 09 39 68 98
POLE-con.
FOOT
POLE
380
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
120 FOOT CLASS 2 CIRC. INCHES
I 1 12 13 14 15 16 17 18 19 20
36.96 37.32 37.68 38.04 38.39 38.75 39.11 39.47 39.83 40.19
34.76 35.11 35.45 35.79 36.13 36.47 36.82 37.16 37.50 37.84
32.62 32.95 33.28 33.61 33.93 34.26 34.59 34.92 35.25 35.58
30.43 30.74 31.05 31.36 31.67 31.98 32.29 32.61 32.92 33.23
28.28 28.58 28.88 29.18 29.47 29.77 30.07 30.37 30.67 30.96
21 22 23 24 25 26 27 28 29 30
40.55 40.91 41.27 41.63 41.99 42.35 42.71 43.07 43.43 43.19
38.18 38.53 38.87 39.21 39.55 39.89 40.24 40.58 40.92 41.26
35.91 36.24 36.57 36.89 37.22 37.55 37.88 38.21 38.54 38.87
33.54 33.85 34.16 34.47 34.79 35.10 35.41 35.72 36.03 36.34
31.26 31.56 31.86 32.16 32.46 32.75 33.05 33.35 33.65 33.95
31 32 33 34 35 36 37 38 39 40
44.15 44.51 44.87 45.23 45.59 45.95 46.31 46.67 47.03 47.39
41.61 41.95 42.29 42.63 42.97 43.32 43.66 44.00 44.34 44.68
39.20 39.53 39.86 40.18 40.51 40.84 41.17 41.50 41.83 42.16
36.65 36.96 37.28 37.59 37.90 38.21 38.52 38.83 39.14 39.46
34.25 34.54 34.84 35.14 35.44 35.74 36.04 36.33 36.63 36.93
41 42 43 44 45 46 47 48 49 50
47.75 48.11 48.46 48.82 49.18 49.54 49.90 50.26 50.62 50.98
45.03 45.37 45.71 46.05 46.39 46.74 47.08 47.42 47.76 48.11
42.49 42.82 43.14 43.47 43.60 44.13 44.46 44.79 45.12 45.45
39.77 40.08 40.39 40.70 41.01 41.32 41.64 41.95 42.26 42.57
37.23 37.53 37.82 38.12 38.42 38.72 39.02 39.32 39.61 39.91
51 52 53 54 55 56 57 58 59 60
51.34 51.70 52.06 52.42 52.78 53.14 53.50 53.86 54.22 54.58
48.45 48.79 49.13 49.47 49.82 50.16 50.50 50.84 51.18 51.53
45.78 46.11 46.43 46.76 47.09 47.42 47.75 48.08 48.41 48.74
42.88 43.19 43.50 43.82 44.13 44.44 44.75 45.06 45.37 45.68
40.21 40.51 40.81 41.11 41.40 41.70 42.00 42.30 42.60 42.89
POLE-con. ____._
APPENDIX
!3
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued ,UUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
120
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
FOOT
CLASS CIRC. INCHES
61 62 63 64 65 66 67 68 69 70
54.94 55.30 55.66 56.02 56.38 56.74 57.10 57.46 57.82 58.18
51 .87 52.21 52.55 52.89 53.24 53.58 53.92 54.26 54.61 54.95
49.07 49.39 49.72 50.05 50.38 50.71 51.04 51.37 51.70 52.03
46.00 46.31 46.62 46.93 47.24 47.55 47.86 48.18 48.49 48.80
43.19 43.49 43.79 44.09 44.39 44.68 44.98 45.28 45.58 45.88
71 72 73 74 75 76 77 18 79 80
58.54 50.89 59.25 59.61 59.97 60.33 60.69 61 .05 61 .41 61 .77
55.29 55.63 55.97 56.32 56.66 57.00 57.34 57.60 58.03 58.37
52.36 52.68 53.01 53.34 53.67 54.00 54.33 54.66 54.99 55.32
49.11 49.42 49.73 50.04 50.36 50.67 50.98 51 .29 51 .60 51.91
46.18 46.47 46.77 47.07 47.37 47.67 47.96 48.26 48.56 48.86
81 82 83 84 85 86 87 88 89 90
62.13 62.49 62.85 63.21 63.57 63.93 64.29 64.65 65.01 65.37
58.71 59.05 59.39 59.74 60.08 60.42 60.76 61.11 61 .45 61 .79
55.64 55.97 56.30 56.63 56.96 57.29 57.62 57.95 58.28 58.61
52.22 52.54 52.05 53.16 53.47 53.78 54.09 54.40 54.71 55.03
49. 16 49.46 49.75 50.05 50.35 50.65 50.95 51 .25 51.54 51 .84
91 92 93 94 95 96 97 98 99 100
65.73 66.09 66.45 66.81 67.17 67.53 67.89 68.25 68.61 68.96
62.13 62.47 62.82 63.16 63.50 63.84 64.18 64.53 64.87 65.21
58.93 59.26 59.59 59.92 60.25 60.58 60.91 61 .24 61 .57 61 .89
55.34 55.65 55.96 56.27 56.58 56.09 57.21 57.52 57.83 58.14
52. 14 52.44 52.74 53.04 53.33 53.63 53.93 54.23 54.53 54.82
101 102 103 104 105 106 107
69.32 69.68 70.04 70.40 70.76 71.12 71.48 ----GROUND 71 .a4 72.20 72.56
58.45 50.76 59.07 59.39 59.70 60.01 60.32
55.12 55.42 55.72 56.02 56.32 56.61 56.91 -----
60.63 60.94 61 .25
57.21 57.51 57.81
108 109 110
65.55 65.09 66.24 66.58 66.92 67.26 67.61 LINE 67.95 68.29 68.63
(12
62.22 62.55 62.88 63.21 63.54 63.87 64.20 FEET. 0 64.53 64.86 65.18
INCHES)------
2
POLE-Con.
TRANSMISSION
382
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
111 112 113 114 115 116 117 118 119 120
SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. 1 NCHES
72.92 73.28 73.64 74.00 74.36 74.72 75.08 75.44 75.80 76.16
CLASS H-l CIRC. INCHES
68.97 69.32 69.66 70.00 70.34 70.68 71.03 71.37 71.71 72.05
65.51 65.84 66.17 66.50 66.83 67.16 67.49 67.82 68.14 68.47
CLASS CIRC. INCHES
1
FOOT
CLASS CIRC.
INCHES
61 .57 61 .88 62.19 62.50 62.81 63.12 63.43 63.75 64.06 64.37
58.11 58.40 58.70 59.00 59.30 59.60 59.89 60.19 60.49 60.79
125 2
CLASS H-l CIRC.
INCHES
INCHES
INCHES
INCHES
INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.35 33.71 34.06 34.41 34.76 35.12 35.47 35.82 36.18 36.53
31 .oo 31.34 31 .67 32.01 32.34 32.68 33.02 33.35 33.69 34.03 34.36
29.00 29.32 29.65 29.97 30.29
27.00 27.31 27.61 27.92 28.23 28.53 28.84 29.15 29.45 29.76 30.07
25.00 25.29 25.58 25.87 26.16 26.45 26.74 27.03 27.32 27.61 27.90
11 12 13 14 15 16 17 18 19 20
36.88 37.24 37.59 37.94 38.29 38.65 39.00 39.35 39.71 40.06
34.70 35.03 35.37 35.71 36.04 36.38 36.71 37.05 37.39 37.72
32.56 32.88 33.53 33.85 34.18 34.50 34.82 35.15 35.47
30.37 30.68 30.99 31.29 31 .60 31.91 32.21 32.52 32.83 33.13
28.19 28.48 28.77 29.06 29.35 29.64 29.93 30.22 30.51 30.80
21 22 23 24 25 26 27 28 29 30
40.41 40.76 41.12 41.47 41 .82 42.18 42.53 42.88 43.24 43.59
38.06 38.39 38.73 39.07
35.79 36.12 36.44 36.76 37.09 37.41 37.74 38.06 38.38 38.71
33.44 33.75 34.05 34.36 34.67 34.97 35.28 35.59 35.89 36.20
31.09 31 .38 31 .67 31 .96 32.25 32.54 32.83 33.12 33.41 33.70
39.40 39.74
40.08 40.41 40.75 41 .08
30.62 30.94
31 .26 31.59 31.91 32.24
33.21
CLASS CIRC.
POLE-Con.
2
FIR CLASS H-2 CIRC.
TOP
AND DOUGLAS CLASS H-3 CIRC.
120
FIR CLASS H-2 CIRC. INCHES
1
CLASS CIRC.
FOOT
POLE
APPENDIX
383
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued SOUTHERN
YELLOW PINE DISTANCE FROM TOP FEET
AND DOUGLAS CLASS H-3 CIRC. INCHES
FIR CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
125 FOOT CLASS 2 CIRC. INCHES
31 32 33 34 35 36 37 38 39 40
43.94 44.29 44.65 45.00 45.35 45.71 46.06 46.41 46.76 47.12
41 .42 41 .76 42.09 42.43 42.76 43. IO 43.44 43.77 44.11 44.45
39.03 39.35 39.68 40.00 40.32 40.65 40.97 41.29 41 .62 41.94
36.51 36.82 37.12 37.43 37.74 38.04 38.35 38.66 38.96 39.27
33.99 34.28 34.57 34.86 35.15 35.44 35.73 36.02 36.31 36.60
41 42 43 44 45 46 47 48 49 50
47.47 47.82 48.18 48.53 48.88 49.24 49.59 49.94 50.29 50.65
44.78 45.12 45.45 45.79 46.13 46.46 46.80 47.13 47.47 47.81
42.26 42.59 42.91 43.24 43.56 43.88 44.21 44.53 44.85 45.18
39.58 39.88 40.19 40.50 40.80 41.11 41 .42 41 .72 42.03 42.34
36.89 37.18 37.47 37.16 38.05 38.34 38.63 38.92 39.21 39.50
51 52 53 54 55 56 57 58 59 60
51 .oo 51.35 51.71 52.06 52.41 52.76 53.12 53.47 53.82 54.18
48.14 48 ‘48 48.82 49.15 49.49 49.82 50.16 50.50 50.83 51.17
45.50 45.82 46.15 46.47 46.79 47.12 47.44 47.76 48.09 48.41
42.64 42.95 43.26 43.56 43.87 44.18 44.48 44.79 45.10 45.40
39.79 40.08 40.37 40.66 40.95 41 .24 41.53 41.82 42.11 42.39
61 62 63 64 65 66 67 68 69 70
54.53 54.88 55.24 55.59 55.94 56.29 56.65 57.00 57.35 57.71
51.50 51.84 52.18 52.51 52.85 53.18 53.52 53.86 54.19 54.53
48.74 49.06 49.38 49.71 50.03 50.35 50.68 51 .oo 51 .32 51 .65
45.71 46.02 46.32 46.63 46.94 47.24 47.55 47.86 48.16 48.47
42.68 42.97 43.26 43.55 43.84 44.13 44.42 44.71 45.00 45.29
71 72 73 74 75 76 77 78 79 80
58.06 58.41 58.76 59.12 59.47 59.82 60.18 60.53 60.88 61 .24
54.87 55.20 55.54 55.87 56.21 56.55 56.88 57.22 57.55 57.89
51.97 52.29 52.62 52.94 53.26 53.59 53.91 54.24 54.56 54.88
48.78 49.08 49.39 49.70 50.00 50.31 50.62 50.92 51 .23 51.54
45.58 45.87 46.16 46.45 46.74 47.03 47.32 47.61 47.90 48.19
POLE-con.
APPENDIX
385
B
Table B-4.-Pole circumferences for western red cedar rlESTERN
RED
30
CEDAR DISTANCE FROM TOP FEET
CLASS CIRC. INCHES
TOP
WESTERN
1 2 3 4 5 6 7 8 9 10
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
3
CLASS CIRC. INCHES
2 3 4 5 6 I 8 9 10
27 27 28 28 29 29 30 30 31 31 32
00 54 08 63 17 71 25 79 33 88 42
25.00 25.52 26.04 26.56 27.08 27.60 28.13 28.65 29.17 29.69 30.21
23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 21.00 27.50 28.00
21 .oo 21 .48 21 .96 22.44 22.92 23.40 23.88 24.35 24.83 25.31 25.79
I I 12 13 14 15 16 17 18 19 20
32 33 34 34 35 35 36 36 37 31
96 50 04 58 12 67 21 75 29 83
30.73 31 .25 31 .-II 32.29 32.81 33.33 33.85 34.37 34.90 35.42
28.50 29.00 29.50 30.00 30.50 31 .oo 31.50 32.00 32.50 33.00
26.27 26.75 27.23 27.71 28.19 28.61 29.15 29.63 30.10 30.58
21 22 23 24 ------GROUND 25 26 27 28 29 30
38 38 39 40
37 92 46 00
35.94 36.46 36.98 37.50 (5 FEET, 38.02 38.54 39.06 39.58 40.10 40.62
RED CEDAR DISTANCE CLASS H-2 FROM TOP CIRC. FEET INCHES TOP
1
31 .oo 31.59 32.17 32.76 33.34 33.93 34.52 35.10 35.69 36.28 36.86
LINE 40.54 41 .08 41 .62 42.17 42.71 43.25
CLASS H-l CIRC. INCHES 29.00 29.57 30.14 30.71 31 .28 31 .84 32.41 32.98 33.55 34.12 34.69
CLASS CIRC. INCHES 27.00 27.53 28.07 28.60 29.14 29.67 30.21 30.74 31 .28 31 .81 32.34
33.50 34.00 34.50 35.00 6 INCHE!S------35.50 36.00 36.50 37.00 37.50 38.00
I
CLASS CIRC. INCHES 25 25 26 26 27 27 28 28 29 29 30
00 52 03 55 07 59 10 62 14 66 17
2
FOOT
POLE
35 FOOT CLASS 4 CIRC. INCHES
POLE
4
31 .06 31.54 32.02 32.50 32.98 33.46 33.94 34.42 34.90 35.37
CLASS CIRC. INCHES 23.00 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00
3
-
21 .oo 21.47 21.93 22.40 22.86 23.33 23.79 24.26 24.72 25.19 25.66
386
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE CLASS H-2 FROM TOP CIRC. FEET INCHES
11 12 13 I4 15 16
17 19 19 20 21 22 23 24 25 26 27 28 29 --30
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
33 33 34 34 35 36 36 37 37 38 39 39
40 40 41 42 42 43 43 44 45
30.69
31.21 31 .72 32.24 32.76 33.28 33.79
32 33 33 34 35 35 36 36 37 37
43.31 43.90 44.4E 45.07 45.66 46.24 46.83 47.41 48.00
40 41 42 42 43 43 44 44 45
95
38.22 38.76 39.29 39.83 40.36 40.90 41.43 41.97 42.50
LINE
(6
CLASS CIRC. INCHES
88
26 83 40 97 53 IO 67 24 81 30 52 09 66 22 79 36 93 50
1
41 95 48 02 55 09 62 16 69
35 35 36 36 37 30 30 39 39 40
FEET.
CLASS CIRC. INCHES
FOOT POLE-con. CLASS 4 CIRC. 1 NCHES
34.83 35.34
26.12 26.59 27.05 27.52 27.98 28.45 28.91 29.38 29.84 30.31
35.86 36.38 36.90 37.41 37.93 39.45 38.97 39.48 40.00
33.50 34.00 34.50 35.00 35.50 36.00 36.50 37.00 37.50
30.78 31 .24 31.71 32.17 32.64 33.10 33.57 34.03 34.50
34.31
0
35 3
28.50 29.00 29.50 30.00 30.50 31 .oo 31.50 32.00 32.50 33.00
INCHES)-
46 07
43.03
40.52
38.00
34.97
49.17 49.76
46 47 47 48 48
43 57 44 10 44 64 45 17 45 71
41.03 41.55 42.07 42.59 43.10
38.50 39.00 39.50 40.00 40.50
35.43 35.90 36.36 36.03 37.29
CLASS H-2 CIRC. INCHES
64 21 70 34 91
CLASS H-l CIRC.
INCHES
CLASS CIRC. INCHES
60 21 81 41 01 62 22 82 43 03
31 .oo 31.59 32.18 32.76 33.35 33.94 34.53 35.12 35.71 36.29 36.88
30.12 30.68 31 .24 31.79 32.35 32.91 33.47 34.03 34.59
27.00 27.53 28.06 28.59 29.12 29.65 30.18 30.71 31 .24 31 .76 32.29
63 24 84 44 04 65 25 85 46 06
37.47 38.06 38.65 39.24 39.82 40.41 41 .oo 41.59 42.18 42.76
35.15 35.71 36.26 36.82 37.38 37.94 38.50 39.06 39.62 40.18
32.92 33.35 33.88 34.41 34.94 35.47 36.00 36.53 37.06 37.59
00
2
40.59
50.34 50.93 51.52
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS CIRC. INCHES
37.45 38.03 38.62 39.21 39.79 40.38 40.97 41.55 42.14 42.72
.-GROUND
31 32 33 34 35
TOP
CLASS H-l CIRC. 1 NCHES
29.00 29.56
1
CLASS CIRC.
2
40 FOOT POLE 3 CLASS 4 CIRC.
INCHES
CLASS CIRC. INCHES
25.00 25.51 26.03 26.54 27.06 27.57 28.09 28.60 29.12 29.63 30.15
23.00 23.49 23.97 24.46 24.94 25.43 25.91 26.40 26.88 27.37 27.85
21 .oo 21 .46 21.91 22.37 22.82 23.28 23.74 24.19 24.65 25.10 25.56
30.66 31.18 31 .69 32.21 32.72 33.24 33.75 34.26 34.78 35.29
28 28 29 29 30 30 31 31 32 32
26.01 26.47 26.93 27.38 27.84 28.29 28.75 29.21 29.66 30.12
34 82 31 79 28 76 25 74 22 71
INCHES
APPENDIX
387
B
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
45.66 46.26 46.87 47.47 48.07 48.68 49.28 49.88 50.49 51.09 51 .69 52.29 52.90 ____--------_ 53.50 54.10 54.71 55.31 55.91 56.51 57.12
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES TOP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
40 CLASS H-2 CIRC. INCHES 43 43 44 45 45 46 46 47 48 48
35 94 53 12 71 29 88 47 06 65
49.24 49.82 50.41 .--GROUND 51 .oo 51.59 52.18 52.76 53.35 53.94 54.53
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES 40.74 41.29 41.85 42.41 42.97 43.53 44.09 44.65 45.21 45.76 46.32 46.88 47.44 LINE (6 48.00 48.56 49.12 49.68 50.24 50.79 51.35
FEET,
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
38.12 38.65 39.18 39.71 40.24 40.76 41.29 41 .82 42.35 42.88
35 36 36 37 37 38 38 39 39 40
43.41 43.94 44.47 0 INCHES)------45.00 45.53 46.06 46.59 47.12 47.65 48.18
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
2
81 32 84 35 87 38 90 41 93 44
FOOT
CLASS CIRC. INCHES
3
POLE-con. CLASS CIRC. INCHES
33.19 33.68 34.16 34.65 35.13 35.62 36.10 36.59 37.07 37.56
30 31 31 31 32 32 33 33 34 34
57 03 49 94 40 85 31 76 22 68
40.96 41.47 41.99
38.04 38.53 39.01
35 35 36
13 59 04
42.50 43.01 43.53 44.04 44.56 45.07 45.59
39.50 39.99 40.47 40.96 41.44 41.93 42.41
36 36 37 37 38 38 39
50 96 41 87 32 78 24
CLASS CIRC. INCHES
33.00 33.59 34.18 34.77 35.36 35.95 36.54 37.13 37.72 38.31 38.90
31 31 32 32 33 33 34 35 35 36 36
00 58 15 73 31 88 46 04 62 19 77
29.00 29.55 30.10 30.65 31.21 31 .76 32.31 32.86 33.41 33.96 34.51
27.00 27.53 28.05 28.58 29.10 29.63 30.15 30.68 31.21 31.73 32.26
25 25 26 26 27 27 28 28 29 29 30
00 50 00 50 00 50 00 50 00 50 00
39.49 40.08 40.67 41 .26 41 .85 42.44 43.03 43.62 44.21 44.79
37 37 38 39 39 40 40 41 41 42
35 92 50 08 65 23 81 38 96 54
35.06 35.62 36.17 36.72 37.27 37.82 38.37 38.92 39.47 40.03
32.78 33.31 33.83 34.36 34.88 35.41 35.94 36.46 36.99 37.51
30.50 31 .oo 31.50 32.00 32.50 33.00 33.50 34.00 34.50 35.00
2
CLASS CIRC. INCHES
4
45 FOOT POLE 3 CLASS 4 CIRC. INCHES
23.00 23.47 23.95 24.42 24.90 25.37 25.85 26.32 26.79 27.27 27.74
21 21 21 22 22 23 23 24 24 25 25
28.22 28.69 29.17 29.64 30.12 30.59 31 .06 31.54 32.01 32.49
25.94 26.38 26.83 27.28 27.73 28.18 28.63 29.08 29.53 29.97
00 45 90 35 79 24 69 14 59 04 49
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES 21 22 23 24 25 26 27 28 29 30
CLASS H-2 CIRC. INCHES
45.38 45.91 46 56 47 15 47 74 48 33 48 92 49 51 50.10 50.69
43.12 43.69 44.27 44.85 45.42 46.00 46.58 47.15 47.73 48.31
31 51.28 32 51.87 33 52.46 34 53.05 35 53.64 36 54.23 37 54.82 38 55.41 -----------------------GROUND 39 56.00 40 56.59
48.66 49.46 50.04 50.62 51.19 51.77 52.35 52.92
41 42 43 44 45
54.65 55.23 55.81 56.38 56.96
57.18 57.77 58.36 58.95 59.54
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
53.50 54.08
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
40.58 41.13 41.68 42.23 42.70 43.33 43.88 44.44 44.99 45.54
38.04 30.56 39.09 39.62 40.14 40.67 41.19 41.72 42.24 42.77
35.50 36.00 36.50 37.00 37.50 38.00 38.50 39.00 39.50 40.00
43.29 43.82 44.35 44.87 45.40 45.92 46.45 46.97 6 INCHES)--47.50 48.03
40 41 41 42 42 43 43 44
48.55 49.08 49.60 50.13 50.65
46.09 46.64 47.19 47.74 48.29 48.85 49.40 49.95 LINE (6 50.50 51.05
FEET,
51.60 52.15 52.71 53.26 53.81
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
1
CLASS CIRC. INCHES
2
45 FOOT POLE-Con. CLASS CLASS 3~ CIRC. CIRC. INCHES INCHES 32.96 33.44 33.91 34.36 34.86 35.33 35.81 36.28 36.76 37.23
30.42 30.87 31.32 31.77 32.22 32.67 33.12 33.56 34.01 34.46
50 00 50 00 50 00 50 00 --
37.71 38.18 38.65 39.13 39.60 40.08 40.55 41.03 ---_---
34.91 35.36 35.81 36.26 36.71 37.15 37.60 38.05
44 45
50 00
41.50 41.97
38.50 38.95
45 46 46 47 47
50 00 50 00 50
42.45 42.92 43.40 43.87 44.35
39.40 39.05 40.29 40.74 41.19
CLASS CIRC. INCHES
.oo
2
CLASS CIRC. INCHES
50 3
FOOT POLE CLASS 4 CIRC. INCHES
; 6 7 8 9 IO
35 36 37 37 38 38
00 58 16 74 32 90 48 06 64 22 80
31.00 31.56 32.11 32.67 33.23 33.78 34.34 34.90 35.45 36.01 36.57
29.00 29.53 30.07 30.60 31.14 31.67 32.20 32.74 33.27 33.81 34.34
27.00 27.51 28.02 28.53 29.05 29.56 30.07 30.58 31.09 31.60 32.11
25 25 25 26 26 27 27 28 28 29 29
.49 .98 .47 .95 44 :93 .42 .91 40 :89
23.00 23.47 23.93 24.40 24.86 25.33 25.80 26.26 26.73 27.19 27.66
21.00 21.43 21.86 22.30 22.73 23.16 23.59 24.02 24.45 24.89 25.32
11 12 13 14 15 16 17 18 19 20
39.37 39.95 40.53 41 11 41 69 42 27 42.85 43.43 44 01 44 59
37.12 37.68 38.24 38.80 39.35 39.91 40.47 41.02 41.58 42.14
34.87 35.41 35.94 36.48 37.01 37.55 38.08 38.61 39.15 39.68
32.63 33.14 33.65 34.16 34.67 35.18 35.69 36.20 36.72 37.23
30.37 30.86 31.35 31.84 32.33 32.82 33.31 33.80 34 28 34 77
26.12 28.59 29.06 29.52 29.99 30.45 30.92 31.39 31.65 32.32
25.75 26.18 26.61 27.05 27.48 27.91 28.34 28.77 29.20 29.64
TOP 1 2 3
33 33 34 34
4
APPENDIX
B
Table B-4.-Pole circumferences for western red cedar-Continued HESTERN RED CEDAR DISTANCE CLASS H-3 f-ROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
50 FOOT CLASS 3 CIRC. INCHES
Pot-E-con. CIASS CIRC. INCHES
21 22 23 24 25 26 27 28 29 30
45.17 45.15 46.33 46.91 47.49 48.07 48.65 49.23 49.81 50.39
42.69 43.25 43.81 44.36 44.92 45.48 46.03 46.59 47.15 47.70
40.22 40.75 41 .28 41.62 42.35 42.89 43.42 43.95 44.49 45.02
37.74 38.25 38.76 39.27 39.78 40.30 40.81 41 .32 41 .83 42.34
35.26 35.75 36.24 36.73 37.22 37.70 38.19 36.68 39.17 39.66
32.78 33.25 33.72 34.18 34.65 35.11 35.58 36.05 36.51 36.98
30.07 30.50 30.93 31 .36 31 .80 32.23 32.66 33.09 33.52 33.95
31 32 33 34 35 36 31 38 39 40
50.97 51.55 52.12 52.70 53.28 53.86 54.44 55.02 55.60 56.18
48.26 48.82 49.37 49.93 50.49 51.05 51 .60 52.16 52.72 53.27
45.56 46.09 46.62 47.16 47.69 48.23 48.76 49.30 49.83 50.36
42.85 43.36 43.87 44.39 44.90 45.41 45.92 46.43 46.94 47.45
40.15 40.64 41.12 41 .61 42.10 42.59 43.08 43.57 44.06 44.55
37.44 37.91 38.37 36’. 84 39.31 39.77 40.24 40.70 41.17 41 .64
34.39 34.82 35.25 35.68 36.11 36.55 36.98 37.41 37.84 38.27
41 42
56.76 57.34
42.10 42.57
38.70 39.14
51.92 58.50 59.08 59.66 60.24 60.82 61 .40 61 .98
47.97 48.48 0 INCHES)------48.99 45.50 50.01 50.52 51.03 51.55 52.06 52.57
45.03 45.52
43 44 45 46 47 48 49 50
53.83 54.39 ---GROUND 54.94 55.50 56.06 56.61 57.17 57.13 58.28 58.84
46.01 46.50 46.99 47.48 47.97 48.45 48.94 49.43
43.03 43.50 43.97 44.43 44.90 45.36 45.83 46.30
39.57 40.00 40.43 40.86 41.30 41.73 42.16 42.59
IHESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES TOP 2 3 4 5 6 7 8 9 10
33 33 34 34 35 35 36 37 37 38 38
00 57 14 71 29 86 43 00 57 14 71
50.90 51.43 LINE (7 51.97 52.50 53.03 53.57 54.10 54.64 55.17 55.70
FEET
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
31 .oo 31.54 32.08 32.62 33.16 33.70 34.24 34.79 35.33 35.87 36.41
29.00 29.52 30.04 30.56 31 .08 31 .60 32.12 32.64 33.16 33.68 34.20
CLASS CIRC. INCHES 27.00 27.50 28.00 28.50 29.00 29.50 30.00 30.50 31 .oo 31.50 32.00
1
CLASS CIRC. INCHES 25 25 25 26 26 27 27 28 26 29 29
00 48 96 44 92 40 88 36 84 32 80
2
CLASS CIRC. INCHES 23.00 23.45 23.90 24.35 24.80 25.24 25.69 26.14 26.59 27.04 27.49
4
55 FOOT POLE 3 CLASS 4 CIRC. INCHES 21 .oo 21.43 21.86 22.29 22.71 23.14 23.57 24.00 24.43 24.86 25.29
390
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. i NCHES
CLASS CIRC. INCHES
I
CLASS 2 CIRC. 1 NCHES
55 FOOT CLASS 3 CIRC. INCHES
POLE-Con. CLASS CIRC. INCHES
11 12 13 14 15 I6 17 18 19 20
39.29 39.86 40.43 41 .oo 41.57 42.14 42.71 43.29 43.86 44.43
36.95 37.49 38.03 38.57 39.11 39.65 40.19 40.73 41.28 41 .82
34.72 35.24 35.77 36.29 36.81 37.33 37.85 38.37 38.89 39.41
32.50 33.00 33.50 34.00 34.50 35.00 35.50 36.00 36.50 37.00
30.28 30.76 31 .23 31.71 32.19 32.67 33.15 33.63 34.1 I 34.59
27.94 28.39 28.84 29.29 29.73 30.18 30.63 31 .oa 31.53 31.98
25.71 26.14 26.57 27.00 27.43 27.86 28.29 28.71 29.14 29.57
21 22 23 24 25 26 27 28 29 30
45.00 45.57 46.14 46.71 47.29 47.86 48.43 49.00 49.57 50.14
42.36 42.90 43.44 43.98 44.52 45.06 45.60 46.14 46.68 47.22
39.93 40.45 40.97 41.49 42.01 42.53 43.05 43.57 44.09 44.61
37.50 38.00 38.50 39.00 39.50 40.00 40.50 41 .oo 41.50 42.00
35.07 35.55 36.03 36.51 36.99 37.47 37.95 38.43 38.91 39.39
32.43 32.88 33.33 33.78 34.22 34.67 35.12 35.57 36.02 36.47
30.00 30.43 30.86 31.29 31.71 32.14 32.57 33.00 33.43 33.86
31 32 33 34 35 36 37 38 39 40
50.71 51.29 51 .86 52.43 53.00 53.57 54.14 54.71 55.29 55.86
47.77 48.31 48.85 49.39 49.93 50.47 51 .Ol 51.55 52.09 52.63
45.13 45.65 46.17 46.69 47.21 47.73 48.26 48.78 49.30 49.82
42.50 43.00 43.50 44.00 44.50 45.00 45.50 46.00 46.50 47.00
39.07 40.35 40.83 41.31 41.79 42.27 42.74 43.22 43.70 44.18
36.92 37.37 37.82 38.27 38.71 39.16 39.61 40.06 40.51 40.96
34.29 34.71 35.14 35.57 36.00 36.43 36.86 37.29 37.71 38.14
41 42 43 44 45 46 47 ---
56.43 57.00 57.57 58.14 58.71 59.29 59.86 -----
44.66 45.14 45.62 46.10 46.58 47.06 47.54
41.41 41 .86 42.31 42.76 43.20 43.65 44.10 -----
38.57 39.00 39.43 39.86 40.29 40.71 41.14
48 49 50
60.43 61 .OO 61 .57
47.50 48.00 48.50 49.00 49.50 50.00 50.50 6 INCHES)------51 .oo 51.50 52.00
48.02 48.50 48.98
44.55 45.00 45.45
41.57 42.00 42.43
51 52 53 54 55
62.14 62.71 63.29 63.86 64.43
52.50 53.00 53.50 54.00 54.50
49.46 49.94 50.42 50.90 51.38
45.90 46.35 46.80 47.24 47.69
42.86 43.29 43.71 44.14 44.57
53.17 53.71 54.26 54.80 55.34 55.88 56.42 ---GROUND 56.96 57.50 58.04 58.58 59.12 59.66 60.20 60.74
50.34 50.86 51.38 51.90 52.42 52.94 53.46 LINE (7 53.98 54.50 55.02 55.54 56.06 56.58 57.10 57.62
FEET,
Lt
APPENDIX
391
6
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
1
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
FOOT POLE CLASS Lt CIRC. INCHES
CLASS H-l CIRC. INCHES
33.00 33.56 34.11 34.67 35.22 35.76 36.33 36.89 37.44 38.00 38.56
31 .oo 31.53 32.06 32.58 33.11 33.64 34.17 34.69 35.22 35.75 36.28
29.00 29.51 30.02 30.53 31.04 31.55 32.06 32.56 33.07 33.58 34.09
27.00 27.49 27.98 28.47 28.96 29.45 29.94 30.44 30.93 31 .42 31.91
25.00 25.47 25.94 26.42 26.89 27.36 27.83 28.31 28.78 29.25 29.72
23.00 23.44 23.87 24.31 24.74 25.18 25.61 26.05 26.48 26.92 27.35
21 .oo 21.42 21 .83 22.25 22.67 23.08 23.50 23.92 24.33 24.75 25.17
11 12 13 14 15 16 17 18 19 20
39.11 39.67 40.22 40.78 41.33 41 .89 42.44 43.00 43.56 44.11
36.81 37.33 37.86 38.39 38.92 39.44 39.97 40.50 41.03 41 .56
34.60 35.11 35.62 36.13 36.64 37.15 37.66 38.17 38.68 39.19
32.40 32.89 33.38 33.87 34.36 34.85 35.34 35.63 36.32 36.81
30.19 30.67 31.14 31 .61 32.08 32.56 33.03 33.50 33.97 34.44
27.79 28.22 28.66 29.09 29.53 29.96 30.40 30.83 31 .27 31.70
25.56 26.00 26.42 26.83 27.25 27.67 28.08 28.50 28.92 29.33
21 22 23 24 25 26 27 28 29 30
44.67 45.22 45.78 46.33 46.89 47.44 48.00 48.56 49.11 49.67
42.08 42.61 43.14 43.67 44.19 44.72 45.25 45.78 46.31 46.83
39.69 40.20 40.71 41.22 41.73 42.24 42.75 43.26 43.77 44.28
37.31 37.80 38.29 30.78 39.27 39.76 40.25 40.74 41 .23 41 .72
34.92 35.39 35.86 36.33 36.81 37.28 37.75 38.22 38.69 39.17
32.14 32.57 33.01 33.44 33.08 34.31 34.75 35.19 35.62 36.06
29.75 30.17 30.58 31 .oo 31.42 31 .83 32.25 32.67 33.08 33.50
31 32 33 34 35 36 37 38 39 40
50.22 50.78 51.33 51 .89 52.44 53.00 53.56 54. I1 54.61 55.22
47.36 47.89 48.42 48.94 49.47 50.00 50.53 51 .06 51 .58 52.1 I
44.79 45.30 45.81 46.31 46.82 47.33 47.84 48.35 48.86 49.37
42.21 42.70 43.19 43.69 44.18 44.67 45.16 45.65 46.14 46.63
39.64 40.11 40.58 41 .06 41.53 42.00 42.47 42.94 43.92 43.89
36.49 36.93 37.36 37.80 38.23 38.67 39.10 39.54 39.97 40.41
33.92 34.33 34.75 35.17 35.58 36.00 36.42 36.83 37.25 37.67
41 42 43 44 45 46 47 48 49 50
55.18 56.33 56.89 57.44 58.00 58.56 59.11 59.67 60.22 60.78
52.64 53.17 53.69 54.22 54.75 55.28 55.81 56.33 56.86 57.39
49.88 50.39 50.90 51.41 51.92 52.43 52.94 53.44 53.95 54.46
47.12 47.61 48.10 48.59 49.08 49.57 50.06 50.56 51.05 51.54
44.36 44.83 45.31 45.78 46.25 46.72 47.19 47.67 48.14 48.61
40.84 41 .28 41.71 42.15 42.58 43.02 43.45 43.89 44.32 44.76
38.08 38.50 38.92 39.33 39.75 40.17 40.58 41 .oo 41 .42 41 .83
TOP 1 2 3 4 5 6 7 8 9 10
CLASS CIRC. INCHES
60 3
CLASS H-2 CIRC. INCHES
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. INCHES
51 61.33 -----------------------GROUND
57.92
52 53 54 55 56 57 58 59 60
58.44 58.97 59.50 60.03 60.56 61 .08 61 .61 62.14 62.67
61 .89 62.44 63.00 63.56 64.1 I 64.67 65.22 65.78 66.33
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES TOP
CLASS H-l CIRC. INCHES
1
CLASS CIRC. INCHES
2
60 FOOT CLASS 3 CIRC. 1 NCHES
52.03 49.08 0 INCHES)-------
45.19
55.48 55.99 56.50 57.01 57.52 58.03 58.54 59.05 59.56
52.52 53.01 53.50 53.99 54.48 54.97 55.46 55.95 56.44
45.63 46.06 46.50 46.94 47.37 47.81 48.24 48.68 49.11
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
LINE
54.97
CLASS CIRC. INCHES
(8
FEET,
49.56 50.03 50.50 50.97 51.44 51 .92 52.39 52.86 53.33
1
CLASS CIRC. INCHES
2
CLASS CIRC. INCHES
POLE-Con. CLASS CIRC. INCHES
--------
4
42.25 42.67 43.08 43.50 43.92 44.33 44.75 45.17 45.58 46.00
65 3
FOOT POLE CLASS 4 CIRC. INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.54 34.08 34.63 35.17 35.71 36.25 36.80 37.34 37.88 38.42
31 .oo 31 .52 32.03 32.55 33.07 33.58 34.10 34.62 35.14 35.65 36.17
29.00 29.50 30.00 30.50 31 .oo 31.50 32.00 32.50 33.00 33.50 34.00
27.00 27.47 27.95 28.42 28.90 29.37 29.85 30.32 30.80 31 .27 31.75
25.00 25.45 25.90 26.35 26.80 27.25 27.69 28.14 28.59 29.04 29.49
23.00 23.42 23.85 24.27 24.69 25.12 25.54 25.97 26.39 26.81 27.24
21 .oo 21.41 21 .81 22.22 22.63 23.03 23.44 23.85 24.25 24.66 25.07
11 12 13 14 15 16 17 18 19 20
38.97 39.51 40.05 40.59 41.14 41.68 42.22 42.76 43.31 43.85
36.69 37.20 37.72 38.24 38.75 39.27 39.79 40.31 40.82 41.34
34.50 35.00 35.50 36.00 36.50 37.00 37.50 38.00 38.50 39.00
32.22 32.69 33.17 33.64 34.12 34.59 35.07 35.54 36.02 36.49
29.94 30.39 30.84 31 .29 31.74 32.19 32.64 33.08 33.53 33.98
27.66 28.08 28.51 28.93 29.36 29.78 30.20 30.63 31.05 31.47
25.47 25.88 26.29 26.69 27.10 27.51 27.92 28.32 28.73 29.14
21 22 23 24 25 26 27 28 29 30
44.39 44.93 45.47 46.02 46.56 47.10 47.64 48.19 48.73 49.27
41.86 42.37 42.89 43.41 43.92 44.44 44.96 45.47 45.99 46.51
39.50 40.00 40.50 41 .oo 41.50 42.00 42.50 43.00 43.50 44.00
36.97 37.44 37.92 38.39 38.86 39.34 39.81 40.29 40.76 41 .24
34.43 34.88 35.33 35.78 36.23 36.68 37.13 37.58 38.03 38.47
31.90 32.32 32.75 33.17 33.59 34.02 34.44 34.86 35.29 35.71
29.54 29.95 30.36 30.76 31.17 31 .58 31 .98 32.39 32.80 33.20
APPENDIX
393
B
Table B-4.-Pole circumferences for western red cedar-continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. 1 NCHES
CLASS H-l CIRC. 1 NCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
2
65 FOOT CLASS 3 CIRC. INCHES
POLE--Con. CLASS CIRC. INCHES
31 32 33 34 35 36 3-I 38 39 40
49.81 50.36 50.90 51.44 51.98 52.53 53.07 53.61 54.15 54.69
47.03 47.54 48.06 48.58 49.09 49.61 50.13 50.64 51.16 51 .68
44.50 45.00 45.50 46.00 46.50 47.00 47.50 48.00 48.50 49.00
41.71 42.19 42.66 43.14 43.61 44.08 44.56 45.03 45.51 45.98
38.92 39.37 39.82 40.27 40.72 41.17 41 .62 42.07 42.52 42.97
36. 14 36.56 36.98 37.41 37.83 38.25 38.68 39.10 39.53 39.95
33.61 34.02 34.42 34.83 35.24 35.64 36.05 36.46 36.86 37.27
41 42 43 44 45 46 47 4a 49 50
55.24 55.78 56.32 56.06 57.41 57.95 58.49 59.03 59.58 60.12
52.19 52.71 53.23 53.75 54.26 54.78 55.30 55.81 56.33 56.85
49.50 50.00 50.50 51 .oo 51.50 52.00 52.50 53.00 53.50 54.00
46.46 46.93 47.41 47.88 48.36 48.83 49.31 49.78 50.25 50.73
43.42 43.86 44.31 44.76 45.21 45.66 46.11 46.56 47.01 47.46
40.37 40.80 41.22 41 .64 42.07 42.49 42.92 43.34 43.76 44.19
37.68 30.08 38.49 38.90 39.31 39.71 40.12 40.53 40.93 41.34
51 52 53 54 55 56
60.66 61 .20 61 .75 62.29 62.03 63.37 ------
47.91 48.36 48.81 49.25 49.70 50.15
44.61 45.03 45.46 45.88 46.31 46.73 -----
41.75 42.15 42.56 42.97 43.37 43.78
57 58 59 60
63.92 64.46 65.00 65.54
51.20 51.68 52.15 52.63 53.10 53.58 6 INCHES)------54.05 54.53 55.00 55.47
50.60 51.05 51.50 51.95
47.15 47.58 48.00 48.42
44.19 44.59 45.00 45.41
61 62 63 64 65
66.08 66.63 67.17 67.71 68.25
55.95 56.42 56.90 57.37 57.85
52.40 52.85 53.30 53.75 54.19
48.85 49.27 49.69 50.12 50.54
45.81 46.22 46.63 47.03 47.44
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. INCHES FEET TOP 2 3 4 5 6 7 8 9 10
33.00 33.53 34.06 34.59 35.13 35.66 36.19 36.72 37.25 37.70 38.31
57.36 57.88 58.40 58.92 59.43 59.95 ---GROUND 60.47 60.98 61 .50 62.02 62.53 63.05 63.57 64.08 64.60
54.50 55.00 55.50 56.00 56.50 57.00 LINE (a 57.50 58.00 58.50 59.00
FEE1
59.50 60.00 60.50 61 .OO 61 .50
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
31 .oo 31.51 32.02 32.52 33.03 33.54 34.05 34.55 35.06 35.57 36.08
29.00 29.48 29.97 30.45 30.94 31 .42 31.91 32.39 32.88 33.36 33.84
CLASS CIRC. INCHES 27 27 27 28 28 29 29 30 30 31 31
00 46 92 38 a4 30 77 23 69 15 61
1
CLASS CIRC. INCHES 25.00 25.44 25.88 26.31 26.75 27.19 27.63 28.06 28.50 28.94 29.38
2
CLASS CIRC. INCHES 23 23 23 24 24 25 25 25 26 26 27
70 3
00 41 a3 24 66 07 48 90 31 73 14
4
FOOT POLE CLASS 4 CIRC. INCHES 21 .oo 21.39 21.78 22.17 22.56 22.95 23.34 23.73 24.13 24.52 24.91
394
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
70
18 19 20
38.84 39.38 39.91 40.44 40.97 41.50 42.03 42.56 43.09 43.63
36.59 37.09 37.60 38.11 38.62 39.13 39.63 40.14 40.65 41.16
34.33 34.81 35.30 35.78 36.27 36.75 37.23 37.72 38.20 38.69
32.07 32.53 32.99 33.45 33.91 34.38 34.84 35.30 35.76 36.22
29.81 30.25 30.69 31.13 31 .56 32.00 32.44 32.88 33.31 33.75
27.55 27.97 28.38 28.80 29.21 29.63 30.04 30.45 30.87 31 .28
25.30 25.69 26.08 26.47 26.86 27.25 27.64 28.03 28.42 28.81
21 22 23 24 25 26 27 28 29 30
44.16 44.69 45.22 45.75 46.28 46.81 47.34 47.88 48.41 48.94
41.66 42.17 42.68 43.19 43.70 44.20 44.71 45.22 45.73 46.23
39.17 39.66 40.14 40.63 42.08 42.56 43.05 43.53
36.68 37.14 37.60 38.06 38.52 38.98 39.45 39.91 40.37 40.83
34.19 34.63 35.06 35.50 35.94 36.38 36.81 37.25 37.69 38.13
31.70 32.11 32.52 32: 94 33.35 33.77 34.18 34.59 35.01 35.42
29.20 29.59 29.98 30.38 30.77 31.16 31.55 31.94 32.33 32.72
31 32 33 34 35 36 37 38 39 40
49.47 50.00 50.53 51 .06 51.59 52.13 52.66 53.19 53.72 54.25
46.74 47.25 47.76 48.27 48.77 49.28 49.79 50.30 50.80 51.31
44.02 44.50 44.98 45.47 45.95 46.44 46.92 47.41 47.89 48.38
41.29 41.75 42.21 42.67 43.13 43.59 44.05 44.52 44.98 45.44
38.56 39.00 39.44 39.88 40.31 40.75 41.19 41 .63 42.06 42.50
35.84 36.25 36.66 37.08 37.49 37.91 38.32 38.73 39.15 39.56
33.11 33.50 33.89 34.28 34.67 35.06 35.45 35.84 36.23 36.63
41 42 43 44 45 46 47 48 49 50
54.78 55.31 55.84 56.38 56.91 57.44 57.97 58.50 59.03 59.56
51 .82 52.33 52.84 53.34 53.85 54.36 54.87 55.38 55.88 56.39
48.86 49.34 49.83 50.31 50.80 51 .28 51.77 52.25 52.73 53.22
45.90 46.36 46.82 47.28 47.74 48.20 48.66 49.13 49.59 50.05
42.94 43.38 43.81 44.25 44.69 45.13 45.56 46.00 46.44 46.88
39.98 40.39 40.80 41.22 41 .63 42.05 42.46 42.88 43.29 43.70
37.02 37.41 37.80 38.19 38.58 38.97 39.36 39.75 40.14 40.53
51 52 53 54 55 56 57 58 59 60
60.09 60.63 61.16 61 .69 62.22 62.75 63.28 63.81 64.34 64.88
56.90 57.41 57.91 56.42 58.93 59.44 59.95 60.45 60.96 61.47
53.70 54.19 54.67 55.16 55.64 56.13 56.61 57.09 57.58 58.06
50.51 50.97 51.43 51.89 52.35 52.81 53.27 53.73 54.20 54.66
47.31 47.75 48. 19 48.63 49.06 49.50 49.94 50.38 50.81 51 .25
44.12 44.53 44.95 45.36 45.77 46.19 46.60 47.02 47.43 47.84
40.92 41.31 41.70 42.09 42.48 42.88 43.27 43.66 44.05 44.44
11 12 13
14 15 16 17
41.11 41.59
1
CLASS CIRC.
INCHES
2
CLASS CIRC. INCHES
3
POLE-con.
CLASS H-l ClRC.
INCHES
CLASS CIRC. INCHES
FOOT
CLASS H-2 CIRC. INCHES
CLASS CIRC. INCHES
4
APPENDIX
395
I3
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
70 CLASS H-2 CIRC.
-----------------------GROUND 51 65.41 62 65.94 63 66.41 64 67.00 65 67.53 66 68.06 67 68.59 68 69.13 69 69.66 70 70.19
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-l CIRC. INCHES
INCHES
LINE
(9
CLASS ClRC. INCHES
FEET,
58.55 59.03 59.52 60.00 60.48 60.97 61 .45 61 .9’t 62.42 62.91
61 .98 62.48 62.99 63.50 64.01 64.52 65.02 65.53 66.04 66.55
0
1
INCHES)
55.12 55.58 56.04 56.50 56.96 57.42 57.88 58.34 58.80 59.27
CLASS CIRC. INCHES
2
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
POLE--con.
3
CLASS CIRC. INCHES
---------
1
48.26 48.67 49.09 49.50 49.91 50.33 50.74 51.16 51.57 51.98
CLASS CIRC.
2
44.83 45.22 45.61 46.00 46.39 46.78 47.17 47.56 47.95 48.34
75 FOOT CLASS 3 CIRC.
INCHES
INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.51 34.03 34.54 35.06 35.57 36.09 36.60 37.12 37.63 38.14
31 .oo 31.49 31.99 32.48 32.97 33.46 33.96 34.45 34.94 35.43 35.93
29.00 29.47 29.94 30.41 30.88 31 .36 31 .83 32.30 32.77 33.24 33.71
27.00 27.45 27.90 28.35 28.80 29.25 29.70 30.14 30.59 31.04 31.49
25.00 25.43 25.86 26.28 26.71 27.14 27.57 27.99 28.42 28.85 29.28
23.00 23.41 23.81 24.22 24.62 25.03 25.43 25.84 26.25 26.65 27.06
11 12 13 14 15 16 17 18 19 20
38.66 39.17 39.69 40.20 40.72 41.23 41.75 42.26 42.78 43.29
36.42 36.91 37.41 37.90 38.39 38.88 39.38 39.87 40.36 40.86
34.18 34.65 35.12 35.59 36.07 36.54 37.01 37.48 37.95 38.42
31.94 32.39 32.84 33.29 33.74 34.19 34.64 35.09 35.54 35.99
29.70 30.13 30.56 30.99 31.41 31 .84 32.27 32.70 33.12 33.55
27.46 27.87 28.28 28.68 29.09 29.49 29.90 30.30 30.71 31.12
21 22 23 24 25 26 27 28 29 30
43.80 44.32 44.83 45.35 45.86 46.38 46.89 47.41 47.92 48.43
41.35 41 .84 42.33 42.83 43.32 43.81 44.30 44.80 45.29 45.78
38.89 39.36 39.83 40.30 40.78 41 .25 41 .72 42.19 42.66 43.13
36.43 36.88 37.33 37.78 38.23 38.68 39.13 39.58 40.03 40.48
33.98 34.41 34.83 35.26 35.69 36.12 36.54 36.97 37.40 37.83
31 .52 31.93 32.33 32.74 33.14 33.55 33.96 34.36 34.77 35.17
TOP
‘-t
.-----
51.69 52.13 52.56 53.00 53.44 53.88 54.31 54.75 55.19 55.63
CLASS H-2 CIRC. INCHES
FOOT
CLASS CIRC. INCHES
POLE
TRANSMISSION
396
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l ClRC. INCHES
CLASS CIRC. INCHES
1
CLASS ClRC. INCHES
75 2
FOOT POLE-con. CLASS 3 CIRC. INCHES
31 32 33 34 35 36 37 38 39 40
48.95 49.46 49.98 50.49 51.01 51.52 52.04 52.55 53.07 53.50
46 46 47 47 48 48 49 49 50 50
28 77 26 75 25 74 23 72 22 71
43.60 44.07 44.54 45.01 45.49 45.96 46.43 46.90 47.37 47.84
40.93 41.38 41.83 42.28 42.72 43.17 43.62 44.07 44.52 44.97
38.25 30.60 39.11 39.54 39.96 40.39 40.82 41.25 41.67 42.10
35.50 35.99 36.39 36.80 37.20 37.61 38.01 38.42 38.83 39.23
41 42 43 44 45 46 47 48 49 50
54.09 54.61 55.12 55.64 56.15 56.67 57.18 57.70 58.21 50.72
51 51 52 52 53 53 54 54 55 55
20 70 19 68 17 67 16 65 14 64
48.31 48.78 49.25 49.72 50.20 50.67 51.14 51.61 52.08 52.55
45.42 45.87 46.32 46.77 47.22 47.67 48.12 48.57 49.01 49.46
42.53 42.96 43.38 43.81 44.24 44.67 45.09 45.52 45.95 46.38
39.64 40.04 40.45 40.86 41.26 41.67 42.07 42.48 42.88 43.29
51 52 53 54 55 56 57 58 59 60
59.24 59.75 60.27 60.78 61.30 61.81 62.33 62.84 63.36 63.87
56 56 57 57 58 58 59 59 60 60
13 62 12 61 10 59 09 58 07 57
53.02 53.49 53.96 54.43 54.91 55.38 55.85 56.32 56.79 57.26
49.91 50.36 50.81 51.26 51.71 52.16 52.61 53.06 53.51 53.96
46.80 47.23 47.66 48.09 48.51 48.94 49.37 49.80 50.22 50.65
43.70 44.10 44.51 44.91 45.32 45.72 46.13 46.54 46.94 47.35
61 62 63 64 65 ---
64.38 64.90 65.41 65.93 66.44 _------__-
51.08 51.51 51.93 52.36 52.79
47.75 48.16 48.57 48.97 49.38
66 67 68 69 70
66.96 67.47 67.99 68.50 69.01
56.65 57.10 57.55 58.00 58.45
53.22 53.64 54.07 54.50 54.93
49.78 50.19 50.59 51.00 51.41
71 72 73 74 75
69.53 70.04 70.56 71.07 71.59
58.90 59.35 59.80 60.25 60.70
55.36 55.78 56.21 56.64 57.07
51.81 52.22 52.62 53.03 53.43
____
61 06 61 55 62 04 62 54 63 03 GROUND LINE 63.52 64.01 64.51 65.00 65.49 65.99 66.48 66.97 67.46 67.96
(
57.73 58.20 58.67 59.14 59.62 9 FEET, 60.09 60.56 61.03 61.50 61.97 62.44 62.91 63.38 63.06 64.33
6
54.41 54.86 55.30 55.75 56.20 *NCHES)---------.
APPENDIX
B
397
Table B-4.-Pole circumferences for western red cedar-continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES TOP I
2 3 4 5 6 7 8 9 10
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC.
1
CLASS CIRC.
2
80 FOOT CLASS 3 CIRC.
INCHES
INCHES
INCHES
25.00 25.42 25.84 26.26 26.68 27.09 27.51 27.93 28.35 28.77 29.19
23.00 23.39 23.78 24.18 24.57 24.96 25.35 25.74 26.14 26.53 26.92
33.00 33.51 34.01 34.52 35.03 35.53 36.04 36.55 37.05 37.56 38.07
31 .oo 31.49 31.97 32.46 32.95 33.43 33.92 34.41 34.89 35.38 35.86
29.00 29.46 29.92
30.38 30.84 31.30 31 .76 32.22 32.68 33.14 33.59
27.00 27.44 27.88 20.32 28.76 29.20 29.64 30.07 30.51 30.95 31.39
38.57 39.08 39.59 40.09 40.60
34.05 34.51 34.97 35.43 35.89 36.35 36.81 37.27 37.73 38.19
31 .83 32.27 32.71 33.15 33.59 34.03 34.47 34.91 35.34 35.78
29.61 30.03 30.45 30.86 31.28 31.70 32.12 32.54 32.96 33.38
27.31 27.70 28.09 28.49 28.88 29.27 29.66 30.05 30.45 30.84
15 16 17
41.11 41 .61
18 19 20
42.12 42.63 43.14
36.35 36.84 37.32 37.81 38.30 38.78 39.27 39.76 40.24 40.73
21 22 23 24 25 26 27 28 29 30
43.64 44.15 44.66 45.16 45.67 46.18 46.68 47.19 47.70 48.20
41.22 41.70 42.19 42.68 43.16 43.65 44.14 44.62 45.11 45.59
38.65 39.11 39.57 40.03 40.49 40.95 41.41 41.86 42.32 42.78
36.22 36.66 37.10 37.54 37.98 38.42 38.86 39.30 39.74 40.18
33.80 34.22 34.64 35.05 35.47 35.89 36.31 36.73 37.15 37.57
31 .23 31 .62 32.01 32.41 32.80 33.19 33.58 33.97 34.36 34.76
31 32 33 34 35 36 37 38 39 40
48.71 49.22 49.72 50.23 50.74 51 .24 51.75 52.26 52.76 53.27
46.08 46.57 47.05 47.54 48.03 48.51 49.00 49.49 49.97 50.46
43.24 43.70 44.16 44.62 45.08 45.54 46.00 46.46 46.92 47.38
40.61 41.05 41.49 41.93 42.37 42.81 43.25 43.69 44.13 44.57
37.99 38.41 38.82 39.24 39.66 40.08 40.50 40.92 41.34 41 .76
35.15 35.54 35.93 36.32 36.72 37.11 37.50 37.89 38.28 38.68
41 42 43 44 45 46 47 48 49 50
53.78 54.28 54.79 55.30 55.80 56.31 56.02 57.32 57.83 58.34
50.95 51.43 51.92 52.41 52.89 53.38 53.86 54.35 54.84 55.32
47.84 48.30 48.76 49.22 49.68 50.14 50.59 51.05 51.51 51.97
45.01 45.45 45.89 46.32 46.76 47.20 47.64 48.08 48.52 48.96
42.18 42.59 43.01 43.43 43.85 44.27 44.69 45.11 45.53 45.95
39.07 39.46 39.85 40.24 40.64 41.03 41 .42 41 .81 42.20 42.59
11 12 13
14
POLE
398
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES 51 52 53 54 55 56 57 58 59 60
58.84 59.35 59.86 60.36 60.87 61.38 61 .89 62.39 62.90 63.41
61 :: 64 65 66 67 68 69 __------
63.91 64.42 64.93 65.43 65.94 66.45 66.95 67.46 67.97 -----------
70
68.47
71 72 73 74 75 76 77 78 79 80
68.98 69.49 69.99 70.50 71 .Ol 71.51 72.02 72.53 73.03 73.54
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. INCHES FEET TOP
1 2 3 4 5 6 7 8 9
10
33.00 33.49 33.99 34.46 34.97 35.47 35.96 36.46 36.95 37.44 37.94
CLASS H-2 CIRC.
INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC.
52.43 52.89 53.35 53.81 54.27 54.73 55.19 55.65 56.11 56.57
49.40 49.84 50.28 50.72 51.16 51.59 52.03 52.47
1
INCHES
80 2
CLASS CIRC. INCHES
FOOT POLE-Con. CLASS 3 CIRC. 1NCHES
53.35
46.36 46.78 47.20 47.62 48.04 48.46 48.86 49.30 49.72 50.14
53.79 54.23 54.67 55.11 55.55 55.99 56.43 56.86 57.30
50.55 50.97 51 .39 51.81 52.23 52.65 53.07 53.49 53.91
57.74
54.32
50.43
61 .62 62.08 62.54 63.00 63.46 63.92 64.38 64.84 65.30 65.76
58.18 58.62 59.06 59.50 59.94 60.38 60.82 61 .26 61 .70 62.14
54.74 55.16 55.58 56.00 56.42 56.84 57.26 57.68 58.09 58.51
50.82 51.22 51 .61 52.00 52.39 52.78 53.18 53.57 53.96 54.35
CLASS CIRC.
INCHES
CLASS H-l CIRC. 1 NCHES
31 .oo 31.47 31.95 32.42 32.90 33.37 33.85 34.32 34.80 35.27 35.75
29.00 29.45 29.90 30.35 30.80 31 .25 31.70 32.15 32.59 33.04 33.49
27.00 27.43 27.86 28.29 28.72 29.15 29.58 30.01 30.44 30.87 31.30
55.81 56.30 56.78 57.27 57.76 58.24 58.73 59.22 59.70 60.19 60.68 61.16 61.65 62.14 62.62 63.11 63.59 64.08 64.57 -GROUND 65.05
L INE
65.54 66.03 66.51 67.00 67.49 67.97 68.46 68.95 69.43 69.92
CLASS H-2 CIRC.
57.03 57.49 57.95 58.41 58.86 59.32 59.78 60.24 60.70 ( 10 FEET 61.16
52.91
0
INCHES )------------
INCHES
1
42.99 43.38 43.77 44.16 44.55 44.95 45.34 45.73 46.12 46.51
CLASS CIRC.
INCHES 25 25 25 26 26 27 27 27 28 28 29
00 41
81 22 62 03 43 84 24 65 05
46.91 47.30 47.69 48.08 48.47 48.86 49.26 49.65 50.04 ----_--
2
85 FOOT POLE CLASS 3 CIRC. INCHES 23.00 23.39 23.77 24.16 24.54 24.93 25.32 25.70 26.09 26.47 26.86
APPENDIX
399
B
Table B-4.-Pole circumferences for western red cedar-continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
CLASS CIRC. INCHES
85 2
FOOT POLE-Con. CLASS 3 CIRC. INCHES
11 12 13 I4 15 16 17 18 19 20
38.43 30.92 39.42 39.91 40.41 40.90 41.39 41.69 42.36 42.87
36.22 36.70 37.17 37.65 39.12 38.59 39.07 39.54 40.02 40.49
33.94 34.39 34.84 35.29 35.74 36.19 36.64 37.09 37.54 37.99
31.73 32.16 32.59 33.03 33.46 33.89 34.32 34.75 35.18 35.61
29.46 29.86 30.27 30.67 31.08 31.48 31.89 32.29 32.70 33.10
27.25 27.63 28.02 28.41 28.79 29.18 29.56 29.95 30.34 30.72
21 22 23 24 25 26 :i 29 30
43.37 43.06 44.35 44.85 45.34 45.84 46.33 46.82 47.32 47.81
40.97 41.44 41.92 42.39 42.87 43.34 43.82 44.29 44.77 45.24
38.44 38.89 39.34 39.78 40.23 40.68 41.13 41.58 42.03 42.48
36.04 36.47 36.90 37.33 37.76 38.19 38.62 39.05 39.48 39.91
33.51 33.91 34.32 34.72 35.13 35.53 35.94 36.34 36.75 37.15
31.11 31.49 31.88 32.27 32.65 33.04 33.42 33.81 34.20 34.58
31 32 33 34 35 36 37 38 39 40
48.30 48.80 49.29 49.78 50.28 50.77 51.27 51.76 52.25 52.75
45.72 46.19 46.66 47.14 47.61 48.09 48.56 49.04 49.51 49.99
42.93 43.38 43.83 44.28 44.73 45.18 45.63 46.08 46.53 46.97
40.34 40.77 41.20 41.63 42.06 42.49 42.92 43.35 43.78 44.22
37.56 37.96 38.37 38.77 39.18 39.58 39.99 40.39 40.80 41.20
34.97 35.35 35.74 36.13 36.51 36.90 37.28 37.67 38.06 38.44
41 42 43 44 45 46 47 40 49 50
53.24 53.73 54.23 54.72 55.22 55.71 56.20 56.70 57.19 51.68
50.46 50.94 51.41 51.89 52.36 52.84 53.31 53.78 54.26 54.73
47.42 47.87 48.32 48.77 49.22 49.67 50.12 50.57 51.02 51.37
44.65 45.08 45.51 45.94 46.37 46.80 47.23 47.66 48.09 48.52
41.61 42.01 42.42 42.82 43.23 43.63 44.04 44.44 44.85 45.25
38.83 39.22 39.60 39.99 40.37 40.76 41.15 41.53 41.92 42.30
51 52 53 54 55 56 57 58 59 60
58.18 58.61 59.16 59.66 60.15 60.65 61.14 61.63 62.13 62.62
55.21 55.68 56.16 56.63 51.11 51.58 58.06 58.53 59.01 59.48
51.92 52.37 52.82 53.27 53.72 54.16 54.61 55.06 55.51 55.96
48.95 49.38 49.81 50.24 50.67 51.10 51.53 51.96 52.39 52.82
45.66 46.06 46.47 46.87 47.28 47.68 48.09 48.49 48.90 49.30
42.69 43.08 43.46 43.85 't4.23 44.62 45.01 45.39 45.78 46.16
TRANSMISSION
400
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES 61
62 63 64 65 66 61 68 69 70 71 72 13 74 75 76 77 78 79 80 81 82 83 84
63.11 63.61
64. IO 64.59 65.09 65.58 66.08 66.51 67.06 67.56 68.05 68.54 69.04 69.53 ----------_ 70.03 70.52 71 .Ol 71.51 72.00 72.49 72.99 73.48 73.97 74.47 74.96
WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES TOP
1 2
33.00 33.48
33.96 34.45 34.93 35.41 35.89
36.37 36.86 37.34 37.82 11
38.30
12 13 14 15 16 17 18 19
38.79
20
39.27 39.75 40.23 40.71 41.20 41.68 42.16 42.64
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
59.96 60.43 60.91 61 .38 61 .a5 62.33
56.41 56.86 57.31
63.28 63.75 64.23
57.76 58.21 58.66 59.11 59.56 60.01 60.46
64.70 65.18 65.65 66.13
60.91 61 .35 61 .80 62.25
62.80
-GROUND
L INE
66.60 67.08
61.55 68.03 68.50
68.97 69.45 69.92 70.40
( 10
FEET
62.70 63.15 63.60 64.05 64.50 64.95
CLASS CIRC.
1
INCHES 53.25 53.68 54.11 54.54 54.97 55.41
85 CLASS 2 CIRC. 1 NCHES
FOOT POLE-Con. CLASS 3 CIRC. INCHES
49.71 50.11 50.52 50.92 51.33 51.73 52.14 52.54 52.95 53.35
46.55 46.94 47.32 47.71
53.76 54.16 54.57 58.85 54.97 6 INCHES I---------59.28 55.38 55.78 59.71 56.19 60.14 56.59 60.57 57.00 61 .OO 61 .43 57.41
50.41 50.80 51.18 51.51 ----51.96 52.34 52.73 53.11 53.50
55.84
56.27 56.70 57.13
48.09
48.48 48.87
49.25 49.64 50.03
57.56 57.99 58.42
61 .86 62.29 62.72 63.15 63.58
53.89
57.81 58.22
54.27 54.66 55.04 55.43
70.87 71.35
65.40 65.85 66.30 66.75 67.20
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
INCHES
31 .oo 31 .46 31.93
29.00 29.44 29.88 30.32 30.76 31.20 31 .64
27.00 21.42
25.00 25.40
23.00
27.85 28.27 28.69 29.11
25.80
23.75 24.13 24.50 24.88 25.25 25.63 26.00
32.39 32.86
33.32 33.79 34.25 34.71 35.18 35.64 36.11 36.57 37.04 37.50 37.96 38.43 38.89
39.36 39.82 40.29
CLASS CIRC.
58.62
59.03 59.43
1
CLASS CIRC.
32.08
29.54 29.96
26.20 26.60 26.99 21.39 27.79
32.52 32.96 33.40
30.38 30.80 31 .23
28.19 28.59 28.99
31 .65
29.39 29.79 30.18
33.85 34.29 34.73 35.17 35.61 36.05 36.49 36.93 37.31 37.81
32.07 32.49 32.92 33.34 33.76 34.18 34.61
35.03 35.45
30.58 30.98
31.38 31.78
32. la 32.58 32.98
55.82
2
90 FOOT CLASS 3 CIRC. 1 NCHES
23.38
26.38
26.75 27.13 27.50 27.88 28.25 28.63
29.00 29.38 29.75 30.13 30.50
POLE
APPENDIX
401
B
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
CLASS H-2 CIRC. 1NCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
SO FOOT POLE-Con. 2 CLASS 3 CIRC. INCHES INCHES
CLASS CIRC.
22 23 24 25 26 27 28 29 30
43.12 43.61 44.09 44.57 45.05 45.54 46.02 46.50 46.98 47.46
40.75 41.21 41 .68 42.14 42.61 43.07 43.54 44.00 44.46 44.93
38.25 30.69 39.13 39.57 40.01 40.45 40.89 41.33 41.77 42.21
35.88 36.30 36.72 37.14 37.57 37.99 38.41 38.83 39.26 39.68
33.38 33.77 34.17 34.57 34.97 35.37 35.77 36.17 36.57 36.96
30.88 31.25 31 .63 32.00 32.38 32.75 33.13 33.50 33.88 34.25
31 32 33 34 35 36 37 38 39 40
41.95 48.43 48.91 49.39 49.87 50.36 50.84 51 .32 51 .80 52.29
45.39 45.86 46.32 46.79 47.25 47.71 48.18 48.64 49.11 49.57
42.65 43.10 43.54 43.98 44.42 44.86 45.30 45.74 46.18 46.62
40.10 40.52 40.95 41.37 41 .I9 42.21 42.64 43.06 43.48 43.90
31.36 37.76 38.16 38.56 38.96 39.36 39.76 40.15 40.55 40.95
34.63 35.00 35.38 35.75 36.13 36.50 36.88 37.25 37.63 38.00
41
52.77 53.25 53.73 54.21 54.70 55.18 55.66 56.14 56.62 57.11
50.04 50.50 50.96 51.43 51 .89 52.36 52.82 53.29 53.75 54.21
47.06 47.50 47.94 48.38 48.82 49.26 49.70 50.14 50.58 51.02
44.33 44.75 45.17 45.60 46.02 46.44 46.86 47.29 47.71 48.13
41.35 41.75 42.15 42.55 42.95 43.35 43.74 44.14 44.54 44.94
38.38 38.75 39.13 39.50 39.88 40.25 40.63 41 .oo 41 .38 41.75
57 58 59 60
57.59 58.07 50.55 59.04 59.52 60.00 60.48 60.96 61 .45 61 .93
54.68 55.14 55.61 56.07 56.54 57.00 57.46 57.93 58.39 58.06
51 .46 51.90 52.35 52.79 53.23 53.67 54.11 54.55 54.99 55.43
48.55 48.98 49.40 49.82 50.24 50.67 51.09 51.51 51.93 52.36
45.34 45.74 46.14 46.54 46.93 47.33 47.73 48.13 48.53 40.93
42.13 42.50 42.88 43.25 43.63 44.00 44.38 44.75 45.13 45.50
61 62 63 64 65 66 67 68 69 70
62.41 62.89 63.37 63.66 64.34 64.82 65.30 65.79 66.27 66.75
59.32 59.79 60.25 60.71 61.18 61 .64 62.11 62.57 63.04 63.50
55.87 56.31 56.75 57.19 57.63 58.07 58.51 58.95 59.39 59.83
52.78 53.20 53.62 54.05 54.47 54.89 55.32 55.74 56.16 56.58
49.33 49.73 50.12 50.52 50.92 51 .32 51 .72 52.12 52.52 52.92
45.88 46.25 46.63 47.00 47.38 47.75 48.13 48.50 48.88 49.25
21
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
TRANSMISSION
402
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN RED CEDAR DISTANCE CLASS H-3 FROM TOP CIRC. FEET INCHES
WESTERN
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC.
63.96 64.43 64.89 65.36 65.82 66.29 66.75 67.21
INCHES
71 72 73 74 75 76 77 78 ----79 80
67.23 67.71 68.20 68.68 69.16 69.64 70.12 70.61 71.09 71.57
67.68 68.14
60.27 60.71 61.15 61 .60 62.04 62.48 62.92 63.36 ( 1 1 FEET 63.80 64.24
81 82 83 84 85 86 87 88 89 so
72.05 72.54 73.02 73.50 73.98 74.46 74.95 75.43 75.91 76.39
68.61 69.07 69.54 70.00 70.46 70.93 71.39 71.86 72.32 72.79
64.68 65.12 65.56 66.00 66.44 66.88 67.32 67.76 68.20 68.64
.-GROUND
RED CEDAR DISTANCE FROM TOP FEET
L INE
CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
TOP
CLASS CIRC. INCHES
1
57.01 57.43 57.85 58.27 58.70 59.12 59.54 59.96 0
SO FOOT POLE -Con. 2 CLASS 3 CIRC. INCHES I TiCHiS
CLASS CIRC.
53.32 53.71 54.11 54.51 54.91 55.31 55.71 56.11
49.63 50.00 50.38 50.75 51.13 51.50 51.88
60.39 60.81
56.51 56.90
52.25 -----52.63 53.00
61 .23 61 .65 62.08 62.50 62.92 63.35 63.77 64.19 64.61 65.04
57.30 57.70 58.10 58.50 58.90 59.30 59.70 60.10 60.49 60.89
53.38 53.75 54.13 54.50 54.88 55.25 55.63 56.00 56.38 56.75
INCHESl---
INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. 1 NCHES
33.00 33.47 33.94 34.42 34.89 35.36 35.83 36.30 36.78 37.25 37.72
31 .oo 31 .46 31.91 32.37 32.82 33.28 33.73 34.19 34.64 35.10 35.55
29.00 29.43 29.87 30.30 30.73 31.16 31 .60 32.03 32.46 32.89 33.33
27.00 27.41 27.82 28.23 28.64 29.05 29.46 29.87 30.28 30.69 31.10
25.00 25.39 25.78 26.16 26.55 26.94 27.33 27.71 28.10 28.49 28.88
38.19 38.66 39.13 39.61 40.08 40.55 41.02 41.49 41.97 42.44
36 36 36 37 37 38 38 39 39 40
33.76 34.19 34.62 35.06 35.49 35.92 36.35 36.79 37.22 37.65
31.51 31 .92 32.33 32.74 33.15 33.56 33.97 34.38 34.79 35.20
29.26 29.65 30.04 30.43 30.81 31.20 31.59 31 .98 32.37 32.75
01 46 92 37 83 28 74 19 65 10
I
CLASS CIRC.
95 2
INCHES
FOOT
POLE
APPENDIX
403
B
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC.
CLASS H-2 CIRC.
CLASS H-l CIRC. 1 NCHES
CLASS CIRC. INCHES
INCHES
INCHES
21
42.91
22 23 24 25 26 27 28 29 30
43.38 43.85 44.33 44.80 45.27 45.74 46.21 46.69 47.16
40.56 41 .Ol 41.47 41.92 42.38 42.83 43.29 43.74 44.20 44.65
38.08 38.52 38.95 39.38 39.81 40.25 40.68
35.61
31 32 33 34 35 36 37 38 39 40
47.63 48.10 48.57 49.04 49.52 49.99 50.46 50.93 51.40 51.88
45.11 45.56 46.02 46.47 46.93 47.38 47.84 48.29 48.75 49.20
42.41
41 42 43 44 45 46 47 48 49 50
52.35 52.82 53.29 53.76 54.24 54.71 55.18 55.65 56.12 56.60
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
1
95 FOOT CLASS 2 CIRC.
INCHES
36.02 36.43 36.84 37.25 37.66 38.07 38.48 38.89 39.30
33.14 33.53 33.92 34.30 34.69 35.08 35.47 35.85 36.24 36.63
42.84 43.28 43.71 44.14 44.57 45.01 45.44 45.87 46.30
39.71 40.12 40.53 40.94 41.35 41 .76 42.17 42.58 42.99 43.40
37.02 37.40 37.79 38.18 38.57 38.96 39.34 39.73 40.12 40.51
49.66 50.11 50.57 51.02 51.48 51.93 52.39 52.84 53.30 53.75
46.74 47.17 47.60 48.03 48.47 48.90 49.33 49.76 50.20 50.63
43.81 44.22 44.63 45.04 45.46 45.87 46.28 46.69 47.10 47.51
40.89 41 .28 41 .67 42.06 42.44 42.83 43.22 43.61 43.99 44.38
57.07 57.54 58.01 58.48 58.96 59.43 59.90 60.37 60.84 61 .31
54.21 54.66 55.12 55.57 56.03 56.48 56.94 57.39 57.85 58.30
51 .06 51.49 51.93 52.36 52.79 53.22 53.66 54.09 54.52 54.96
47.92 48.33 48.74 49.15 49.56 49.97 50.38 50.79 51.20 51.61
44.77 45.16 45.54 45.93 46.32 46.71 47.10 47.48 47.87 48.26
61 .79 62.26 62.73 63.20 63.67 64.15 64.62 65.09 65.56 66.03
58.76 59.21 59.67 60.12 60.58 61.03 61 .49 61.94 62.40 62.65
55.39 55.82 56.25 56.69 57.12 57.55 57.98 58.42 58.85 59.28
52.02 52.43 52.84 53.25 53.66 54.07 54.48 54.89 55.30 55.71
48.65 49.03 49.42 49.81 50.20 50.58 50.97 51 .36 51.75 5‘2.13
41.11 41.54 41.98
POLE-Cot-I.
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
95 FOOT CLASS 2 CIRC.
66.51
63.31
72 73 74 75 76 77 78 79 80
66.98 67.45 67.92 68.39 68.87 69.34 69.81 70.28 70.75
63.76 64.22 64.67 65.13 65.50 66.04 66.49 66.95 67.40
59 71 60 15 60 58 61 01 61 44 61 98 62 31 62.74 63.17 63.61
56 12 56 53 56 94 57 35 57 76 59 17 58 58 58 99 59 40 59 81
52.52 52.91 53.30 53.69 54.07 54.46 54.85 55.24 55.62 56.01
81 82 83
71.22 71.70 72.17
67.86 68.31 68.77
64.04 64.47 64.90
60 60 61
22 63 04
56.40 56.79 57.17
LINE
(11
FEET.
0
INCHES)--
84 85 06 87 08 89 90
72.64 73.11 73.58 74.06 74.53 75.00 75.47
69.22 69.60 70.13 70.59 71.04 71.50 71 .96
65.34 65.77 66 20 66 63 67 07 67.50 67.93
61 61 62 62 63 63 63
45 86 27 68 09 50 91
57.56 57.95 58.34 58.72 59.11 59.50 59.89
91 92 93 94 95
75.94 76.42 76.89 77.36 77.83
72.41 72.87 73.32 73.78 74.23
68 68 69 69 70
37 80 23 66 10
64 64 65 65 65
32 73 14 55 96
60.28 60.66 61 .05 61 .44 61 .83
RED CEDAR DISTANCE FROM TOP FEET TOP
2 3 4
5 6 8 9
10 11 12 13 14 15 16 17
ia 19 20
100 CLASS H-3 CIRC.
INCHES 33.00 33.46 33.93
34.39 34.85 35.31 35.78 36.24 36.70 37.16 37.63 38.09 38.55 39.02 39.48 39.94
40.40 40.87 41.33 41.79 42.26
CLASS H-2 CIRC. INCHES 31 .oo
POLE-Con.
INCHES
71
-------------GROUND
WESTERN
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC.
INCHES 29 00 29 43 29.85
31.44 31.88 32.32 32.77 33.21 33.65 34.09 34.53 34.97 35.41
30.28 30 70 31 13 31 55 31.98 32.40 32.83 33.26
35.96 36.30 36.74 37.18 37.62 38.06 38.51 38.95 39.39 39.83
33 34 34 34 35 35 36 36 37 37
68 11 53 96 38 81 23 66 09 51
CLASS CIRC.
1
CLASS CIRC.
INCHES
INCHES
27.00 27.40 27.81 29.21 28.62 29.02 29.43 30.23 30.64 31.04
25.00 25.39 25.77 26.15 26.53 26.91 27.30 27.68 28.06 20.45 28.83
31.45 31 .85 32.26 32.66 33.06 33.47 33.97 34.28 34.68 35.09
29.21 29.60 29.98 30.36 30.74 31.13 31.51 31 .89 32.28 32.66
29.83
2
FOOT
POLE
APPENDIX
405
B
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
100 FOOT CLASS 2 CIRC.
CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
22 23 24 25 26 27 28 29 30
42.72 43.18 43.64 44.11 44.57 45.03 45.49 45.96 46.42 46.88
40.27 40.71 41.15 41 .60 42.04 42.48 42.92 43.36 43.80 44.24
37.94 38.36 38.79 39.21 39.64 40.06 40.49 40.91 41.34 41.77
35.49 35.89
36.30 36.70 37.11 37.51 37.91 38.32 38.72 39.13
33.04 33.43 33.81 34.19 34.57 34.96 35.34 35.72 36.11 36.49
31 32 33 34 35 36 37 38 39 40
47.35 47.81 48.27 48.73 49.20 49.66 50.12 50.59 51.05 51.51
44.69 45.13 45.57 46.01 46.45 46.89 47.34 47.78 48.22 48.66
42.19 42.62 43.04 43.47 43.89 44.32 44.74 45.17 45.60 46.02
39.53 39.94 40.34 40.74 41.15 41.55 41 .96 42.36 42.77 43.17
36.87 37.26 37.64 38.02 38.40 38.79 39.17 39.55 39.94 40.32
41 42 43 44 45 46 47 48 49 50
51.97 52.44 52.90 53.36 53.82 54.29 54.75 55.21 55.68 56. 14
49.10 49.54
43.57 43.98 44.38 44.79 45.19 45.60 46.00 46.40 46.81 47.21
40.70 41.09
50.43 50.87 51.31 51.75 52.19 52.63 53.07
46.45 46.87 47.30 47.72 48.15 48.57 49.00 49.43 49.85 50.28
42.23 42.62 43.00 43.38 43.77 44.15
51 52 53 54 55 56 57 58 59 60
56.60 57.06 57.53 57.99 58.45 58.91 59.38 59.84 60.30 60.77
53.52 53.96 54.40 54.84 55.28 55.72 56.16 56.61 57.05 57.49
50.70 51.13 51.55 51 .98 52.40 52.83 53.26 53.68 54.11 54.53
47.62 48.02 48.43 48.83 49.23 49.64 50.04 50.45 50.85 51 .26
44.53 44.91 45.30 45.68 46.06 46.45 46.83 47.21 47.60 47.98
61 62 63 64 65 66 67 68 69 70
61 .23 61 .69 62.15 62.62 63.08 63.54 64.01 64.47 64.93 65.39
57.93 58.37 58.81 59.26 59.70 60.14 60.58 61 .02 61 .46 61.90
54.96 55.38 55.81 56.23 56.66 57.09 57.51 57.94 58.36 58.79
51.66 52.06 52.47 52.87 53.28 53.68 54.09 54.49 54.89 55.30
48.36 48.74 49.13 49.51
21
49.98
1
INCHES
41.47 41.85
49.89
50.28 50.66 51.04 5 l_. 43 51 .a1
POLE-Con.
406
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET 71
72 73 74 75 76 77 78 79 80 81 82 83 04 05 86 87 88 ------89 so 91
92 93 94 95 96 97 98 99 100
WESTERN
RED CEDAR DISTANCE FROM TOP FEET TOP
1 2 3 4 5 6 7 8 9 10
100 CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC. INCHES
65.06 66.32 66.78 67.24 67.71 68.17 68.63 69.10 69.56 70.02
62.35 62.79 63.23 63.67 64.11 64.55 64.99 65.44 65.88 66.32
59 21 59 64 60 06 60 49 60 91 61 34 61 77 62 19 62 62 63 04
55.70 56.11 56.51 56.91 57.32 57.72 58.13 58.53 58.94 59.34
70.48 70.95 71.41 71.87 72.34 72.80 73.26 73.72
66.76 67.20 67.64 68.09 68.53 60.97 69.41 69.85
63 63 64 64 65 65 66 66
59.74 60.15 60.55 60.96 61 .36 61 .77 62.17 62.57
CLASS H-l CIRC. INCHES
1
INCHES
FOOT
CLASS CIRC. INCHES
74.19 74.65
70.29 70.73
66.87 67.30
62.98 63.38
75.11 75.57 76.04 76.50 76.96 77.43 77.89 78.35 78.81 79.28
71.18 71 .62 72.06 72.50 72.94 73.38 73.82 74.27 74.71 75.15
67.72 68.15 68.51 69.00 69.43 69.85 70.28 70.70 71.13 71.55
63.79 64.19 64.60 65.00 65.40 65.81 66.21 66.62 67.02 67.43
59.85 60.23 60.62 61 .OO 61 .38 61 .77 62.15 62.53 62.91 63.30
CLASS H-3 CIRC.
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
CIRC. INCHES
CIRC. INCHES
33.00 33.45 33.91 34.36 34.82 35.27 35.73 36.18 36.64 37.09 37.55
31 .oo 31.43 31 .87 32.30 32.74 33.17 33.61 34.04 34.47 34.91 35.34
29.00 29.41 29.83 30.24 30.66 31.07 31.48 31.90 32.31 32.73 33.14
27.00 27.39 27.79 28.18 28.58 28.97 29.36 29.76 30.15 30.55 30.94
25.00 25.37 25.75 26.12 26.49 26.87 27.24 27.62 27.99 20.36 28.74
LINE
(11
FEET,
0
INCHES)
------
CLASS
POLE-Con.
2
52.19 52.57 52.96 53.34 53.72 54.11 54.49 54.87 55.26 55.64 56.02 56.40 56.79 5-l. 17 57.55 57.94 58.32 58.70 -----59.09 59.47
-----GROUND
47 89 32 74 17 60 02 45
CLASS CIRC.
1
CLASS
105 2
FOOT
POLE
APPENDIX
407
B
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
35.78 36.21 36.65 37.08 37.52 37.95 38.38 38.82 39.25 39.69
33.56 33.97 34.38
14 15 16 17 18 19 20
38.00 38.45 38.91 39.36 39.82 40.27 40.73 41.18 41 .64 42.09
31.33 31.73 32.12 32.52 32.91 33.30 33.70 34.09 34.48 34.88
29.11 29.48 29.86 30.23 30.61 30.98 31.35 31.73 32.10 32.47
21 22 23 24 25 26 27 28 29 30
42.55 43.00 43.45 43.91 44.36 44.82 45.27 45.73 46.18 46.64
40.12 40.56 40.99 41 .42 41.86 42.29 42.73 43.16 43.60 44.03
37.70 38.11
40. la 40.60 41 .Ol 41 .42
35.27 35.67 36.06 36.45 36.85 37.24 37.64 38.03 38.42 38.82
32.85 33.22 33.60 33.97 34.34 34.72 35.09 35.46 35.84 36.21
31 32 33 34 35 36 37 38 39 40
47.09 47.55 48.00 48.45 48.91 49.36 49.82 50.27 50.73 51.18
44.46 44.90 45.33 45.77 46.20 46.64 47.07 47.51 47.94 48.37
41 .84 42.25 42.67 43.08 43.49. 43.91 44.32 44.74 45.15 45.57
39.21 39.61 40.00 40.39 40.79 41.18 41.58 41.97 42.36 42.76
36.59 36.96 37.33 37.71 38.08 38.45 38.83 39.20 39.58 39.95
41 42 43 44 45 46 47 48 49 50
51 .64 52.09 52.55 53.00 53.45 53.91 54.36 54.82 55.27 55.73
48.81 49.24 49.68 50.11 50.55 50.98 51.41 51 .a5 52.28 52.72
45.98 46.39 46.81 47.22 47.64 48.05 48.46 48.88 49.29 49.71
43.15 43.55 43.94 44.33 44.73 45.12 45.52 45.91 46.30 46.70
40.32 40.70 41.07 41.44 41 .82 42.19 42.57 42.94 43.31 43.69
51 52 53 54 55 56 57 58 59 60
56.18 56.64 57.09 57.55 58.00 58.45 58.91 59.36 59.82 60.27
53.15 53.59 54.02 54.45 54.89 55.32 55.76 56.19 56.63 57.06
50.12 50.54 50.95 51 .36 51 .78 52.19 52.61 53.02 53.43 53.85
47.09 47.48 47.88 48.27 48.67 49.06 49.45 49.85 50.24 50.64
44.06 44.43 44.81 45. la 45.56 45.93 46.30 46.68 47.05 47.42
34.80 35.21
35.63 36.04 36.45 36.87 37.28
38.53 38.94 39.35 39.77
1
105 FOOT CLASS 2 CIRC. INCHES
CLASS H-2 CIRC. INCHES
I I 12 13
CLASS H-3 CIRC.
POLE-Con.
408
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
I
105 FOOT CLASS 2 CIRC. INCHES
61 62 63 64 65 66 67 68 69 70
60.73 61.18 61 .64 62.09 62.55 63.00 63.45 63.91 64.36 64.82
57 57 58 58 59 59 60 60 60 61
49 93 36 80 23 67 10 54 97 40
54.26 54.68 55.09 55.51 55.92 56.33 56.75 57.16 57.58 57.99
51.03 51.42 51 .82 52.21 52.61 53.00 53.39 53.79 54.18 54.58
47.80 48.17 48.55 48.92 49.29 49.67 50.04 50.41 50.79 51.16
71 72 73 74 75 76 77 78 79 80
65.27 65.73 66.18 66.64 67.09 67.55 68.00 68.45 68.91 69.36
61 62 62 63 63 64 64 64 65 65
84 27 71 14 58 01 44 88 31 75
58.40 58.82 59.23 59.65 60.06 60.47 60.89 61 .30 61 .72 62.13
54.97 55.36 55.76 56.15 56.55 56.94 57.33 57.73 58.12 58.52
51.54 51.91 52.28 52.66 53.03 53.40 53.78 54.15 54.53 54.90
81 82 83 84 85 86 87 88 89 90
69.82 70.27 70.73 71.18 71 .64 72.09 72.55 73.00 73.45 73.91
66 66 67 67 67 68 68 69 69 70
18 62 05 48 92 35 79 22 66 09
62.55 62.96 63.37 63.79 64.20 64.62 65.03 65.44 65.86 66.27
58.91 59.30 59.70 60.09 60.48 60.88 61 .27 61 .67 62.06 62.45
55.27 55.65 56.02 56.39 56.77 57.14 57.52 57.89 58.26 58.64
91 92 -------93 94 95 96 97 98 99 100 101 102 103 104 105
74.36 74.82 -----GROUND 75.27 75.73 76.18 76.64 77.09 77.55 78.00 78.45 78.91 79.36 79.82 80.27 80.73
70 53 70.96 LINE (12 71.39 71 .83 72.26 72.70 73.13 73.57 74.00 74.43 74 75 75 76 76
87 30 74 17 61
66.69 62.85 67. IO 63.24 FEET, 0 INCHES)----67.52 63.64 67.93 64.03 68.34 64.42 68.76 64.82 69.17 65.21 69.59 65.61 70.00 66.00 70.41 66.39 70.83 71 .24 71.66 72.07 72.48
66.79 67.18 67.58 67.97 68.36
59.01 59.38 59.76 60.13 60.51 60.88 61 .25 61 .63 62.00 62.37 62.75 63.12 63.49 63.87 64.24
POLE-Con.
APPENDIX
409
B
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
33.00 33.45 33.09 34.34 34.79 35.24 35.68 36.13 36.58 37.02 31.47
31 .oo 31.43 31 .86
29.00
CLASS CIRC. INCHES
1
CLASS CIRC.
110 2
INCHES
32.28 32.71 33.14 33.57 34.00 34.42 34.65 35.20
29.41 29.82 30.23 30.63 31.04 31.45 31.86 32.27 32.68 33.09
27.00 27.39 27.70 26.17 28.56 28.95 29.34 29.73 30.12 30.50 30.89
25.00 25.37 25.73 26.10 26.46 26.93 27.19 27.56 27.92 28.29 28.65
16 19 20
37.92 38.37 38.81 39.26 39.71 40.15 40.60 41.05 41.50 41.94
35.71 36.13 36.56 36.99 37.42 37.95 36.27 38.70 39.13 39.56
33.50 33.90 34.31 34.72 35.13 35.54 35.95 36.36 36.76 37.17
31 .28 31 .67 32.06 32.45 32.04 33.23 33.62 34.01 34.40 34.79
29.02 29.38 29.75 30.12 30.48 30.65 31.21 31.58 31.94 32.31
21 22 23 24 25 26 27 29 29 30
42.39 42.04 43.26 43.73 44.18 44.62 45.07 45.52 45.97 46.41
39.99 40.41 40.94 41 .27 41.70 42.12 42.55 42.98 43.41 43.84
37.58 37.99 38.40 38.81 39.22 39.63 40.03 40.44 40.85 41 .26
35.18 35.57 35.96 36.35 36.74 37.12 37.51 37.90 38.29 38.66
32.67 33.04 33.40 33.77 34.13 34.50 34.87 35.23 35.60 35.96
31 32 33 34 35 36 37 38 39 40
46.06 47.31 47.75 48.20 40.65 49.10 49.54 49.99 50.44 50.88
44.26 44.69 45.12 45.55 45.98 46.40 46.83 47.26 47.69 48.12
41.67 42.08 42.49 42.09 43.30 43.71 44.12 44.53 44.94 45.35
39.07 39.46 39.85 40.24 40.63 41.02 41.41 41.80 42.19 42.58
36.33 36.69 37.06 37.42 37.79 36.15 39.52 38.88 39.25 39.62
91 42 43 44 45 46 47 48 49 50
51.33 51.78 52.23 52.67 53.12 53.57 54.01 54.46 54.91 55.36
49.54 48.97 49.40 49.83 50.25 50.68
45.75 46.16 46.57 46.98 47.39 47.80 48.21 46.62 49.02 49.43
42.97 43.36 43.75 44.13 44.52 44.91 45.30 45.69 46.08 46.47
39.98 40.35 40.71 41.08 41.44 41 .81 42.17 42.54 42.90 43.27
TOP
1 2 3 4 5 6 7 8 9 10
11 12 13
14 15 16 17
51.11 51.54
51.97 52.39
FOOT
POLE
410
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
110 FOOT CLASS H-3 CIRC. 1 NCHES
CLASS H-2 CIRC. INCHES
51 52 53 54 55 56 57 58 59 60
55.80 56.25 56.70 57.14 57.59 58.04 58.49 58.93 59.38 59.83
52.82 53.25 53.68 54.11 54.53 54.96 55.39 55.82 56.25 56.67
49.84 50.25 50.66 51.07 51.48 51.88 52.29 52.70 53.1 I 53.52
46.86 47.25 47.64 48.03 48.42 48.81 49.20 49.59 49.98 50.37
43.63 44.00 44.37 44.73 45.10 45.46 45.83 46.19 46.56 46.92
61 62 63 64 65 66 67 68 69 70
60.27 60.72 61.17 61 .62 62.06 62.51 62.96 63.40 63.85 64.30
57.10 57.53 57.96 58.38 58.81 59.24 59.67 60.10 60.52 60.95
53.93 54.34 54.75 55.15 55.56 55.97 56.38 56.79 57.20 57.61
50.75 51.14 51.53 51.92 52.31 52.70 53.09 53.48 53.87 54.26
47.29 47.65 48.02 48.38 48.75 49.12 49.48 49.85 50.21 50.58
71 72 73 74 75 76 77 78 79 80
64.75 65.19 65.64 66.09 66.53 66.98 67.43 67.87 68.32 68.77
61.38 61.81 62.24 62.66 63.09 63.52 63.95 64.37 64.80 65.23
58.01 58.42 58.83 59.24 59.65 60.06 60.47 60.87 61 .28 61 .69
54.65 55.04 55.43 55.82 56.21 56.60 56.99 57.37 57.76 58.15
50.94 51.31 51 .67 52.04 52.40 52.77 53.13 53.50 53.87 54.23
81 82 83 84 85 86 87 88 89 90
69.22 69.66 70.11 70.56 71 .oo 71.45 71.90 72.35 72.79 73.24
65.66 66.09 66.51 66.94 67.37 67.80 68.23 68.65 69.08 69.51
62.10 62.51 62.92 63.33 63.74 64.14 64.55 64.96 65.37 65.78
58.54 58.93 59.32 59.71 60.10 60.49 60.88 61 .27 61 .66 62.05
54.60 54.96 55.33 55.69 56.06 56.42 56.79 57.15 57.52 57.88
73.69 74.13 74.58 75.03 75.48 75.92 76.37
69.94 70.37 70.79 71.22 71 .65 72.08 72.50
66.19 66.60 67.00 67.41 67.82 68.23 68.64
62.44 62.83 63.22 63.61 64.00 64.38 64.77
58.25 58.62 58.98 59.35 59.71 60.08 60.44 ----60.81 61.17 61 .54
91 92 93 94 95 96 97 --98 99 100
----GROUND
76.82 77.26 77.71
LINE
72.93 73.36 73.79
(12
CLASS H-l CIRC. INCHES
FEET,
0
69.05 69.46 69.87
CLASS CIRC. INCHES
INCHES)------
65.16 65.55 65.94
1
CLASS CIRC.
INCHES
2
POLE-Con.
APPENDIX
411
6
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
101 102 103 104 105 106 107 108 109 110
WESTERN
RED CEDAR DISTANCE FROM TOP FEET
110 CLASS H-3 CIRC.
CLASS H-2 CIRC.
INCHES
INCHES
CLASS H-l CIRC. INCHES
78.16 78.61 79.05 79.50 79.95 80.39 80.84 81.29 81.74 82.18
74.22 74.64 75.07 75.50 75.93 76.36 76.78 77.21 77.64 78.07
70.27 70.68 71.09 71.50 71.91 72.32 72.73 73.13 73.54 73.95
CLASS H-3 CIRC.
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
1 2 3 4 5 6 7 8 9 10
33.00 33.44 33.87 34.31 34.74 35.18 35.61 36.05 36.49 36.92 37.36
31 .oo 31.42 31.83 32.25 32.67 33.09 33.50 33.92 34.34 34.76 35.17
29.00 29.40 29.80
11 12 13 14 15 16 17 18 19 20
37.79 38.23 38.67 39.10 39.54 39.97 40.41 40.84 41.28 41.72
21 22 23 24 25 26 27 28 29 30
42.15 42.59 43.02 43.46 43.89 44.33 44.77 45.20 45.64 46.07
TOP
CLASS
1
CIRC. INCHES
POLE-Con.
INCHES
66.33 66.72 67.11 67.50 67.09 68.28 68.67 69.06 69.45 69.84
CLASS CIRC.
FOOT CLASS 2 CIRC.
61.90
62.27 62.63 63.00 63.37 63.73 64.10 64.46 64.83 65.19
1
CLASS CIRC.
115 2
INCHES
INCHES
30.20 30.60 31 .oo 31.39 31.79 32.19 32.59 32.99
27.00 27.38 27.76 28.14 28.52 28.90 29.28 29.67 30.05 30.43 30.81
25.00 25.36 25.72 26.07 26.43 26.79 27.15 27.50 27.86 28.22 28.58
35.59 36.01 36.43 36.84 37.26 37.68 38.10 38.51 38.93 39.35
33.39 33.79 34.19 34.59 34.99 35.39 35.76 36.18 36.58 36.98
31.19 31.57 31.95 32.33 32.71 33.09 33.47 33.85 34.23 34.61
28.94 29.29 29.65 30.01 30.37 30.72 31.08 31.44 31.80 32.16
39.77 40.18 40.60 41.02 41.44 41.85 42.27 42.69 43.1 I 43.52
37.38 37.78 38.18 38.58 38.98 39.38 39.78 40.17 40.57 40.97
35.00 35.38 35.76 36.14 36.52 36.90 37.28 37.66 38.04 38.42
32.51 32.87 33.23 33.59 33.94 34 * 30 34.66 35.02 35.38 35.73
FOOT
POLE
TRANSMISSION
412
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC. INCHES
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
115 FOOT CLASS 2 CIRC. INCHES
31 32 33 34 35 36 37 38 39 40
46.51 46.94 47.38 47.82 48.25 48.69 49.12 49.56 50.00 50.43
43.94 44.36 44.78 45.19 45.61 46.03 46.44 46.86 47.28 47.70
41.37 41.77 42.17 42.57 42.97 43.37 43.77 44.17 44.56 44.96
38.80 39.18 39.56 39.94 40.33 40.71 41.09 41.47 41 .85 42.23
36.09 36.45 36.81 37.17 37.52 37.88 38.24 38.60 38.95 39.31
41 42 43 44 45 46 47 48 49 50
50.87 51.30 51.74 52.17 52.61 53.05 53.48 53.92 54.35 54.79
48.11 48.53 48.95 49.37 49.78 50.20 50.62 51.04 51.45 51 .81
45.36 45.16 46.16 46.56 46.96 47.36 47.76 48.16 48.56 48.95
42.61 42.99 43.37 43.75 44.13 44.51 44.89 45.28 45.66 46.04
39.67 40.03 40.39 40.74 41.10 41 .46 41 .82 42.17 42.53 42.89
51 52 53 54 55 56 57 58 59 60
55.22 55.66 56.10 56.53 56.97 57.40 57.84 58.28 58.71 59.15
52.29 52.71 53.12 53.54 53.96 54.38 54.79 55.21 55.63 56.05
49.35 49.75 50.15 50.55 50.95 51.35 51.75 52.15 52.55 52.94
46.42 46.80 47.18 47.56 47.94 48.32 48.70 49.08 49.46 49.84
43.25 43.61 43.96 44.32 44.68 45.04 45.39 45.75 46.11 46.47
61 62 63 64 65 66 67 68 69 70
59.58 60.02 60.45 60.89 61 .33 61 .76 62.20 62.63 63.07 63.50
56.46 56.88 57.30 57.72 58.13 58.55 58.97 59.39 59.80 60.22
53.34 53.74 54.14 54.54 54.94 55.34 55.74 56.14 56.54 56.94
50.22 50.61 50.99 51.37 51.75 52.13 52.51 52.89 53.27 53.65
46.83 47.18 47.54 47.90 48.26 48.61 48.97 49.33 49.69 50.05
71 72 73 74 75 76 77 78 79 80
63.94 64.38 64.81 65.25 65.68 66.12 66.56 66.99 67.43 67.86
60.64 61 .06 61 .47 61 .89 62.31 62.72 63.14 63.56 63.98 64.39
57.33 57.73 58.13 58.53 58.93 59.33 59.73 60.13 60.53 60.93
54.03 54.41 54.79 55.17 55.56 55.94 56.32 56.70 57.08 57.46
50.40 50.76 51.12 51 .48 51 .83 52.19 52.55 52.91 53.27 53.62
POLE-Con.
APPENDIX
6
413
Table B-4.-Pole circumferences for western red cechr-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
1
115 FOOT CLASS 2 CIRC. INCHES
81 62 83 84 85 86 87 88 89 90
68.30 68.73 69.17 69.61 70.04 70.48 70.91 71.35 71.78 72.22
64 81 65 23 65 65 66.06 66.48 66 90 67 32 67 73 15 68 68 57
61 33 61 72 12 62 62.52 62.92 63 32 63 72 64 12 64 52 64 92
57 84 58 22 58 60 58.98 59.36 59 74 60 12 60 50 60 89 61 27
53.98 54.34 54.70 55.06 55.41 55.77 56.13 56.49 56.84 57.20
91 92 93 94 95 96 97 98 99 100
72.66 73.09 73.53 73.96 74.40 74.83 75.27 75.71 76.14 76.58
68 99 69 40 69 82 70.24 70.66 71 07 71 49 71 91 72 33 72 74
65 32 65 72 66 11 66.51 66.91 67.31 67.71 68.11 68.51 68.91
61 65 62 03 62 41 62.79 63.17 63 55 63 93 64 31 64 69 65 07
57.56 57.92 58.28 58.63 58.99 59.35 59.71 60.06 60.42 60.78
65.45 65.83
61.14 61.50
66 22 66 60 66 98 67 36 67 74 68.12 68.50 68 88
61.85 62.21 62.57 62.93 63.28 63.64 64.00 64.36
26 64 02 40 78
64.72 65.07 65.43 65.19 66.15
101 102 -103 104 105 106 107 108 109 110 111 112 113 114 115
WESTERN
CLASS H-3 CIRC. INCHES
RED CEDAR DISTANCE FROM TOP FEET TOP 1 2 3 4 5 6 7 8 9 10
77.01 77.45 -----GROUND 77.89 78.32 78.76 79.19 79.63 80.06 80.50 80.94 81.37 81.81 82.24 82.68 83.11
CLASS H-3 CIRC. INCHES 33.00 33.43 33.86 34.29 34.72 35.15 35.58 36.01 36.44 36.81 37.30
73.16 73.58 LINE (12 74.00 74.41 74.83 75.25 75.67 76.08 76.50 76 92 77 77 78 78 79
33 75 17 59 00
69.31 69.71 FEET, 0 INCHES)-70.11 70.50 70.90 71.30 71.70 72.10 72.50 72 90 73 73 74 74 74
30 70 10 50 89
.--
69 69 70 70 70
CLASS H-2 CIRC. INCHES
CLASS H-l CIRC. INCHES
CLASS CIRC. INCHES
31 00 31 41 31 82 32 24 32 65 33.06 33.47 33 89 34 30 34 71 35 12
29.00 29.39 29.79 30.18 30.58 30.97 31.37 31.76 32.16 32.55 32.95
27.00 27.37 27.75 28.12 28.49 28.86 29.24 29.61 29.98 30.36 30.73
1
120 CLASS 2 CIRC. INCHES 25.00 25.35 25.70 26.05 26.40 26.75 27.11 27.46 27.81 28.16 28.51
POLE-con.
FOOT
POLE
414
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-2 CIRC. INCHES
18 19 20
37.73 38.16 38.59 39.02 39.45 39.88 40.31 40.74 41.17 41.60
35.54 35.95 36.36 36.77 37.18 37.60 38.01 38.42 38.83 39.25
33.34 33.74 34.13 34.53 34.92 35.32 35.71 36.1 I 36.50 36.89
31.47 31 .85 32.22 32.59 32.96 33.34 33.71 34.08 34.46
28.86 29.21 29.56 29.91 30.26 30.61 30.96 31.32 31.67 32.02
21 22 23 24 25 26 27 28 29 30
42.03 42.46 42.89 43.32 43.75 44.18 44.61 45.04 45.46 45.89
39.66 40.07 40.48 40.89 41.31 41 .72 42.13 42.54 42.96 43.37
37.29 37.68 38.08 38.47 38.87 39.26 39.66 40.05 40.45 40.84
34.83 35.20 35.57 35.95 36.32 36.69 37.07 37.44 37.81 38.18
32.37 32.72 33.07 33.. 42 33.77 34.12 34.47 34.82 35.18 35.53
31 32 33 34 35 36 37 38 39 40
46.32 46.75 47.18 47.61 48.04 48.47 48.90 49.33 49.76 50.19
43.78 44.19 44.61 45.02 45.43 45.84 46.25 46.67 47.08 47.49
41.24 41 .63 42.03 42.42 42.82 43.21 43.61 44.00 44.39 44.79
38.56 38.93 39.30 39.68 40.05 40.42 40.79 41.17 41.54 41.91
35.88 36.23 36.58 36.93 37.28 37.63 37.98 38.33 38.68 39.04
41 42 43 44 45 46 47 48 49 50
50.62 51.05 51.48 51.91 52.34 52.77 53.20 53.63 54.06 54.49
47.90 48.32 48.73 49.14 49.55 49.96 50.38 50.79 51.20 51.61
45.18 45.58 45.97 46.37 46.76 47.16 47.55 47.95 48.34 48.74
42.29 42.66 43.03 43.40 43.78 44.15 44.52 44.89 45.27 45.64
39.39 39.74 40.09 40.44 40.79 41.14 41.49 41 .84 42.19 42.54
51 52 53 54 55 56 57 58 59 60
54.92 55.35 55.78 56.21 56.64 57.07 57.50 57.93 58.36 58.79
52.03 52.44 52.85 53.26 53.68 54.09 54.50 54.91 55.32 55.74
49.13 49.53 49.92 50.32 50.71
46.01 46.39 46.76 47.13 47.50 47.88 48.25 48.62 49.00 49.37
42.89 43.25 43.60 43.95 44.30 44.65 45.00 45.35 45.70 46.05
11 12 13 I4 15 16 17
CLASS H-l CIRC. INCHES
51.11 51.50
51.89 52.29 52.68
CLASS CIRC. INCHES 31.10
1
120 FOOT CLASS 2 CIRC.
CLASS H-3 CIRC. 1 NCHES
INCHES
POLE-Con.
APPENDIX
415
B
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-l CIRC. INCHES
60.08 60.51 60.94 61.37 61.80 62.23 62.66 63.09
56.15 56.56 56.97 57.39 57.80 58.21 50.62 59.04 59.45 59.06
53.08 53.47 53.87 54.26 54.66 55.05 55.45 55.04 56.24 56.63
50.11 50.49 50.86 51 .23 51 .61 51.98 52.35 52.72 53.10
46.40 46.75 Lt7.11 47.46 47.81 48.16 48.51 48.06 49.21 49.56
71 72 73 74 75 76 77 78 79 80
63.52 63.95 64.30 64.81 65.24 65.67 66.10 66.53 66.96 67.39
60.27 60.68 61.10 61.51 61.92 62.33 62.75 63.16 63.57 63.90
57.03 57.42 57.02 58.21 58.61 59.00 59.39 59.79 60.18 60.50
53.47 53.04 54.21 54.59 54.96 55.33 55.71 56.08 56.45 56.02
49.91 50.26 50.61 50.96 51 .32 51 .67 52.02 52.37 52.72 53.07
81 02 83 84 85 86 87 80 89 90
67.02 60.25 60.60 69.11 69.54 69.96 70.39 70.82 71 .25 71.60
64.39 64.81 65.22 65.63 66.04 66.46 66.07 67.20 67.69 68.11
60.97 61 .37 61 .76 62.16 62.55 62.95 63.34 63.74 64.13 64.53
57.20 57.57 57.94 50.32 50.69 59.06 59.43 59.81 60.18 60.55
53.42 53.77 54.12 54.47 54.02 55.18 55.53 55.80 56.23 56.50
91 92 93 94 95 96 97 98 99
72.11 72.54 72.97 73.40 73.03 74.26 74.69 75.12 75.55 75.90
60.52 68.93 69.34 69.75 70.17 70.58 70.99 71.40 71.02 72.23
64.92 65.32 65.71 66.11 66.50 66.09 67.29 67.60 68.08 68.47
60.93 61.30 61 .67 62.04 62.42 62.79 63.16 63.54 63.91 64.28
56.93 57.20 57.63 57.90 50.33 50.60 59.04 59.39 59.74 60.09
76.41 76.04 77.27 77.70 70.13 70.56 70.99
72.64 73.05 73.46 73.80 74.29 74 .‘70 75.11
68.87 69.26 69.66 70.05 70.45 70.84 71 .24
64.65 65.03 65.40 65.77 66.14 66.52
60.44 60.79 61.14 61 .49 61 .84 62.19 62.54
62 63 64 65 66 67 68 69 70
100
101 102 103
104 105 106 107
59.22 59.65
-------------GROUND
108 109 110
79.42 79.85 80.28
LINE
75.53 75.94 76.35
(12
FEET,
0
71.63 72.03 72.42
CLASS CIRC. INCHES 49.74
66.09 INCHES)---------------
67.26 67.64 68.01
1
120 FOOT CLASS 2 CIRC. INCHES
CLASS H-2 CIRC. INCHES
61
CLASS H-3 CIRC. INCHES
62.89 63.25 63.60
POLE-con.
416
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red Cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
111 112 113 114 115 116 117 118 119 120
WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC. 1 NCHES 80.71
81.14 81.57 82.00 82.43 82.86 83.29 83.72 84.15 84.58
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
76 77 77 78 78 78 79 79 80 80
72.82 73.21 73.61 74.00 74.39 74.79 75.18 75.58 75.97 76.37
1
12_p FOOT POLE CLASS 2 CIRC.
INCHES
CLASS H-2 CIRC. INCHES
33.00 33.42 33.84 34.26 34.68 35.10 35.52 35.94 36.36 36.78 37.20
31 31 31 32 32 33 33 33 34 34 35
1I 12 13 14 15 16 17 18 19 20
37.62 38.04 38.46 38.88 39.30 39.72 40.14 40.56 40.98 41.40
21 22 23 24 25 26 27 28 29 30
41.82 42.24 42.66 43.08 43.50 43.92 44.34 44.76 45.18 45.61
00 40 81 21 61 02 42 82 23 63 03
CLASS H-l CIRC.
68 38 68 75 69 13 69 50 69 87 70 25 70 62 70 99 71 36 71 74
INCHES
CLASS CIRC. INCHES
63.95 64.30 64.65 65.00 65.35 65.70 66.05 66.40 66.75 67.11
1
CLASS CIRC.
INCHES
30.16 30.55 30.93 31 .32 31.71 32.09 32.48 32.87
27.00 27.37 27.73 28.10 28.46 28.83 29.19 29.56 29.92 30.29 30.66
25.00 25.34 25.69 26.03 26.38 26.72 27.07 27.41 27.76 28.10 28.45
35.44 35.84 36.24 36.65 37.05 37.45 37.86 38.26 38.66 39.07
33.25 33.64 34.03 34.41 34.80 35.18 35.57 35.96 36.34 36.73
31.02 31.39 31.75 32.12 32.48 32.85 33.21 33.58 33.95 34.31
28.79 29.13 29.48 29.82 30.17 30.51 30.86 31.20 31.55 31 .89
39.47 39.87 40.28 40.68 41 .08 41.49 41 .89 42.29 42.70 43.10
37.12 37.50
34.68 35.04 35.41 35.77 36.14 36.50 36.87 37.24 37.60 37.97
32.24 32.58 32.92 33.27 33.61 33.96 34.30 34.65 34.99 35.34
29.00 29.39 29.77
37.89
38.28 38.66 39.05 39.44 39.82 40.21 40.60
-Con.
INCHES
125 CLASS H-3 CIRC.
1 2 3 4 5 6 7 8 9 10
TOP
76 18 59 00 41 82 24 65 06 47
CLASS CIRC. 1 NCHES
FOOT
POLE
APPENDIX
B
417
Table B-4.-Pole circumferences for western red cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
CLASS H-3 CIRC.
CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
31 32 33 34 35 36 37 38 39 40
46.03 46.45 46.87 47.29 47.71 48.13 48.55 48.97 49.39 49.81
43.50 43.91 44.31 44.71 45.12 45.52 45.92 46.33 46.73 47.13
40.98 41.37 41 .I6
41 42 43 44 45 46 41 48 49 50
50.23 50.65 51.07 51.49 51.91 52.33 52.75 53.17 53.59 54.01
51 52 53 54 55 56 57 58 59 60
CLASS CIRC. INCHES
I
125 FOOT CLASS 2 CIRC.
INCHES
42.14 42.53 42.92 43.30 43.69 44.08 44.46
38.33 38.70 39.06 39.43 39.79 40.16 40.53 40.89 41 .26 41 .62
35.68 36.03 36.37 36.71 37.06 37.40 37.75 38.09 38.44 38.78
47.54 47.94 48.34 48.75 49.15 49.55 49.96 50.36 50.76 51.17
44.85 45.24 45.62 46.01 46.39 46.78 47.17 47.55 47.94 48.33
41.99 42.35 42.72 43.08 43.45 43.82 44.18 44.55 44.91 45.28
39.13 39.47 39.82 40.16 40.50 40.85 41.19 41.54 41.88 42.23
54.43 54.85 55.27 55.69 56.11 56.53 56.95 57.37 57.79 58.21
51.57 51.97 52.38 52.78 53.18 53.59 53.99 54.39 54.80 55.20
48.71 49.10 49.49 49.87 50.26 50.65 51.03 51 .42 51 .81 52.19
45.64 46.01 46.37 46.74 47.1 I 47.47 47.84 48.20 48.57 48.93
42.57 42.92 43.26 43.61 43.95 44.29 44.64 44.98 45.33 45.67
61 62 63 64 65 66 67 68 69 70
58.63 59.05 59.47 59.89 60.31 60.73 61.15 61 .57 61 .99 62.41
55.61 56.01 56.41 56.82 57.22 57.62 58.03 58.43 58.83 59.24
52.58 52.97 53.35 53.74 54.13 54.51 54.90 55.29 55.67 56.06
49.30 49.66 50.03 50.39 50.76 51.13 51.49 51.86 52.22 52.59
46.02 46.36 46.71 47.05 47.39 47.74 48.08 48.43 48.77 49.12
71 72 73 74 75 76 77 78 79 80
62.83 63.25 63.67 64.09 64.51 64.93 65.35 65.77 66.19 66.61
59.64 60.04 60.45 60.85 61 .25 61.66 62.06 62.46 62.87 63.27
56.45 56.83 57.22 57.61 57.99 58.38 58.76 59.15 59.>4 59.92
52.95 53.32 53.68 54.05 54.42 54.78 55.15 55.51 55.88 56.24
49.46 49.81 50.15 50.50 50.84 51.18 51.53 51 .87 52.22 52.56
POLE-con.
418
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red Cedar-Continued WESTERN
RED CEDAR DISTANCE FROM TOP FEET
125 CLASS H-2 CIRC.
CLASS H-l CIRC.
INCHES
INCHES
INCHES
81 82 83 84 85 86 87 88 89 90
67.03 67.45 67.87 68.29 68.71 69.13 69.55 69.97 70.39 70.82
63.67 64.08 64.48 64.88 65.29 65.69 66.09 66.50 66.90 67.30
60 60 61 61 61 62 62 63 63 63
31 70 08 47 86 24 63 02 40 79
56 56 57 57 58 58 58 59 59 59
61 97 34 71 07 44 80 17 53 90
52.91 53.25 53.60 53.94 54.29 54.63 54.97 55.32 55.66 56.01
91 92 93 94 95 96 97 98 99 100
71.24 71.66 72.08 72.50 72.92 73.34 73.76 74.18 74.60 75.02
67.71 68.11 68.51 68.92 69.32 69.72 70.13 70.53 70.93 71.34
64 64 64 65 65 66 66 66 67 67
18 56 95 34 72 11 50 88 27 66
60 60 61 61 61 62 62 62 63 63
26 63 00 36 73 09 46 82 19 55
56.35 56.70 57.04 5%. 39 57.73 58.08 58.42 58.76 59.11 59.45
101 102 103 104 105 106 107 108 109 110
75.44 75.86 76.28 76.70 77.12 77.54 77.96 78.38 78.80 79.22
71.74 72.14 72.55 72.95 73.35 73.76 74.16 74.56 74.97 75.37
68 68 68 69 69 69 70 70 71 71
04 43 82 20 59 97 36 75 13 52
63 64 64 65 65 65 66 66 66 67
92 29 65 02 38 75 11 48 84 21
59.80 60.14 60.49 60.83 61.18 61.52 61.87 62.21 62.55 62.90
111 112 -------113 114 115 116 117 118 119 120
79.64 80.06
75.77 76.18
71.91 72.29
121 122 123 124 125
-----GROUND
LINE
I12
FEET,
0
CLASS CIRC.
INCHES
67.58 67.94 INCHES)-----
80.48 80.90 81 .32 81.74 82.16 82.58 83.00 83.42
76.58 76.98 77.39 77.79 78.19 78.60 79.00 79.40
72.68 73.07 73.45 73.84 74.23 74.61 75.00 75.39
68.31 68.67 69.04 69.40 69.77 70.13 70.50 70.87
83.84 84.26 84.68 85.10 85.52
79.81 80.21 80.61 81.02 81 .42
75 77 76 16 76 55 76 93 77.32
71 23 71 60 71 96 72 33 72.69
1
FOOT
CLASS H-3 CIRC.
CLASS CIRC.
INCHES
63.24 63.59 -. _------_63.93 64.28 64.62 64.97 65.31 65.66 66.00 66.34 66.69 67.03 67.38 67.72 68.07
2
POLE-Con.
APPENDIX
Table B-S.-Permanent Maximum conductor tension Percent of rated strength
419
B
set values for Alumoweld strand
Permanent set mm/mm or in/in
Maximum conductor tension Percent of rated strength
Permanent set mm/mm 01 in/in
096 104 112 120 129
40 41 42 43 44
15 16 17 18 19
.ooo 138 .OOO 148 .ooo 159 .ooo 171 .OOO183
45 46 47 48 49
.OOO600 .OOO622 .OOO645 .ooo 668 .OOO691
:i
.OOO206 .ooo 195
22 23 24
.OOO217 .OOO228 .OOO240
50 51 52 53 54
.ooo 714 .ooo 737 .OOO760 .OOO783 .OOO807
25 26 27
.OOO253 .OOO267 .OOO282
ii
.ooo 298 .OOO 314
55 56 57 58 59
.OOO832 .OOO858 .OOO885 .ooo 912 .ooo 940
30
.ooo 330 :Y 62 63 64
.OOO968 .ooo 997 .001027 .001057 .001087
10 11 12 13 14
0.000 .ooo .ooo .ooo .ooo
i: 33 34
.ooo 347 .OOO 364 .OOO381 .OOO398
ii
.OOO415 .ooo 432
2 39
.ooo 449 .OOO 466 .OOO484
65
Initial modulus: Final modulus:
148.238 GPa (21.5 x 10” lb/in2) 158.580 GPa (23 x 10” lb/in2)
0.000 .ooo .ooo .ooo .ooo
502 521 540 559 5 79
zt
.OOl .OOl .OOl .OOl .OOl
118 149 181 214 248
70
.OOl 283
420
TRANSMISSION
Table B-6.-Permanent Tension
LINE DESIGN MANUAL
set values for steel strand
10 mm (3/8 in)
13 mm (l/2 in)
11 mm (7/16 in) HS’
EHS2
lb
HS’
EHS’
8 896 9 341 9 786 10 231 10 657
2 000 2 100 2 200 2 300 2 400
0.000 136 .OOO142 .ooo 147 .ooo 154 .OOO162
0.000 036 .ooo 037 .OOO038 .ooo 039 .ooo 040
0.000 091 .OOO096 .ooo 100 .ooo 105 .ooo 110
0.000 019 .ooo 020 .ooo 021 .ooo 022 .OOO023
0.000 060 .OOO063 .ooo 066 .ooo 070 .ooo 074
0.000 012 .ooo 013 .ooo 014 .ooo 015 .OOO016
11 11 12 12 12
121 565 010 455 900
2 500 2 600 2 700 2 800 2 900
.ooo 170 .ooo 179 .ooo 188 .OOO198 .OOO208
.ooo 041 .OOO042 .ooo 043 .ooo 045 .ooo 047
.ooo 115 .ooo 120 .OOO125 .ooo 130 .ooo 135
.OOO024 .OOO025 .OOO026 .OOO027 .OOO028
.OOO078 .OOO082 .ooo 086 .ooo 090 .ooo 094
.ooo 017 .OOO018 xl00 019 .ooo 020 .ooo 021
13 13 14 14 15
345 789 234 679 124
3 000 3 100 3 200 3 300 3 400
.ooo 219 .OOO230 .OOO242 .OOO253 .OOO264
.ooo 049 .OOO052 .ooo 055 .OOO058 .OOO061
.ooo 140 .ooo 145 .ooo 150 .ooo 155 .OOO 160
.ooo 029 .ooo 030 .ooo 031 .OOO032 .ooo 033
.OOO098 .ooo 102 .OOO 106 .ooo 111 .ooo 115
.ooo 022 .OOO023 .OOO024 .OOO025 .OOO026
15 16 16 16 17
569 014 458 903 348
3 500 3 600 3 700 3 800 3 900
.OOO275 .OOO287 .ooo 299 .ooo 311 .OOO323
,000 064 .ooo 068 .OOO072 .OOO076 .OOO081
.OOO165 .ooo 170 .ooo 175 .OOO180 .OOO 185
.ooo 034 .ooo 035 .OOO036 .ooo 037 .OOO038
.ooo 119 .OOO123 .OOO127 .ooo 131 .ooo 135
.OOO027 ,000 028 .ooo 029 .ooo 030 .ooo 031
17 18 18 19 19
793 238 682 127 572
4 000 4 100 4,200 4 300 4 400
.OOO336 .ooo 350 .OOO365 .OOO381 .OOO398
.ooo 086 .ooo 092 .OOO098 .ooo 104 .ooo 110
.ooo 190 .ooo 195 .ooo 202 .OOO208 .OOO214
.ooo .ooo .ooo .ooo .ooo
040 04 1 043 045 047
.ooo 139 .ooo 143 .OOO148 .OOO152 .OOO156
.OOO032 .ooo 033 .ooo 034 .ooo 035 .OOO036
20 20 20 21 21
017 462 907 351 796
4 4 4 4 4
500 600 700 800 900
.OOO416 .ooo 435 .ooo 455 .ooo 475 .OOO496
.ooo 117 .OOO124 .ooo 131 .OOO138 .OOO146
.ooo 220 .OOO227 .OOO234 .OOO242 .OOO250
.ooo 049 .ooo 05 1 .ooo 053 .OOO056 .OOO05 8
.OOO160 .OOO164 .ooo 168 .OOO172 .OOO176
.ooo 037 .OOO038 .ooo 039 .ooo 040 .ooo 041
22 22 23 23 24
241 686 131 575 020
5 000 5 100 5 200 5 300 5 400
.ooo 519 .ooo 544 .ooo 571 .OOO600 .OOO631
.ooo 154 .OOO162 .ooo 171 .OOO180 ‘:OOO189
.ooo 259 .OOO268 .OOO277 .OOO286 ,000 295
.OOO062 .OOO065 .ooo 068 .ooo 07 1 .ooo 074
.OOO180 .OOO185 .ooo 190 .ooo 195 .ooo 200
.OOO042 .ooo 043 .ooo 044 .ooo 045 .OOO046
24 24 25 25 26
465 910 355 800 244
5 5 5 5 5
500 600 700 800 900
.ooo 199 .ooo 209 .ooo 219 .OOO230 .OOO241
.ooo 305 .ooo 315 .OOO325 .ooo 335 .ooo 347
.ooo 077 .OOO080 .OOO083 .ooo 086 .OOO089
.OOO205 .ooo 210 .OOO215 .ooo 220 .OOO225
.ooo 047 .OOO048 .ooo 049 .ooo 050 .ooo 05 1
26 27 27 28 28
689 134 576 024 468
6 000 6 100 6 200 6 300 6 400
.OOO252 .OOO263 .OOO275 .OOO287 .ooo 299
.ooo .ooo ,000 .ooo .ooo
.ooo .ooo .ooo .ooo .ooo
092 095 099 103 107
.OOO230 .OOO236 .OOO243 .OOO250 .OOO257
.OOO052 .ooo 053 .ooo 054 .OOO056 .OOO058
28 29 29 30 30
913 358 803 248 693
6 500 6 600 6 700 6 800 6 900
.ooo 311 .OOO324 .ooo 337 .ooo 351 .OOO365
.ooo 417 .ooo 429 .ooo 441 .ooo 453 .OOO465
.ooo 111 .ooo 115 .ooo 119 .OOO123 .OOO128
.OOO264 .OOO271 .OOO278 .OOO285 .ooo 292
.OOO060 .OOO062 .OOO064 .OOO067 .ooo 070
359 371 382 393 405
EHS2
HS’
N
APPENDIX
Table B-6.-Permanent Tension
421
6
set values for steel strand-continued
10 mm (3/8 in) EHS2 HS'
N
lb
31 137 31 582 32 027 32 472 32 917
7 000 7 100 7 200 7 300 7 400
0.000 380 .OOO396 .ooo 413 .ooo 431 .ooo 45 1
33 362 33 806 34 251 34 696 35 141
7 500 7 600 7 700 7 800 7 900
.OOO472 .ooo 493 .ooo 515
35 586 36 030 36 475 36 920 37 365
11 mm (7/16 in) HS' EHS2 0.000 477 .OOO489 .ooo 501 .ooo 513
13 mm (l/2 in) HS' EHS2
0.000 133 ,000 139 ,000 146 .OOO152 .ooo 159
0.000 299 .OOO306 .ooo 313 .OOO320 .OOO327
0.000073 .ooo075 .OOO 078 .OOO 081 .OOO 083
.OOO165 .OOO172 .OOO178 .OOO185 .ooo 191
.ooo 334 .ooo 341 .OOO348 .ooo 355 .OOO363
.OOO085 .OOO087 .ooo 090 .ooo 093 .OOO096
8 000 8 100 8 200 8 300 8 400
.OOO198 .OOO204 .ooo 211 .OOO217 ,000 224
.ooo 371 .OOO378 .OOO387 .OOO396 .ooo 405
.ooo 099 .ooo 102 .ooo 105 .OOO108 .ooo 111
37 810 38 255 38 699 39 144 39 589
8 500 8 600 8 700 8 800 8 900
.OOO230 .OOO237 .OOO243 .ooo 249 .OOO256
.ooo 414 .OOO424 .ooo 434 .ooo 444 .ooo 454
.ooo 114 .OOO118 .ooo 122 .OOO126 .ooo 130
40 034 40 479 40 923 41 368 41 813
9 000 9 100 9 200 9 300 9 400
.OOO262 .OOO268 .OOO274 .OOO280 .OOO287
.OOO464 ,000 474 .OOO484 .ooo 495 .OOO506
.ooo 135 .ooo 139 .ooo 143 .ooo 147 .ooo 151
42 258 42 703 43 148 43 592 44 037
9 500 9 600 9 700 9 800 9 900
.ooo 295 .OOO306 .OOO318 ,000 329 .ooo 341
.ooo 155 .ooo 159 .OOO164 .ooo 168 .ooo 173
44 482 44 927 45 372 45 816 46 261
10 000 10 100 10 200 10 300 10 400
.OOO352 .OOO364 .ooo 375 .OOO387 .ooo 403
.OOO178 .OOO183 .ooo 188 .ooo 192 .ooo 197
46 706 47 151 47 596 48 041 48 485
10 500 10 600 10 700 10 800 10 900
.ooo 201 .OOO205 .ooo 209 .OOO213 .OOO218
48 930 49 375 49 820 50 265 50 709
11000 11 100 11 200 11300 11400
.OOO223 .OOO228 .OOO233 .OOO238 ,000 243
51 154 51599 52 044 52 489 52 934
11500 11 600 11700 11 800 11900
.OOO255 .OOO261 .OOO267 .OOO273
.ooo 249
422
TRANSMISSION
Table B-6.-Permanent Tension
10
N
lb
HS’
mm (3/8
LINE DESIGN MANUAL
set values for steel strand-Continued
in) EHS’
11 HS’
mm (7/16
in) F2-d
13 mm (l/2 in) HS’
EHS2
53 53 54 54 55
378 823 268 713 158
12 12 12 12 12
000 100 200 300 400
0.000 280 .OOO287 .ooo 295 .OOO302 .ooo 309
55 56 56 56 57
603 047 492 937 382
12 12 12 12 12
500 600 700 800 900
.ooo 317 .OOO325 .ooo 333 .ooo 341 .ooo 350
57 58 58 59 59
827 271 716 161 606
13 13 13 13 13
000 100 200 300 400
.ooo 359 .OOO368 .ooo 377 .OOO386 .OOO396
Ultimate
strength
48 040 N (10 800 lb)
68 500 N (15 400 lb)
64 500 N (14 500 lb)
92 520 N (20 800 lb)
83 625 N (18 800 lb)
119 655 N (26 900 lb)
t High strength. Initial modulus = 158.580 GPa (23 x lo6 lb/in2). Final modulus = 177.885 GPa (25.8 x lo6 lb/in2). ’ Extra-high strength. Initial modulus = 162.028 GPa (23.5 x lo6 lb/in2). Final modulus = 177.885 GPa (25.8 x 10 6 lb/in2).
APPENDIX
423
B
Table B- 7.-Flashover characteristics of suspension insulator strings and air gaps Impulse air gap,
in
mm
8
Impulse flashover (positive critical), kV
Number of insulator units’
Wet 6082 flashover,
Wet 60-Hz air gap,
kV
mm
in
130 170 215
254 305 406 508 660
10 12 16 20 26
762 889 991 1118 1245
;t 39 44 49
203 356 533 660 813
150 255 355 440 525
965 1092 1245 1397 1524
610 695 780 860 945
5 9 10
255 295 335 375 415
1025 1105 1185 1265 1345
11 12 13 14 15
455 490 525 565 600
1346 1473 1575 1676 1778
53 58
I; 88
1676 1803 1956 2083 2235
;3 104 110 115
2362 2515 2642 2794 2921
1425 1505 1585 1665 1745
16 17 18
630 660 690 720 750
1880 1981 2083 2184 2286
74 78 82 86 90
121 126 132 137 143
3073 3200 3353 3480 3632
1825 1905 1985 2065 2145
21 22 23
780 810 840 870 900
2388 2464 2565 2692 2794
94 97 101 106 110
148 154 159 165 171
3759 3912 4039 4191 4343
2225 2305 2385 2465 2550
26 27
930 960 990 1020 1050
2921 3023 3124 3251 3353
115 119 123 128 132
14 21 26 32 38 43 49 z; 66 71
6
:Fl
z
ii 30
ifi 70
1 Insulator units are 146 by 254 mm (5-3/4 by 10 in) or 146 by 267 mm (5-3/4 by 10-l/2 in).
424
TRANSMISSION
LINE DESIGN
Table B-8.-Flashover _
Ahgap
mm
in
Flashover 60-Hz wet, Pos. critical kV impulse, kV
MANUAL
values of air gaps AirgaP mm
in
Flashover 60-Hz wet, Pos. critical kV impulse, kV
25 51 76 102 127
1 2 3 4 5
38 60 75 91-95 106-114
1295 1321 1346 1372 1397
51 52 53 54 55
438 447 455 464 472
814 829 843 858 872
152 178 203 229 254
6 7 8 9 10
80
128-141 141-15’5 159-166 175-178 190
1422 1448 1473 1499 1524
56 57 58 59 60
481 489 498 506 515
887 901 916 930 945
279 305 330 356 381
11 12 13 14 15
89 98 107 116 125
207 224 241 258 275
1549 1575 1600 1626 1651
:: 63 64 65
523 532 540 549 557
960 975 990 1005 1020
406 432 457 483 508
16 17 18 19 20
134 143 152 161 170
290 305 320 335 350
1676 1702 1727 1753 1778
66 z’8 69 70
566 574 583 591 600
1035 1050 1065 1080 1095
533 559 584 610 635
21 22 23 24 25
178 187 195 204 212
365 381 396 412 427
1803 1829 1854 1880 1905
71 72 73 74 75
607 615 622 630 637
1109 1124 1138 1153 1167
660 686 711 737 762
26 27 28 29 30
221 229 238 246 255
443 458 474 489 505
1930 1956 1981 2007 2032
76 77 78 79 80
645 652 660 667 675
1182 1196 1211 1225 1240
787 813 838 864 889
31 32 33 34 35
264 273 282 291 300
519 534 548 563 577
2057 2083 2108 2134 2159
81 82 83 84 85
683 691 699 707 715
1254 1269 1283 1298 1312
914 940 965 991 1016
36 ;;: 39 40
309 318 327 336 345
592 606 621 635 650
2184 2210 2235 2261 2286
86 87 88 89 90
723 731 739 747 755
1327 1341 1356 1370 1385
1041 1067 1092 1118 1143
41 42 43 44 45
353 362 370 379 387
665 680 695 710 725
2311 2337 2362 2388 2413
91 92 93 ;:
763 771 779 787 795
1399 1414 1428 1443 1457
1168 1194 1219 1245 1270
46 47 48 49 50
396 404 413 421 430
740 755 770 785 800
2438 2464 2489 2515 2540
;4 98 99 100
803 811 819 827 835
1472 1486 1501 1515 1530
APPENDIX
Table B-8.-Flashover bc gap
Flashover 60-Hz wet, Pos. critical kV imuulse. kV
mm
in
2565 2591 2616 2642 2667
101 102 103 104 105
842 848 855 862 869
2692 2718 2743 2769 2794
106 107 108 109 110
2819 2845 2870 2896 2921
425
B
values of air gaps-Continued Air gap
Flashover 60-Hz wet, Pos. critical kV impulse, kV
mm
in
1544 1559 1573 1588 1602
3835 3861 3886 3912 3937
15: 152 153 154 155
1176 1182 1188 1194 1200
2269 2284 2298 2313 2327
875 882 889 896 902
1617 1631 1646 1660 1675
3962 3988 4013 4039 4064
156 157 158 159 160
1206 1212 1218 1224 1230
2342 2356 2371 2385 2400
111 112 113 114 115
909 916 923 929 936
1689 1704 1718 1733 1747
4089 4115 4140 4166 4191
161 162 163 164 165
1236 1242 1248 1254 1260
2414 2429 2443 2458 2472
2946 2972 2997 3023 3048
116 117 118 119 120
943 950 956 963 970
1762 1776 1791 1805 1820
4216 4242 4267 4293 4318
166 167 168 169 170
1266 1272 1278 1284 1290
2487 2501 2516 2530 2545
3073 3099 3124 3150 3175
121 122 123 124 125
977 984 991 998 1005
1834 1849 1863 1878 1892
4343 4369 4394 4420 4445
171 172 173 174 175
1296 1302 1308 1314 1320
2559 2574 2588 2603 2617
3200 3226 3251 3277 3302
126 127 128 129 130
1012 1019 1026 1033 1040
1907 1921 1936 1950 1965
4470 4496 4521 4547 4572
176 177 178 179 180
1326 1332 1338 1344 1350
2632 2646 2661 2675 2690
3327 3353 3378 3404 3429
131 132 133 134 135
1047 1054 1061 1068 1075
1979 1994 2008 2023 2037
4597 4623 4648 4674 4699
181 182 183 184 185
1355 1361 1366 1372 1377
2704 2719 2733 2748 2762
3454 3480 3505 3531 3556
136 137 138 139 140
1082 1089 1096 1103 1110
2052 2066 2081 2095 2110
4724 4750 4775 4801 4826
186 187 188 189 190
1383 1388 1394 1399 1405
2777 2791 2806 2820 2835
3581 3607 3632 3658 3683
141 142 143 144 145
1116 1122 1128 1134 1140
2124 2139 2153 2168 2182
4851 4877 4902 4928 4953
191 192 193 194 195
1410 1416 1421 1427 1432
2849 2864 2878 2893 2907
3708 3734 3759 3785 3810
146 147 148 149 150
1146 1152 1158 1164 1170
2197 2211 2226 2240 2255
4978 5004 5029 5055 5080
196 197 198 199 200
1438 1443 1449 1454 1460
2922 2936 2951 2965 2980
426
TRANSMISSION
Table B-9.-Relative Elevation m
LINE DESIGN
air density and barometric pressure Barometric mm
ft
pressure in
Relative air density at 25 OC at II OF
0 328.08 656.17 984.25 1312.34
1 2 3 4
0 000 000 000 000
760 733 107 681 656
29.92 28.86 21.82 26.81 25.84
1 .oo 0.96 .93 .90 .86
1.00 0.96 .93 .90 .86
1640.42 1968.>0 2296.59 2624.67 2952.16
5 6 I 8 9
000 000 000 000 000
632 609 581 564 544
24.89 23.98 23.10 22.22 21.40
.83 .80 .77 .I4 .I2
.83 .80 .I1 .I4 .I2
3280.84 3608.92 3937.01 4265.09 4593.18
10 000 11000 12 000 13 000 14 000
523 503 484 465 447
20.58 19.81 19.05 18.31 17.58
.69 .66 .64 .61 .59
.69 .66 .64 .61 .59
4921.26 5249.34
15 000 16 000
429 412
16.88 16.21
.56 .54
.56 .54
Table B- 1O.-Barometric Nonstandard air factor
MANUAL
Barometric mm of mercury
pressure inches of mercury r
Elevation m ft
pressure versus elevation Nonstandard air factor
Barometric mm of mercury
pressure inchesof mercury 1
m
Elevation ft
1 .oo 1.01 1.02 1.03 1.04
760 152 145 131 730
29.92 29.62 29.32 29.02 28.12
8: 171 256 343
0 280 561 841 1126
1.23 1.24 1.25 1.26 1.27
585 578 570 562 555
23.04 22.74 22.44 22.14 21.84
2154 2258 2362 2468 2580
1.05 1.06 1.07 1.08 1.09
722 114 101 699 692
28.42 28.12 27.83 27.53 21.23
432 521 609 691 788
1417 1709 1999 2287 2584
1.28 1.29 1.30 1.31 1.32
547 540 532 524 517
21.54 21.24 20.94 20.64 20.35
2691 2803 2914 3026 3139
8 9 9 9 10
1.10 1.11 1.12 1.13 1.14
684 676 669 661 654
26.93 26.63 26.33 26.03 25.13
878 971 1065 1159 1253
2881 3186 3495 3804 4112
1.33 1.34 1.35 1.36 1.37
509 502 494 486 419
20.05 19.75 19.45 19.15 18.85
3258 3317 3491 3617 3740
10 688 11079 11414 11 868 12 270
1.15 1.16 1.17 1.18 1.19
646 638 631 623 616
25.43 25.13 24.83 24.53 24.24
1347 1440 1534 1638 1739
4418 4724 5034 5375 5705
1.38 1.39 1.40 1.41 1.42
471 464 456 448 441
18.55 18.25 17.95 17.65 17.35
3864 3987 4113 4238 4369
12 13 13 13 14
1.20 1.21 1.22
608 600 593
23.94 23.64 23.34
1843 1946 2050
6045 6386 6727
1.43 1.44 1.45
433 426 418
17.05 16.76 16.46
4501 4630 4765
14 768 15 191 15 632
r Barometric
pressure = (29.92) (2 minus nonstandard
air factor).
7 068 7 409 I 750 8 098 8 463 829 195 561 921 299
676 082 493 904 333
APPENDIX
427
B
Table B-l 1.-Mass per unit volume and relative mass density of wood species used for poles 1 Green
Air-dry (15 percent moisture content)
Species k/m3 Bald cypress
lb/ft3
kg/m3
lb/ft3
Relative mass density 2
512
32
0.42
801
Douglas-fn Coast type Rocky Mountain
625 657
39 41
545 480
34 30
.45 .40
Hemlock, western
657
41
464
29
.38
Larch, western
801
50
609
38
.51
Pine Jack Loblolly 3 Lodgepole Longleaf’ Ponderosa Red Shortleaf
641 849 625 881 721 785 833
40 53 39 55 45 49 52
480 577 464 657 448 496 561
30 ;; 41 28 31 35
.40 .47 .38 .54 .38 .41 .46
Red cedar Eastern Western
593 432
37 27
529 368
33 23
.44 .31
Redwood
801
50
400
25
.38
Spruce (red, sitka, and white)
545
34
448
28
.37
White cedar Atlantic Northern
400 432
25 27
368 352
23 22
.31 .29
type
r From “Wood Handbook,” Agriculture.
Forest Products Laboratory,
U.S. Forest Service, Department
of
2 Based on volume when green, and mass when oven dry. 3 Part of southern yellow pine group.
Volume of pole Metric V= 2.616 x lo-‘h(d,’ + d,d2)m3 where, h = length of pole, m dr = diameter of pole at top, mm di = diameter of pole at bottom, mm
U.S. Customary V= 1.818 x lo-’ h(d12 +d,d2)ft3 where, h = length of pole, ft dr = diameter of pole at top,-in d2 = diameter of pole at bottom,
in
428
TRANSMISSION
LINE DESIGN MANUAL
Table B- 12 .-Conductor
temperature coefficients of expansion for normal sag-tension computations Temperature
coefficient
of expansion
Conductor
Stranding
InitialJOF x 1o-6
Final/OF x 1o-6
Initial/OC x lo+
Final/OC x 1o-6
EC aluminum Steel ACSR 1 ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR ACSR
all all
12.8
12.8 6.4
23.0 11.5 18.3
23.0
6/l l/l 18/l 24/i' 26/l 30/l 45/l 54/l
54119 84119
6.4 10.2
9.5 11.6 10.5
9.9 9.5 11.2 10.2 10.4 11.2
10.5 9.8 11.1 10.8 10.5 9.9 11.5 10.1 10.8 11.5
11.1 20.8
18.9 11.8
11.0 20.2 18.3 18.8 20.1
11.5 18.9 11.1 21.1 19.5 18.9 11.8 20.7
19.3 19.5 20.6
’ For ACSR conductors, the values shown apply only when the stress is borne by both the steel and aluminum strands.
APPENDIX
429
6
Table B-l 3.-Pressure on a projected area due to wind velocity Indicated velocity
Actual velocity Cylindrical
m/s 0.894 1.788 2.682 3.576 4.470
mi/h
: 6 8 10 12 14 16
m/s
mi/h
kPa
Pressure on projected area surface Flat surface lblft=
kPa
lb/ft2
0.894 1.743 2.593 3.442 4.291
2.0 3.9 5.8 7.7 9.6
0.000 48 .OOl 82 .004 03 .007 10 .01103
0.01 .c4 .08 .15 .23
0.0008 .0031 .0068 .0119 .0185
0.02 .06 .14 .25 .39
11.2 12.9 14.5 16.2 17.8
.015 01 .019 91 .025 17 .03141 .037 92
.31 .42 .53 .66 .79
.0252 .0335 .0423 .0528 .0637
.53 .70 .88 1.10 1.33
5.364 6.258 7.152 8.046 8.940
to8
5.006 5.766 6.482 7.241 7.951
11.175 13.410 15.645 17.880 20.115
25 30 35 40 45
9.745 11.488 13.231 14.930 16.584
21.8 25.7 29.6 33.4 37.1
.056 .079 .104 .133 .164
88 05 86 51 73
1.19 1.65 2.19 2.79 3.44
.0956 .1328 .1762 .2243 .2768
2.00 2.77 3.68 4.68 5.78
22.350 24.585 26.820 29.055 31.290
50 55 60 65 70
18.238 19.892 21.500 23.065 24.630
40.8 44.5 48.1 51.6 55.1
.199 ,237 .276 .318 .363
23 01 87 65 36
4.16 4.95 5.78 6.66 7.59
.3347 .3982 .4652 .5353 .6104
6.99 8.32 9.72 11.18 12.75
33.525 35.760 37.995 40.230 42.465
75 8”: 90 95
26.194 27.893 29.368 30.971 32.542
58.6 62.4 65.7 69.3 72.8
.410 .466 .516 .574 .634
97 01 60 76 30
8.58 9.73 10.79 12.01 13.25
.6904 .7829 .8679 .9656 1.0656
14.42 16.25 18.13 20.17 22.26
44.700 46.935 49.170 51.405 53.640
100 105 110 115 120
34.061 35.626 37.190 38.755 40.319
76.2 79.7 83.2 86.7 90.2
.694 .760 .828 .899 .973
90 22 43 62 70
14.52 15.88 17.31 18.79 20.34
1.1674 1.2772 1.3918 1.5114 1.6358
24.39 26.68 29.07 31.57 34.17
55.875 58.110 60.345 62.580 64.815
125 130 135 140 145
41.884 43.448 45.013 46.622 48.187
93.7 97.2 100.7 104.3 107.8
1.050 1.130 1.213 1.301 1.390
75 69 62 93 80
21.95 23.62 25.35 27.20 29.05
1.7653 1.8996 2.0389 2.1872 2.3365
36.87 39.68 42.59 45.69 48.81
67.050 71.520 75.990 80.460 84.930
150 160 170 180 190
49.751 52.835 55.964 59.093 62.178
111.3 118.2 125.2 132.2 139.1
1.482 1.672 1.875 2.091 2.315
55 05 96 59 68
30.97 34.93 39.19 43.69 48.37
2.4907 2.8090 3.1516 3.5139 3.8903
52.03 58.68 65.84 73.40 81.26
430
TRANSMISSION
Table B-14.-Equivalent
LINE DESIGN
MANUAL
metric data for standard electrical conductors U.S. customary
Code word
Stranding
Turkey swan sparrow Robin Raven
6/l 611 6/l 6/l 6/l
Quail Pigeon Penguin Partridge Ostrich
6/l 6/l 6/l
z;::
Size of conductor Thousand AWG circular No. mlls @mill 6 4 2
Diameter, in
0.198
Metric
Area, in2 Aluminum Total
13.29 21.16 33.61 42.39
10.11
53.48
15.48 24.11 39.23 49.48 62.39
0.1219 0.1538 0.1939
11.35
0.2436 0.2140
16.31 11.21
61.42 85.03 101.23 135.16 152.00
18.65 99.23 125.10 151.16 116.17
0.2642 0.3122 0.3122 0.3146 0.3146
0.3012 0.3630 0.3850 0.4232 0.4356
18.31 20.41
198.19 234.19 248.39
21.19
110.45 201.42 201.42 241.68 241.68
213.03 281.03
0.4938 0.5083 0.5368 0.5526 0.5643
23.22 23.55 24.21 24.54 24.82
282.00 282.00 306.58 306.58 322.26
318.58 321.93 346.32 356.52 364.06
322.26 331.14 402.84 402.84 483.42
314.11 381.55 468.45 430.11 516.84 546.06 559.81
0.0206 0.0328 0.0521 0.0651 0.0829
0.0240 0.0383 0.0608 0.0161 0.0961
266.8 300.0
0.441 0.502 0.563 0.642 0.680
0.1045 0.1318 0.1662 0.2095 0.2356
0.721 0.183 0.806 0.846 0.858
0.914
210 3/o 4/o
Area, mm2 Aluminum Total
5.03 6.35 8.03 9.02
0.250 0.316 0.355 0.398
If0
Diameter, mm
12.15
14.30
Linnet Ibis Lark Flicker Hawk
2617 26/l 30/l WI 26/l
336.4 391.5 397.5 411.0 411.0
Parakeet Dove Peacock Squab Rook
24/l 26/l 24/l 26/l 24/l
556.5 556.5 605.0 605.0 636.0
0.911
0.4311 0.4311 0.4152 0.4152 0.4955
Grosbeak Flamingo Drake Tern Rail
26/l 24/l 26/l 45/l 45/l
636.0 666.0 195.0 195.0 954.0
0.990 1.000 1.108 1.063 1.165
0.4995 0.5235 0.6244 0.6244 0.1493
0.5809 0.1261 0.6676 0.8011
25.15 25.40 28.14 21.00 29.59
C~dilld Ortolan Curlew Bluejay Finch
54/l
954.0 1033.5
30.38 30.81
1033.5 1113.0 1113.0
0.1493 0.8111 0.8117 0.8141 0.8141
0.8464 0.8618
2;: 45/l 54119
1.196 1.213 1.246 1.259 1.293
0.9169 0.9346 0.9849
31.65 31.98 32.84
483.42 523.68 523.68 563.93 563.93
45/l
1212.0 1212.0
1.345 1.382
1431.0 1431.0 1590.0
1.421 1.465 1.502
0.9990 0.9990 1.124 1.124
1.068 1.126 1.202 1.266 1.335
34.16 35.10 36.25 31.21 38.15
644.51 644.51 125.16 125.16 805.80
689.03 126.45 115.48 816.17
1590.0
1.545 1.602 1.762 1.131
1.401 1.512 1.831 1.116
39.24 40.69 44.15 44.12
805.80
901.93 1092.26 1098.06
901.74 915.48
Bittern Pheasant Bobolink Plover Lapwing Falcon ChUkiU
Bluebird Kiwi
54119 45/l 54119 45/l
54119 84119 84119 1217
1180.0 2156.0 2161.0
0.921
0.953 0.966
1.249 1.249 1.398 1.693 1.102
0.5914
19.89 21.49
591.55 602.91 635.42
861.29
1181.29 1145.80
APPENDIX
Table B-15.-Selected
B
431
U-metric conversions. From /20/ Area
To convert
from
To
acre (U.S. survey1 are barn circular mil (cmil) hectare (ha) section [U.S. survey] square centimeter (cm’ ) square chain square foot [International (ft2 1 square foot [U.S. survey] ut* 1 square inch (in* ) square kilometer (km* ) square mile [International (mi*) square mile [U.S. survey] (mi* ) square rod [U.S. survey] hd* 1 square yard (yd*) township l
Exact
square square square square square square square square square
meter meter meter meter meter meter meter meter meter
______ Multiply (m*) (m*) (m* ) (m*) (m* ) (m* (m* (m* (m*
f
4.046 * 1 .ooo l 1 .ooo 5.067 “I .ooo 2.589 *I .ooo * 1.562 “9.290
by
873
500 304
E+03 E+02 E- 28 E-10 E+04 E+06 E- 04 E- 04 E-02
341
E- 02
“6.451 600 1 .ooo 2.589 988
E- 04 E+OG E+06
075 998
square meter
(m*
square meter square meter square meter
(m* (m* (m2
square meter
(m*
2.589
998
E+06
square meter
(m*
2.529
295
E+Ol
square meter square meter
(m* (m*
8.361 9.323
274 993 --
E-01 E+07
9.290
l
conversion.
Force To convert
from ---
To
---
crinal dyne (dyn) kilogram force
(kgf)
kilopond kip ounce force pound force (Ibf) poundal (pdl) ton force Exact
l
I
newton newton newton newton newton newton newton newton newton
Multiply (N) (N) (N) (N) (N) (N) (N) (N) (N)
*1 .ooo “I ,000 “9.806 “9.806 4.448 2.780 4.448 1.382 8.896
by E-01 E- 05
650 650 222 139 222 550 444
E+03 E-01 E-01 E+03
conversion.
Force per length To convert
from
dyne per centimeter (dyn/cm) kilogram force per meter (W/m) pound per foot (Ib/ft) pound per inch (lb/in) l
Exact
conversion.
To
Multiolv
newton
per meter
(N/m)
* 1 .ooo
newton
per meter
(N/m)
“9.806
newton newton
per meter per meter
(N/m) (N/m)
1.459 1.751
bv E- 03
650 390 268
E+Ol E+O2
TRANSMISSION
432
LINE DESIGN MANUAL
Table B-15. -Selected X-metric conversions-Continued Density-Mass To convert
from
gram per cubic centimeter (g/cm3 1 gram per liter (g/L) megagram per cubic meter &b/m3 1 metric ton per cubic meter (t/m3 1 milligram per liter (mg/L) ounce per cubic inch (oz/in3 ) ounce per gallon (oz/gal) ounce per pint (oz/pt) pound per (Ib/in3) pound per (Ib/ft3) pound per (I b/yd3 1 pound per
cubic
inch
cubic foot cubic yard gallon
(lb/gall
slug per cubic foot (slug/ft3 ) ton [short] per cubic yard (ton/yd3 1 l
Exact
capacity
To kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter
per cubic (kg/m3 1 per cubic (kg/m3 1 per cubic (kg/m3 1 per cubic (kg/m3 l per cubic (kg/m3 1 per cubic (kg/m3 1 per cubic (kg/m3 1 per cubic (kg/m3 1 per cubic (kg/m3 l per cubic (kg/m’ 1 per cubic (kg/m3 1 per cubic (kg/m31 per cubic (kg/m3 1 per cubic (kg/m3 1
Multiply
by
“1 .ooo
E+03
*I .ooo *I .ooo
E+03
*I a00
E+03
*I .ooo
E-03
1.729 994
E+03
7.489
152
9.361
440
E-01
2.767
990
E+04
1.601
846
E+OI
5.932
764
E-01
1.198
264
E+02
5.153
788
E+02
1.186
553
E+03
conversion.
Time To convert
from
day [mean solar1 (dl day [sidereal] hour [mean solar] (hr) hour [sidereal] minute [mean solar] (min) minute [sidereal] month [mean calendar] (mol second [sidereal] week 17 days1 (wkl year [calendar] (al year [sidereal] l
Exact
conversion.
Multiply
To second second second second second second second second second second second
(s) (sl (s) (s) (s) (sl (sl (sl (sl (s) (sl
“8.640 8.616 “3.600 3.590 l 6.000 5.983 l 2.628 9.972 “6.048 l 3. I53 3.155
409 170 617 696 600 815
by E+O4 E+O4 E+03 E+03 E+Ol E+OI E+O6 E-01 E+05 E+07 E+07
APPENDIX
B
433
Table B- 15 .-Selected SI-metric conversions-Continued Length
-To convert
from
To
angstrom unit (A) astronomical unit (AU) caliber centimeter (cm) chain, surveyor’s chain, engineer’s chain, nautical fathom fermi [obsolete replaced by femtometer] femtometer (fm) foot [U.S. survey] (ft) foot [International] (ft) furlong (fur) inch (in) kilometer (km) league link, surveyor’s light year (Iv) microinch (pin) micrometer @m) micron [obsolete, replaced by micrometer] mil (mil) mile [International] (mi mile [Statute] (mi) mile [U.S. survey] (mi) nautical mile (nmi) parsec pica, printer’s point, printer’s rod spat vard (vd)
meter meter meter meter meter meter meter meter
(m) (m) (m) (m) (m) (m) (m) (m)
meter meter meter meter meter meter meter meter meter meter meter meter
(m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m)
l 1 .ooo * 1 .ooo 3.048 “3.048 2.011 l 2.540 l 1 .ooo 4.828 2.011 9.460 “2.540
meter meter meter meter meter meter meter meter meter meter meter meter
(m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m) (m)
“1.000 “2.540 * 1.609 1.609 1.609 l 1 .852 3.085 4.217 3.514 5.029 * 1.000
Exact conversion.
l
Linear
~
l
Exact conversion.
Multiply
density
l
1 .ooo
1.495979 “2.540 l 1 .ooo 2.011 680 “3.048 4.572 l 1.828 800
006 680
032 680 900
l 1.ooo
l 9.144
344 300 347 678 518 598 210
by E-10 E+l 1 E- 02 E-02 E+Ol E+Ol
E-15 E-15 E-01 E-01 E+02 E-02 E+03 E- 03 E-01 E+l5 E-08 E- 06 E-06 E- 05 E+03 E+03 E+03 E+03 E+16 E- 03 E- 04 E+12 E-01
TRANSMISSION
434
Table B-15.-Selected
LINE DESIGN MANUAL
N-metric
conversions-Continued
Load concentration To convert
from
To
gram per square centimeter
(s/cm2 1 megagram per square metet (Mg/m2 ] metric ton per square mete1 (t/m2 ] ounce per square inch (ozlin2) ounce per square foot (oz/ft2 ) ounce per square yard (o&d2 ] pound per square inch (I b/in2 ] pound per square foot (Ib/ft2) pound per square yard (I b&d2 ] ton per square foot (ton/ft2 ) Exact
l
kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter kilogram meter
Multiply
per square (kg/m’ ) per square (kg/m2 ) per square (kg/m’) per square (kg/m’ ] per square (kg/m21 per square (kg/m’ ) per square (kg/m2 ) per square (kg/m2 ) per square ( kg/m2 ) per square (kg/m2 )
by
*I .ooo
E+Ol
*I .ooo
E+03
*I .ooo
E+03
2.119
109
E-03
3.051
517
E-01
3.390
575
E- 02
7.030
696
E+02
4.882
428
5.424
920
E-01
9.071
a47
E+02
conversion.
Power To convert British thermal (Btu,,/h ] British thermal (Btu,,/h ] British thermal (Btul,/min) British thermal
unit [IT]
per hour
unit
per hour
[rc]
unit [tc]
per minute
unit
per second
[tcl
(Btu& calorie [tc] per minute (cal,,/min) calorie [tcl per second (calt,/s) erg per second (erg/s] foot-pound per hour (ftlb/h) foot-pound per minute (ftlb/min) foot-pound per second (ft*lb/s) horsepower (hp) horsepower [boiler] horsepower [electric] horsepower [metric] (hpM) horsepower [water] ton [refrigeration] l
Exact
conversion.
To
from
Multiolv
bv
watt
(W]
2.930
711
E-01
watt
(WI
2.928
751
E-01
watt
(WI
1.757
250
E+Ol
watt watt watt watt watt watt watt watt watt watt watt watt watt
(WI (WI (WI (W] (W] (W] (WI (WI (WI (WI (WI (WI (WI
1.054 6.973 l 4.lB4
350 333
E+03 E-02
l
1
.ooo
3.766 161 2.259 697 1.355 ala 7.456 999 9.809 500 “7.460 7.354 990 7.460 430 3.516 BOO
E-07 E- 04 E-02 E+02 E+03 E+02 E+O2 E+02 E+03
APPENDIX
B
435
Table B- 15 .-Selected S&metric conversions-Continued Mass To convert barrel of cement carat [metric] carat (kt) cental centner centner [metric] grain
from
[376
To
lb]
gram (9) hundredweight [gross or long] (cwt) hundredweight [net or short] (cwt) kilogram force-second squared per meter (kgfx* /m) kilotonne (kt) ounce [avoirdupois] (oz) ounce [troy/apothecary] (oz) megagram (Mg) metric grain metric ton (t) milligram (mg) pennyweight pound [avoirdupois] (lb) pound [troy/apothecary] quintal sack of cement 194 Ibs] slug ton [assay] ton [long] ton [ short] tonne (t) Exact
l
kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram
(kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg)
1.705 “2.000 2.591 4.535 4.535 1 .ooo 6.479 * 1 .ooo 5.080 4.535
kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram
(kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg) (kg)
“9.806 * 1 .ooo 2.834 3.110 * 1 .ooo “5.000 * 1 .ooo * 1 .ooo 1.555 4.535 3.732 “1.000 4.263 1.459 2.916 1 .016 9.071 “1.000
507 956 924 924 891 235 924
by E+02 E- 04 E-04 E+Ol E+Ol E+02a E- 05 E- 03 E+Ol E+Ol
650 952 348
174 924 417 767 390 667 047 847
E+06 E-02 E- 02 E+03 E-05 E+03 E- 06 E-03 E-01 E-01 E+02 E+Ol E+Ol E-02 E+03 E+02 E+03
conversion.
a European applies
Multiply
metric centner
to the centner
is 50 percent
of
this
value;
conversion
factor
presented
as used in the U.S.S.R
Frequency I
To convert
from
To
Multiply
by
hertz
(Hz)
2.777
778
f- 04
cycle per minute
(c/min)
hertz
(Hz)
1.666
667
E-02
cycle per second
(c/s)
hertz
(Hz)
* 1 .ooo
hertz
(Hz)
“1.000
cycle per hour
(c/h)
fresnel
l
Exact
conversion.
E+12
436
TRANSMISSION
Table B-15.4elected
LINE DESIGN MANUAL
S-metric conversions-Continued
Pressure-Stress To convert
from
atmosphere [standard] (atm) bar barye dyne per square centimeter (dyn/crr?) foot of water 14 “Cl gram force per square centimeter (gf/cm’ ) inch of mercury [O “Cl inch of mercury [ I6 “Cl inch of water [4 “C] inch of water [ I6 “C] kilogram force per square meter (kgf/m2 ) kilogram force per square centimeter (kgf/cm’)
To
Multiply
by
Pascal (Pa) Pascal (Pa) Pascal (Pa)
1.013 250 “1.000 *I .ooo
E+05 E+05 E-01
Pascal (Pa) Pascal (Pa)
“I .ooo 2.988 980
E-01 E+03
Pascal Pascal Pascal Pascal Pascal
(Pa) (Pa) (Pa) (Pa) (Pa)
“9.806 3.386 3.376 2.490 2.488
650 380 850 817 400
E+Ol E+03 E+03 E+02 E+02
Pascal (Pa)
l 9.806
650
Pascal (Pa)
“9.806
650
E+04
kip per square inch (kip/in2) kip per square foot (kip/ft2 ) megapascal (MPa) meter-head [meter of water, 4 “C] millibar (mbar) millimeter of mercury [0 “C]
Pascal Pascal Pascal Pascal Pascal Pascal
6.894 757 4.788 026 *I .ooo 9.806 365 “1.000 I .333 220
E+06 E+04 E+06 E+03 E+02 E+02
(mm(W) millimeter
Pascal (Pa)
of water
[4 “C]
(Pa) (Pa) (Pa) (Pa) (Pa) (Pa)
9.806
365
hm(H20)) newton per square meter (N/m2 ) pound per square foot (Ib/ft2 ) pound per square inch (lb/in2 ) poundal per square foot (pdl/ft2 ) tor torr (mm(Hg))
l
Exact
conversion.
Pascal Pascal Pascal Pascal Pascal Pascal
(Pa) (Pa) (Pa) (Pa) (Pa) (Pa)
“I .ooo 4.788 026 6.894 757 I .488 164 * 1 .ooo I .333 220
E+OI E+03
E+02
APPENDIX
437
B
Table B-15. -Selected SI-metric conversions--Continued
Tempera
we
Scale values Degrees Celsius “C
Degrees Fahrenheit OF
-
x “c=
X OF=
$(x-
X K=
x-
x “R=
; (x-
X Or=
x + 273.15
:x+32
-
32)
273.15
fx-
491.67)
fx
+ 491.67
459.67
%x+32
Degrees Reaumur Or
%X
x + 459.67
t (x + 459.67)
$(x-
;(x
;X
x - 459.67
$X
Degrees Rankine “R
Kelvins K
-
fX
$x
+ 273.15
$x
$(x-
K
OF
OR
Or
l”C=l
K=
1
9 5
4 5
IoF=
“R=
5 9
1
4 s
5 4
9 4
1 Or=
- 273.15)
491.67)
-
+491.67
Intervals: “C
32)
1
TRANSMISSION
438
LINE DESIGN MANUAL
Table B- 15 .-Selected S-metric conversions-Continued Velocity-Speed To convert Angular
from
revolution (r/min) revolution (r/s)
per minute per second
by
radian per second (rad/s) radian per second (rad/s) radian per second (rad/s)
1.745
329
E-02
1.047
198
E-01
6.283
185
(L/T):
foot per second (ft/s) foot per minute (ft/min) foot per hour (ft/h) foot per day (ft/d) foot per year (ft/a) inch per second (in/s) inch per hour (in/h) kilometer per hour (km/h knot [nautical miles per hour1 (kn) mile per hour (mi/h) meter per hour (m/h) meter per year (m/a) millimeter per second (mm/s) speed of light (c) l
Multiply
(e/r):
degree per second
Linear
To
Exact
meter meter meter meter meter meter meter meter
per per per per per per per per
second second second second second second second second
(m/s) (m/s) (m/s) (m/s) (m/s) (m/s) (m/s) (m/s)
“3.048 “5.080 8.466 3.527 9.695 “2.540 7.055 2.777
meter meter meter meter
per per per per
second second second second
(m/s) (m/s) (m/s) (m/s)
5.144 4.470 2.777 3.170
meter meter
per second per second
(m/s) (m/s)
*I .ooo 2.997
556 778
E-01 E- 03 E-05 E- 06 E- 09 E-02 E-06 E-01
444 400 778 979
E-01 E-01 E- 04 E-08
925
E-03 E+08
667 778 890
conversion.
Torque-Bending To convert
from
dyne centimeter (dyncm) kilogram force meter (kgfem) kip-foot (kip.ft) ounce inch (oz.in)aS b pound-foot (Ib*ft) aSb pound-inch (Ib*in)aS b
moment Multiply
To newton
meter
(N-m)
l 1.ooo
newton newton newton newton newton
meter meter meter meter meter
(N.m) (N*m) (N*m) (N-m) (N-m)
“9.806 650 1.355 818 7.061 552 1.355 818 1.129848
l Exact conversion. iThe addition of the force designator Most USBR engipeers reverse the equivalent terminology.
may be desirable, torque units, for
e.g., Ibf-ft. example, foot-pound;
by E- 07
E+02 E- 03 E-01
this
is
APPENDIX
B
439
Table B- 15 .-Selected S&metric conversions-Continued
Volume-Capacity To convert
from
To
Multiply
acre-foot [U.S. survey1 (acre-ft) barrel [oil] (bbl) barrel [water] (bbl) board foot [l ft x 1 ft x 1 in]
cubic cubic cubic
meter meter meter
(m3) (m3) (m3 1
(fbm) bushel [U.S., dry] (bu) cord cubic centimeter (cm3) cubic decimeter (dm3) cubic dekameter (dam3 ) cubic foot (ft3) cubic inch (in3 ) cubic kilometer (km3) cubic mile (mi3) cubic millimeter (mm3) cubic yard (yd3 )
cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic cubic
meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter meter
(m3) (m3 (m3) (m3 (m3) (m3) (m3) (m3 (m3) (m3 (m3) (m3 (m3 (m3 (m3 (m3 (m3 (m3) (m3 (m3 (m3) (m3 (m3 (m3 (m3) (m3) (m3 (m3) (m3) (m3 (m3 (m3
cubic cubic cubic cubic cubic
cup firkin fluid dram fluid ounce [U.S.] (fl.oz.) gallon Ilmperiall gallon [U.S., dry1 gallon [U.S., liquid] (gal) gill [U.S.] kiloliter (kL) liter (L) megaliter (ML) milliliter (mL) peck [U.S.] pint [U.S., dry1 pint [U.S., liquid] quart [U.S., dry1 quart [U.S., liquid] stere [timber] tablespoon teaspoon ton [sea freight or shipping capacity] ton [internal cap. of ships or register ton] ton [vol. of oil] ton [timber] tun [U.S., liquid] l
Exact conversion.
1 1
1.233 1.589 1.192
489 873 405
E+O3 E-01 E-01
2.359 737 3.523 907 3.624 556 * 1 .ooo
E-03 E- 02
549 737 871 691 353 060 884 412 941
E- 06 E-03 E+03 E-02 E- 05 E+09 E+09 E-09 E-01 E- 03 E-02 E- 06 E- 05 E-03 E- 03 E- 03 E-04
l 1.ooo ) ) ) ) ) 1 ) ) 1 )
by
*1 .ooo 2.831 1.638 *1 .ooo 4.168 l 1 .ooo 7.645 2.359 3.406 3.696 2.957 4.546 4.404 3.785 1.182 “1.000 “1 .ooo
685 706 182
768 105 765 221 529
) ) )
*1 .ooo 8.809 5.506 4.731 1.101 9.463 *1 .ooo 1.478 4.928
E-03 E+03 E-06 E- 03 E-04 E-04 E-03 E-04
676 922
E-05 E-06
meter
(m3 1
1.132
674
meter meter meter meter
(m3) (m3 1 (m3) (m3 1
2.831 6.700 1.415 9.539
685 179 842 238
1 ) )
)
l 1.ooo
E-O!
<
C
CONDUCTORANDOVERHEADGROUNDWIREDATATABLES The
tables
in this
and stress-strain and based on information and
Wire
Initial loading
Co.
(U.S.
appendix creep from Steel)
have
catalog
modulus values shown curve between the point
at 50 percent
of the
ultimate
been
prepared
for
ACSR
curves prepared by the Aluminum Copperweld Steel Co., and the
conductor
based
upon
conductor
data
Association. The Alumoweld data are steel data are based on American Steel
information. in the where
tables were determined the entire conductor
from starts
the
average the
to share
slope load
of the initial the point
and
strength.
Permanent set values were determined at 50 percent of the conductor ultimate strength as it represents the maximum stress permitted under full load conditions. Creep values were determined at 18 percent of the ultimate strength of the conductor because ma no-load tension on a conductor. this would be about equal to the 15.5 ‘C (60 OF) f 1
441
442
TRANSMISSION
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final modulus values (metric)
103.42 110.32 117.21 124.11 131 .oo 137.90 144.79 151.69 158.58 165.48 172.37 179.26 186.16 193.05 199.95 206.84
.00070146
.00123350
’ Calculated at 18 percent of ultimate strength.
APPENDIX
443
C
Table C-l .-Permanent set, creep, and initial and final modulus values (metric&Continued DS AND
Code word
Size, mm2
WANATE PARATE
21.13 33.64
1 STFFI
1O-year creep’
S
Tension’ , N
I
1
1.00048932 .00047536
1
1889.6
AND
Final modulus, GPa 87.012 87.012
L
Stress, MPa 6.89 13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58 165.48 172.37 i79.26 186.16 193.05 199.95 206.84 213.74 220.63 227.53 234.42
Permanent set .00002236 .00003009 .00003766 .00004518 .00005282 .00006070 .00006896 .00007776 .00008723
.00009751 .00010874 .00012106 .00013462 .00014955 .00016600 .00018410 .00020401 to0022585 .00024977 .00027591 .00030442 .00033543 .00036908 .00040552 .00044488 .00048731 .00053295
.00058194 .00063441 .00069052 .00075040
.00081419 .00088204 .00095408
Calculatedat 18 percentof ultimate strength.
Initial modulus, GPa 79.271 79.351 79.389 79.383 79.335 79.244 79.112 78.939 78.726 78.474 78.186 77.862 77.505 77.115 76.696 76.249 75.776 75.280 74.761 74.223 73.666 73.094 72.507
71.909 71.299 70.680 70.054
69.421 68.784 68.143 67.500 66.856 66.211
444
TRANSMISSION
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final modulus values (metric&Continued
r
STRANDS
Code word
Size, mm2 135.19 170.45 201.41 241.70
‘AXW I NG IERL IN HICKADEE ‘ELICAN SPREY INGBIRD
287.05 322.26
Stress, MPa 6.89 13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58 165.48
’ Calculated at 18 &ent
AN
1O-year creep’
Tension’, N
.00058691 .00058702 .00056698 .00056019 .00055702 .00055886
5508.7 6949.9 7958.7 9448.0 10969.3 12570.6
Permanent set .00007997 .00011682 .00015029 .00018134 .00021094 .00024002 .00026954 .00030046 .00033374 .00037032 .00041116 .00045722 .00050944 .00056879 .00063621 .00071266 .00079909 .00089647 .00100573 .00112784 .00126375 .00141442
.00158079 .00176383
of ultimate
1
1 STE!=l S
strength.
Final modulus, GPa 68.031 68.031 68.031 68.031 68.031 68.031
Initial modulus, GPa 49.893 50.516 51.036 51.441 51.725 51.885 51.919 51.831 51.627 51.313 50.900 50.400 49.824 49.183 48.489 47.754 46.985 46.194 45.387 44.570 43.751 42.933 42.120
APPENDIX
C
445
Table C-l .-Permanent set, creep, and initial and final modulus values (metric&Continued
r
7 STFFI
Code word
Size, mm2
7ANT I CKER ~RAKEET IACOCK IOK -AM I NGO JCKOO
201.41 241.70 281 .98 306.81 322.26 337.46 402.83
1O-year creep’
Tension’, N 11689.9 13771.6 15853.4 17294.6 17614.9 18976.0 22338.9
.00050955 .00049932 .00049191 .00049382 .00047682 .00049160 .0004845a
S’ LBANDS
Final modulus, GPa 72.602 72.602 72.602 72.602 72.602 72.602 72.602
L
Stress, MPa 6.89 13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo 137.90 144.79 151.69 158.58 165.48 172.37 i79.26 186.16 193.05 199.95
’ Calculated
at 18 percent
Permanent set .0000444 I .00007736 ,000 I 0696 .00013378 .OOOI 5840 .00018138 .000203 30 .00022474 .00024627 .00026846 .00029 I 89 .00031713 .00034475 .00037532 .00040943 .ooO44764 .00049053 .00053867 .00059263 .00065299 ,00072033 .0007952 I .0008782 i .00096990 . 00 I 07086 .OOl 18166 .00130287 .00143507 .00157883
of ultimate
strength.
Initial modulus, GPa 53 .900 54.625 55.288 55.880 56.395 56.827 57.170 57.422 57.581 57 646 57.620 57.506 57.307 57 .029 56.678 56 .262 55.787 55.259 54.687 54.077 53.435 52.767 52.079 51.375 50.660 49.939 49.213 48.487
TRANSMISSION
446
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final modulus values (metric&Continued
r
STRANDSAM2 Code word 4RTR I DGE STR I CH I NNET 31s 4WK IJVE IJUAB ?OSBEAK TARL I NG ?AKE
Size, mm2 135.19 152.01 170.45 201.41 241.70 281.98 306.55 322.26 362.54 402.83
1O-year creep’
10168.6
11289.5 13051 .o 15613.2 18095.3 19456.4 20177.0 22739.2 25221.3
-1
L
6.89 13.79
.00007464 .00010656
206.84
.00013679 .00016568 .00019357 .00022078 .00024767 .00027456 .00030180 .00032973
.00035868 .00038900 .00042101 .00045507
.00049150 .00053065 .00057285 .00061844 .00066777 .00072116 .00077897 .00084152 .00090915 .00098221 .00106103 .00114595 .00123731 .00133544 .00144069 .00155340
’ Calculated at 18 Ijercent of ultimate
74.188 74.188 74.188 74.188 74.188 74.188 74.188 74.188 74.188 74.188
9047.6
.00050213 .00050168 .00049623 .00048422 .00048255 .00047888 .00047298 .00046581 .00046675 .00046583
Permanent set
137.90 144.79 151.69 158.58 165.48 172.37 i79.26 186.16 193.05 199.95
Final modulus, GPa
Tension’ N
Stress, MPa
20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
ANDS
strength.
L
Initial modulus, GPa 55.223 55.600 55.932 56.215 56.449 56.631 56.761 56.837 56.860 56.831 56.750 56.619 56.440 56.216 55.948 55.640 55.295 54.915 54.505 54.067 53.604
53.119 52.615 52.096 51.562 51.018 50.465 49.905 49.340
1
APPENDIX
C
447
Table C-l .-Permanent set, creep, and initial and final inodulus values (metric&-Continued 30
AI MUJ.M
Size, mm*
Code word RIOLE ARK EN AGLE
170.45 201.41 241.70
281.98
Stress, MPa 6.89
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58 165.48 172.37 i79.26 186.16 193.05 199.95 206.84 213.74
STRANDS
AND
1O-year creep’
7 STFFL
SIjXANDS
Tension’ , N
.00041719 .00041419 .00040398 .00040442
Permanent set .00004619 .00006826 .00008940 .00010977 .00012958 .00014901 .00016823 .00018745 .00020683 .00022657 .00024684 .00026785 .00028976 .00031276 .00033705 .00036280 .00039020 .00041943 .00045068 .00048413 .00051997 .00055839 .00059956 .00064367 .00069091 .00074147 .00079552 .00085325 .00091485 .00098050 .00105038
’ Calculated at 18 percent of ultimate strength.
13851.7 16253.7 19056.1 22258.8
Final modulus, GPa 78.187 78.187 78.187 78.187
Initial modulus, GPa 62.536 62.804 63.040 63.241 63.407 63.538 63.633 63.691 63.713 63.698 63.648 63.563 63.444 63.291 63.106 62.890 62.645 62.372 62.072 61.748 61.401 61.033 60.645 60.240 59.818 59.382 58.933 58.472 58.001 57.522
448
TRANSMISSION
LINE DESIGN MANUAL
Table C-l .-Permanent
set, creep, and initial and final modulus values (metric&Continued IlWNDs AND
4
Code word T ERN RUDDY RAIL 0 RTOLAN B LUEJAY B UNT I NG B I TTERN D I PPER BOBOL I NK NNUTHATCH L APWI NG
1O-year creep’
Size, mm2 402.83 456.03 483.39 523.67 563.96 604.24 644.52 684.81 725.09 765.37 805.65
00057764 00056147 00056215 00055394 00055325 00055490 00055412 00055343 00055282 00054804 00054776
Tension’ N
L
Stress, MPa
Permanent set
6.89
.00007248 .00012961 .00017972 ,00022409 .00026402 .00030081 .00033576 .00037017 .00040532 .00044251 .00048305 .00052822 .00057932 .00063765 .00070450 .00078118 .00086897 .00096917 .00108308 .00121199 .00135721 .00152002 .00170172
17694.9 19536.5 20737.5 22178.7 23860.1 25621.6 27303.1 28984.5 30665.9 32107.1 33788.5
- -
-
Final modulus, GPa 64.466 64.466 64.466 64.466 64.466 64.466 64.466 64.466 64.466 64.466 64.466
Initial modulus, GPa -
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58
Calculated at 18percentofultimate
strength.
42.020 42.961 43.828 44.606 45.278 45.830 46.251 46.534 46.679 46.686 46.562 46.317 45.963 45.513 44.982 44.384 43.731 43.036 42.309 41.561 40.799 40.030
APPENDIX
C
449
Table C-l .-Permanent
set, creep, and initial and final modulus values (metric&Continued
Code word
Size,
mm* 402.83 456.03 483.39 523.67
ONDOR ANARY ARD I NAL URLEW
I;_; I 1O-year creep’
00046434 00046390 00046369 00046347
Tension’ , N 22579.1 25541.6 27062.8 29304.7
67.114 67.114 67.114 67.114
-
Stress, MPa 6.89
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58 165.48 172.37 179.26
Permanent set 00005753 00010350 00014543 00018402 00021994 00025388 00028652 00031856 00035066 00038352 00041782 00045425 00049348 00053621 00058311 00063487 00069218 00075571 00082615 00090420 00099052 00108580 00119074 00130600 00143228 00157026
Calculated at 18 percent of ultimate
strength.
Final modulus, GPa
1
Initial modulus, GPa 46.368 47.014 47.606 48.136 48.598 48.987 49.297 49.527 49.674 49.738 49.721 49.624 49.453 49.212 48.907 48.543 48.126 47.665 47.163 46.629 46.066 45.482 44.879 44.264 43.639
450
TRANSMISSION
LINE DESIGN MANUAL
Table C-l .-Permanent set, creep, and initial and final modulus values (metric)-Continued r
9 STFFl
Code word
Size, mm2 563.96 604.24 644.52 684.81 725.09 765.37 805.65
I NCH RACKLE HEASANT ARTIN LOVER ARROT ALCON
1O-year creep’ 00050022 00050043 0004877 1 00048760 00048851 00048704 00048789
S
Tension’ , N 31306.4 33548.3 34909.5 37071.3 39313.2 41394.9 43636.8
Final modulus, GPa 69.706 69.706 69.706 69.706 69.706 69.706 69.706
Stress, MPa 6.89
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131 .oo
137.90 144.79 151.69 158.58 165.48 172.37 179.26 186.16
Permanent set
Initial modulus, GPa
.00002892
.00006013 .00008941 .00011729 .00014431 .00017099 .00019788 .00022551 .00025441 .00028512 .00031817 .00035409 .00039342 .00043669 .00048444 .00053719 .00059549 .00065987 .00073086 .00080900 .00089482 .00098885 .00109163 .00120369 .00132557 .00145779 .00160090
’ Calculated at 18 percent of ultimate
strength.
52.987
53.386 53.717 53.976 54.159 54.267 54.299 54.254 54.136 53.948 53.692 53.374 52.999 52.571 52.097 51.582 51.031 50.451 49.845 49.219 48.577 47.923 47.260 46.592 45.922 45.251
APPENDIX
451
C
Table C-l .-Permanent set, creep, and initial and final modulus values (metric&-Continued 9 STFFL S
Size, mm2
Code word
901.93 092.45 552.53
HUCKAR LUEBIRD
1O-year creep’
Tension’, N
00071310 00069677 00069663
40834.5 48280.8 68617.9
LANDS Final modulus, GPa 66.811 66.811 66.811
L Stress, MPa 6.89
13.79 20.68 27.58 34.47 41.37 48.26 55.16 62.05 68.95 75.84 82.74 89.63 96.53 103.42 110.32 117.21 124.11 131.00
137.90 144.79 151.69 158.58 165.48
Initial modulus, GPa
Permanent set 0.00000000
.00003350 .00006531 .00009538 .00012455 .00015366 .00018356 .00021507 .00024904 .00028631 .00032772 .00037411 .00042632 .00048519 .00055156 .00062627 .00071016 .00080407 .00090885 .00102532 .00115433 .00129672 .00145333 .00162500
50.111
50.590 50.972 51.251 51.423 51.487 51.443 51.296 51.050 50.713 50.293 49.799 49.241 48.628 47.970 47.275 46.551 45.807 45.048 44.280 43.509 42.737 41.970
1t Calculated at 18 percent of .ultimate strength.
TRANSMISSION
452
LINE DESIGN MANUAL
Table C-2.-Permanent set, creep, and initial and final modulus values (U.S. customary)
r
1
1 STFFL S
L
Code word TURKEY SWAN SPARROW ROBIN RAVEN QUAIL PI GEON PENGU I N
Size, AWG 01 kcmil 6 4 2 1 l/O 2/o 3/o 4/o
1O-year creep’
214. 335. 513. 639. 788. 956. 1192. 1503.
.00046458 .00045465 .00043810 .00043228 .00042251 .00040529 .00040014 .00040034
L
Stress, lb/in’
Final modulus, lb/in2
Tension’ , lb
Permanent set
11460000. 11460000. 11460000. 11460000. 11460000. 11460000. 11460000. 11460000.
-
1 Initial modulus, lb/in2
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000. 30000.
.00005034 .00006347 .00007589 .00008791 .00009981 .00011190 .00012448 .00013784 .00015228 .00016810 .00018560 .00020507 .00022682 .00025114 .00027834 .00030870 .00034253 .00038012 .00042178 .00046780 .00051848 .00057412 .00063501 .00070146 .00077376 .00085221 .00093712 .00102877 .00112746 .00123350
L
’ Calculated at 18 percent of ultimate
strength.
9960963.
9996316. 10021891. 10037502. 10043072. 10038633. 10024321. 10000376. 9967127. 9924989. 9874445. 9816035. 9750342. 9677978. 9599568. 9515745. 9427132. 9334340. 9237955. 9138534. 9036604. 8932655. 8827140. 8720474. 8613037. 8505170. 8397179. 8289339. 8181890.
APPENDIX
453
C
Table C-2.-Permanent set, creep, and initial and final modulus values (U.S. customary&Continued
.00007776 .00009751 .00010874
.00014955 .00016600 .00020401
.00036908 .00044488
t Calculated at 18 percent of ultimate
strength.
11497226. 11508882. 11514317. 11513518. 11506512. 11493358. 11474154. 11449026. 11418134. 11381666. 11339833. 11292869. 11241027. 11184574. 11123789. 11058958. 10990372. 10918326. 10843111. 10765016. 10684325. 10601313. 10516247. 10429384.
454
TRANSMISSION
LINE DESIGN
MANUAL
Table C-2.-Permanent
set, creep, and initial and final modulus values (U.S. customary)-Continued 1
1 STFFL S
Code word
Size, AWG or kcmil
WAXWI NG MERL IN CHICKADEE PEL I CAN OSPREY KINGBIRD
266.8 336.4 397.5 477.0 566.5 636.0
Stress, lb/in2 1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000.
1O-year creep’ .00058691 .00058702 .00056698 .00056019 .00055702 .00055886
Permanent set .00007997 .00011682 .00015029 .00018134 .00021094 .00024002 .00026954 .00030046 .00033374 .00037032 .00041116 .00045722 .00050944 .00056879 .00063621 .00071266 .00079909 .00089647 .00100573 .00112784 .00126375 .00141442 .00158079 .00176383
Calculated at 18 percent of ultimate
lb
Final modulus, lb/in2
1238. 1562. 1789. 2124. 2466. 2826.
9867000. 9867000. 9867000. 9867000. 9867000. 9867000.
Tension’,
strength.
Initial modulus, lb/in2 7236257, 7326749. 7402066. 7460835. 7502070. 7525224. 7530226. 7517466. 7487760. 7442273. 7382441. 7309875. 7226273. 7133343. 7032742. 6926027. 6814624. 6699814. 6582724. 6464328. 6345457. 6226811. 6108966.
APPENDIX
C
455
Table C-2.-Permanent set, creep, and initial and .final modulus values (U.S. customary)-Continued TRANDS
Size AWG or kcmil
Code word
AJYR
7
1O-year creep’
STFFL
S‘
ANDS
Final modulus, lb/in*
Tension’, lb
~~ IRANT L I CKER IARAKEET ‘EACOCK !OOK LAM I NGO :UCKOO
397.5 477.0 556.5 605.5 636.0 666.0 795.0
.00050955 .00049932 .00049191 .00049302 .00047682 .00049160 .00048458
1 Stress, lb/in2
Permanent set
1000.
.0000444 .00007736 .00010696 .00013378 .00015840 .00018138 .00020330 .00022474
2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000.
10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000.
19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000.
L
Initial modulus, lb/in2
I
.00024627 .00026846 .00029 I89 .00031713 00034475 : 00037532 .00040943 .00044764 .00049053 00053867 : 00059263 .00065299 .00072033 .0007952 I .0008782 I .00096990 .00107086 .OOll8166 . 00 I 30287 . 00 I43507 .00157883
Calculated at 18 percent qf ultimate
10530000. 10530000. 10530000. 10530000. 10530000. 10530000. 10530000.
2628. 3096. 3564. 3888. 3960. 4266. 5022.
strength.
7817435 7922641 8018775. 8 I 04704 8179403.
. .
824 I 996 829 I796 8328327. 8351347 8360853 8357070. 8340441 a31 1590. 827 I299 8220464. 8 I60059 8091 IO3
.
8014626 793 I642 7843128. 7750010. 7653 I47 7553330. 745 I274 73476 I 9 7242933 7137716. 7032400.
. .
.
. .
. . .
. . . .
456
TRANSMISSION
LINE DESIGN MANUAL
Table C-2.-Permanent
set, creep, and initial and final modulus values (U.S. customary)-Continued
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000. 30000.
at 18 percentofultimate
.00007464 .00010656 .00013679 .00016568 .00019357 .00022078 .00024767 .00027456 .00030180 .00032973 .00035868 .00038900 .00042101 .00045507 .00049150 .00053065 .00057285 .00061844 .00066777 .00072116 .00077897 .00084152 .00090915 .00098221 .00106103 .00114595 .00123731 .00133544 .00144069 .00155340
strength.
8009304. 8064029. 8112144. 8153295. 8187189. 8213600. 8232378. 8243448. 8246813. 8242554. 8230825. 8211848. 8185905. 8153331. 8114503. 8069834. 8019760. 7964731. 7905206. 7841642. 7774488. 7704182. 7631143. 7555770. 7478440. 7399503. 7319286. 7238088. 7156184.
APPENDIX
457
C
Table C-2.-Permament set, creep, and initial and final modulus values (U.S. customary)-Continued
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000. 28000. 29000. 30000. 31000.
.00004619 .00006826 .00008940 .00010977 .00012958 .00014901 .00016823 .00018745 .00020683 .00022657 .00024684 .00026785 .00028976 .00031276 .00033705 .00036280 .00039020 .00041943 .00045068 .00048413 .00051997 .00055839 .00059956 .00064367 .00069091 .00074147 .00079552 .00085325 .00091485 .00098050 .00105038
Calculated at 18 percent o$ ultimate strength.
9069999. 9108929. 9143072.. 9172274. 9196403. 9215362. 9229082. 9237528. 9240698. 9238620. 9231356. 9218997. 9201662. 9179498. 9152671. 9121373. 9085809. 9046200. 9002779. 8955785. 8905464. 8852064. 8795831. 8737012. 8675847. 8612572. 8547413. 8480591. 8412314. 8342782.
458
TRANSMISSION
LINE DESIGN
MANUAL
Table C-2.-Permanent
set, creep, and initial and final modulus values (U.S. customary&-Continued
r
AND
Code word TERN RUCDY RAIL ORTOLAN BLUE JAY BUNT I NG B I TTERN D I PPER BOBOL I NK NUTHATCH LAPW I NG
Size, AWG 01 kcmil 795.0 900.0 954.0 1,033.5 1,113.0
1,192.5 1,272.0 1,351.5 1,431.0 1,510.5 1.590.0
1O-year creel.9
7 STFF’
Tension’, lb
.00057764 .00056147 .00056215 .00055394 .00055325 .00055490 .00055412 .00055343 .00055282 .00054804 eOOO54776
Stress, lb/in2
Permanent set
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000.
.00007248 .00012961 .00017972 .00022409 .00026402 .00030081 .00033576 .00037017 .00040532 .00044251 .00048305 .00052822 .00057932 .00063765 .00070450 .00078118 .00086897 .00096917 .00108308 .00121199 .00135721 .00152002 .00170172
1 Calculated at 18’percent of ultimate
strength.
S
3978. 4392.
4662. 4986. 5364. 5760. 6138. 6516. 6894. 7218. 7598.
-
Final modulus, lb/in2 9350000. 9350000. 9350000. 9350000. 9350000. 9350000. 9350000. 9350000. 9350000. 9350000. 9350000.
Initial modulus, lb/in2 6094514. 6230875. 6356725. 6469544. 6566978. 6647001. 6708064. 6749205. 6770117. 6771136. 6753185. 6717665. 6666327. 6601128. 6524109. 6437290. 6342586. 6241760. 6136388. 6027851. 5917333. 5805834.
APPENDIX
459
C
Table C-2.-Permanent
set, creep, and initial and final modulus values (US. customary&-Continued
Size, AWG or kcmil
Code word CONDOR CANARY CARDINAL CURLEW
795.0 900.0 954.0 1.033.5
1O-year creep’ .00046434 .00046390 .00046369 .00046347
5076. 5742. 6084. 6588.
9734000. 9734000. 9734000. 9734000.
Stress, lb/in’
Permanent set
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000.
.00005753 .00010350 .00014543 .00018402 .00021994 .00025388 .00028652 .00031856 .00035066 .00038352 .00041782 .00045425 .00049348 .00053621 .00058311 .00063487 .00069218 .00075571 .00082615 .00090420 .00099052 .00108580 .00119074 .00130600 .00143228 .00157026
14000.
15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000.
Calculatedat
percentofultimate
strength.
Final modulus, lb/in2
Tension’, lb
1 Initial modulus, lb/in2 6725040. 6818757. 6904585. 6981488. 7048526. 7104893. 7149946. 7183242. 7204543. 7213835. 7211311.
7197364. 7172554. 7137584. 7093261. 7040465. 6980111. 6913128. 6840425. 6762878. 6681315. 6596501. 6509140. 6419866. 6329243.
,
460
TRANSMISSION
LINE DESIGN MANUAL
Table C-2.-Permanent
set, creep, and initial and final modulus values (U.S. customary&Continued
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000. 25000. 26000. 27000.
.00002892 .00006013 .0000894 1 .00011729 .00014431 .00017099 .00019788 .00022551 .00025441 .00028512 .00031817 .00035409 .00039342 .00043669 .00048444 .00053719 .00059549 .00065987 .00073086 .00080900 .00089482 .00098885 .00109163 .00120369 .00132557 .00145779 .00160090
’ Calculated at 18 percent of ultimate strength.
7685036. 7742948. 7790922. 7828437. 7855119. 7870755. 7875301. 7868880. 7851773. 7824407. 7787332. 7741200. 7686737. 7624723. 7555962. 7481264. 7401427. 7317221. 7229375. 7138573. 7045445. 6950565. 6854451. 6757566. 6660319. 6563070.
APPENDIX
461
C
Table C-2.-Permanent set, creep, and initial and final modulus values (U.S. customary&Continued
1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 19000. 20000. 21000. 22000. 23000. 24000.
0.00000000 .00003350 .00006531 .00009538 .00012455 .00015366 .00018356 .00021507 .00024904 .00028631 .00032772 .00037411 .00042632 .00048519 .00055156 .00062627 .00071016 .00080407 .00090885 .00102532 .00115433 .00129672 .00145333 .00162500
Calculated at 18 percent of ultimate strength.
7267970. 7337414. 7392798. 7433244. 7458197. 7467449. 7461150. 7439784. 7404137. 7355238. 7294302. 7222659. 7141699. 7052811. 6957345. 6856575. 6751677. 6643716. 6533641. 6422281. 6310355. 6198473. 6087152.
Table C-3.-Conductor
Code word TURKEY SWAN SWANATE SPARROW SPARATE ROBIN RAVEN QUAIL PIGEON PENGU I N GROUSE PETREL M I NORCA LEGHORN GUINEA DOTTEREL DORK I NG COCH I N OWL WAXWI NG PARTR I DGE OSTR I CH MERLIN LINNET ORIOLE CH I CKADEE BRANT IBIS
Size, mm2 13.28 21.13 21..13 33 864 33.64 42.41 53.46 67.44 85.02 107.22 40.54 51.58 56.14 68.20 80.57 89.64 96.68 107.07 135.19 135.19 135.19 152.01 170.45 170.45 170.45 201.41 201.41 201.41
’ Does not include NEW constant.
Stranding! Xameter, hminum, mm steel 6/ 6/ 7/ 6/ 7/ 6/ 6/ 6/ 6/ 6/ 8/ 12/ 12/ 12/ 12/ 12/ 12/ 12/ 6/ 18/ 26/ 26/ 18/ 26/ 30/ 18/ 24/ 26/
1 1 1 1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7 1 7 7 1 7 7 1 7 7
5.03 6.35 6.53 8.03 8.26 9.02 10.11 11.35 12.75 14.30 9.32 11.71 12.22 13.46 14.63 15.42 16.03 16.84 16.08 15.47 16.31 17.27 17.37 18.31 18.82 18.87 19.61 19.89
and overhead ground wire data (metric)
Area, mm2 15.5 24.7 26.5 39.2 42.1 49.5 62.4 78.6 99.2 125.1 54.6 81.7 88.9 108.0 127.5 141.9 153.1 169.5 152.8 142.6 157.2 176.8 179.9 198.2 210.3 212.6 227.5 234.2
Ultimate strength, N 5293 4715 10497 12677 16191 15791 19483 23619 29447 37142 23130 46261 50264 60495 71171 76953 83181 126328 43058 30603 50264 56492 38610 62719 76953 44215 64943 72505
Coeff. of linear expansion, per “C .0000189 .0000189 .0000176 .0000189 .0000176 .0000189 .0000189 .0000189 .0000189 .0000189 .0000153 .0000153 .0000153 .0000153 .0000153 .0000153 .0000153 .0000153 .0000194 .0000211 .0000189 .0000189 .0000211 .0000189 .0000178 .0000211 .0000194 .0000189
Force, N/m .5268 .8377 .9778 1.3324 1.5572 1.6812 2.1190 2.6721 3.3697 4.2483 2.1745 3.7083 4.0367 4.9036 5.7909 6.4417 6.9511 7.6983 4.9970 4.2235 5.3603 6.0229 5.3312 6.7570 7.6924 6.2987 7.4735 7.9814
I. 192-kPa Resultant, force’ , wind, N/m N/m .963 1.216 1.250 1.537 1.581 1.727 1.936 2.174 2.442 2.739 1.785 2.243 2.340 2.578 2.802 2.953 3.070 3.225 3.079 2.963 3.123 3.308 3.327 3.507 3.605 3.614 3.755 3.809
1.0979 1.4767 1.5872 2.0343 2.2191 2.4102 2.8703 3.4451 4.1616 5.0546 2.8135 4.3337 4.6658 5.5401 6.4332 7.0863 7.5987 8.3466 5.8696 5.1589 6.2038 6.8715 6.2843 7.6131 8.4951 7.2621 8.3641 8.8437
Table C-3 .-Conductor
Code word LARK PEL I CAN FLICKER HAWK HEN OSPREY PARAKEET DO.VE EAGLE PEACOCK SQUAB TEAL KINGBIRD ROOK GROSBEAK EGRET SWIFT FLAMINGO STARLING REDW I NG CUCKOO DRAKE MALLARD COOT TERN CONDOR RUDDY
Size, mm2 201.41 241.70 241.70 241.70 241.70 281.98 281.98 281.98 281.98 306.55 306.55 306.55 322.26 322.26 322.26 322.26 322.26 331.33 337.46 362.54 362.54 402.83 402.83 402.83 402.83 402.83 402.83 456.03
l Does not include NESC constant.
Stranding! luminum, steel
Diameter, mm
30/ 7 18/ 1 24/ 7 26/ 7 30/ 7 18/ 1 24/ 7 26/ 7 30/ 7 24/ 7 26/ 7 30/19 18/ 1 24/ 7 26/ 7 30/19 36/ 1 18/ 3 24/ 7 26/ 7 30/19 24/ 7 26/ 7 30/19 36/ 1 45/ 7 54/ 7 45/ 7
20.47 20.68 21.49 21.79 22.43 22.33 23.22 23.55 24.21 24.21 24.54 25.25 23.88 24.82 25.15 25.88 23.62 24.21 25.40 26.70 27.46 27.74 28.14 28.96 26.42 27.00 27.76 28.73
and .overhead ground wire data (metric&Continued
Area, mm2 248.4 255.1 273.0 281.0 298.1 297.7 318.6 327.9 347.8 346.3 356.5 376.5 340.1 364.1 374.8 395.7 331.2 343.3 381.5 421.6 445.2 455.0 468.5 494.7 413.9 430.7 455.0 487.4
Ultimate strength, N 90298 52488 76509 86739 105867 60940 88074 100529 123659 96081 108091 133446 69836 97860 112094 140118 61385 65833 105422 126328 153907 124104 14011.8 170810 74729 98305 125439 108536
Coeff. of linear expansion, per “C .0000178 .0000211 .0000194 .0000189 .0000178 .0000211 .0000194 .0000189 .0000178 .0000194 .0000189 .0000207 .0000211 .0000194 .0000189 .0000207 .0000220 .0000218 .0000194 .0000189 .0000207 .0000194 .0000189 .0000207 .0000220 .0000207 .0000193 .0000207
Force, N/m 9.0891 7.5596 8.9680 9.5882 10.9016 8.8147 10.4638 11.1789 12.7259 11.3832 12.1567 13.7183 10.0844 11.9524 12.7697 14.4188 9.3941 9.8684 12.5362 14.3750 16.2138 14.9442 15.9657 18.0235 11.7437 13.0761 14.9442 14.8128
3.192-kPa wind, N/m 3.921 3.960 4.115 4.174 4.295 4.276 4.446 4.510 4.636 4.636 4.699 4.835 4.573 4.753 4.816 4.957 4.524 4.636 4.865 5.113 5.259 5.312 5.390 5.546 5.059 5.171 5.317 5.502
Resultant force’ , N/m 9.8987 8.5339 9.8672 10.4573 11.7174 9.7971 11.3693 12.0542 13.5440 12.2911 13.0334 14.5455 11.0727 12.8627 13.6476 15.2471 10.4267 10.9031 13.4469 15.2571 17.0453 15.8602 16.8510 18.8574 12.7871 14.0615 15.8619 15.8016
Table C-3.-Conductor
Code word CANARY CATB I RD RAIL CARDINAL ORTOLAN CURLEW BLUEJAY FINCH BUNT I NG GRACKLE BITTERN PHEASANT D I PPER MART I N BOBOLINK PLOVER NUTHATCH PARROT LAPW I NG FALCON CHUKAR BLUEBIRD KIWI THRASHER JOREE
Size, mm* 456.03 483.39 483.39 483.39 523.67 523.67 563.96 563.96 604.24 604.24 644.52 644.52 684.81 684.81 725.09 725.09 765.37 765.37 805.65 805.65 901.93 .030.63 .092.45 .098.02 .165.41 .171.49 274.35 552.53
’ Does not include NESC constant.
Stranding ’ 1Xameter, Juminum I mm steel 541 7 361 1 451 7 541 7 451 7 541 7 451 7 54/19 451 7 54/19 451 7 54/19 451 7 54/19 451 7 54/19 451 7 54/19 451 7 54/19 84/19 72/ 7 84/19 721 7 96/19 76/19 76/19 84/19
29.51 28.96 29.59 30.38 30.81 31.65 31.98 32.84 33.07 33.99 34.16 35.10 35.20 36.17 36.25 37.21 37.24 38.25 38.15 39.24 40.69 42.70 44.75 44.12 47.17 45.77 47.75 53.37
and overhead ground wire data (metric&Continued
Area, mm* 515.2 496.9 516.8 546.1 559.9 591.5 603.0 635.4 645.8 680.6 689.0 726.5 732.3 771.6 775.5 816.8 818.1 862.6 861.3 907.7 975.5 1075.4 1181.3 1145.8 1313.5 1235.1 1343.6 1679.2
Ultimate strength, N 141897 88074 115208 150349 123215 162804 132556 173924 142342 186379 151683 193941 161024 20595 1 170366 218406 178372 229971 187714 242426 226858 208175 268226 221520 355856 252212 274453 381210
Coeff. of linear expansion, per “C .0000193 .0000220 .0000207 .0000193 .0000207 .0000193 .0000207 .0000194 .0000207 .0000194 .0000207 .0000194 .0000207 .0000194 .0000207 .0000194 .0000207 .0000194 .0000207 .0000194 .0000207 .0000216 .0000207 .0000216 .0000194 .0000211 .0000211 .0000207
Force, N/m 16.9143 14.0977 15.6884 17.9359 17.0019 19.4245 18.3153 20.8839 19.6142 22.3724 20.9277 23.8610 22.2119 25.3496 23.5400 26.8528 24.8388 28.3414 26.1523 29.8299 30.2677 31.5520 36.6453 33.6098 43.3147 36.8642 40.1186 52.1002
0.192-kPa wind, N/m
Resultant force’ ,
5.653 5.546 5.667 5.818 5.901 6.061 6.125 6.290 6.334 6.509 6.543 6.723 6.742 6.927 6.942 7.127 7.132 7.326 7.307 7.516 7.793 8.177 8.571 8.450 9.034 8.766 9.146 10.221
17.8339 15.1493 16.6807 18.8560 17.9968 20.3482 19.3122 21.8105 20.6115 23.3000 21.9266 24.7900 23.2127 26.2791 24.5422 27.7824 25.8423 29.2729 27.1538 30.7622 31.2549 32.5945 37.6344 34.6557 44.2467 37.8921 41.1478 53.0933
N/m
Table C-3.-Conductor
and overhead ground wire data (metric)-Continued
Diameter, mm
Wire type and size
STEEL 3.525 3.525 II.113 II.113 12.7 12.7
HIGH EXTRA HIGH HIGH EXTRA HIGH HIGH EXTRA HIGH
mm mm mm mm mm mm
STRENGTH STRENGTH STRENGTH STRENGTH STRENGTH STRENGTH
9.14 9.14 11.05 11.05 12.57 12.57
Area, mm2
Ultimate strength, N
Coeff. of linear expansion, per “C
Force, N/m
0.192~kpa wind, N/m
Resultant force’ , N/m
STRAND OVERHEAD GROUND WIRE (7-WIRE) 51.1 51.1 74.6 74.6 96.6 96.6
48040 68502 64498 92522 83626 119656
.0000115 .0000115 .0000115 .0000115 .0000115 .0000115
3.9841 3.9841 5.8230 5.8230 7.5450 7.5450
ALUMOWELD STRAND OVERHEAD GROUND WIRE
7 7 7 7 7 7 7 7
8M 10M 12.5M 14M 16M 18M 20M 25M NO. 12 NO. 11 NO. 10 NO. 9 NO. 8 NO. 7 NO. 6 NO. 5
AWG AWG AWG AWG AWG AWG AWG AWG
’ Does not include NESC constant.
6.91 7.77 8.71 9.22 9.80 10.59 11.28 13.18 6.15 6.91 7.77 8.71 9.78 11 .oo 12.34 13.87
29.4 36.9 46.1 51.9 58.1 68.5 77.7 106.1 23.2 29.2 36.8 46.5 58.6 73.9 93.1 117.4
35585 44482 55602 62274 71171 80067 88964 111205 28028 35340 44570 56180 70859 84782 101107 120234
.0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130 .0000130
1.9118 2.4080 3.0355 3.3858 3.8236 4.4657 5.0641 6.9321 1.5119 1.9060 2.4036 3.0297 3.8207 4.8160 6.0754 7.6603
1.323 1.489 1.669 1.766 1.878 2.029 2.160 2.525 1.177 1.323 1.489 1.669 1.873 2.106 2.364 2.656
2.3250 2.8310 3.4639 3.8186 4.2598 4.9049 5.5055 7.3776 1.9162 2.3202 2.8272 3.4588 4.2550 5.2565 6.5192 8.1077
Table C-4.-Conductor
Code word ‘URKEY iWAN ;WANATE iPARROW ;PARATE lOBIN !AVEN !UAlL ’ I GEON ‘ENGU I N iROUSE ‘ETREL I I NORCA .EGHORN iU I NEA IOTTEREL lORK I NG :OCHI N IWL ‘AXW I NG ‘ARTR I DGE lSTR I CH IERLIN I NNET #RlOLE HICKADEE RANT BIS
Size, AWG or kcmil 6 4 4 2 2 1 l/O 2/o 3/o 4/o 80.0 101.8 110.8 134.6 159.0 176.9 190.8 211.3 266.8 266.8 266.8 300.0 336.4 336.4 336.4 397.5 397.5 397.5
Does not include NESC constant.
Stranding duminum steel 6/ 6/ 7/ 6/ 7/ 6/ 6/ 6/ 6/ 6/ 8/ 12/ 12/ 12/ 12/ 12/ 12/ 12/ 6/ 18/ 26/ 26/ 18/ 26/ 30/ 18/ 24/ 26/
1 1 1 1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7 1 7 7 1 7 7 1 7 7
Diameter: in 198 : 250 .257 .316 .325 .355 .398 .447 .502 .563 .367 .461 .481 .530 .576 .607 .631 .663 .633 .609 .642 .680 .684 .721 .741 .743 .772 .783
and overhead ground wire data (U.S. customary)
Area, in2 .0240 .0383 .0411 .0608 .0653 .0767 .0967 .1219 .1538 .1939 .0847 .1266 .1378 .1674 1977 : 2200 .2373 .2628 .2368 .2211 .2436 .2740 .2789 .3072 .3259 .3295 .3527 .3630
Ultimate strength, lb
Coeff. of linear expansion, per OF
Weight, lb/ft
4-lb/ft2 wind, lb/ft
Resultant weight,’ lb/ft
1,190 1,860 2,360 2,850 3,640 3,550 4,380 5,310 6,620 8,350 5,200 10,400 11,300 13,600 16,000 17,300 18,700 28,400 9,680 6,880 11,300 12,700 8,680 14,100 17,300 9,940 14,600 16,300
.0000105 .0000105 .0000098 .0000105 .0000098 .0000105 .0000105 .0000105 .0000105 .0000105 .0000085 .0000085 .0000085 .0000085 .0000085 .0000085 .0000085 .0000085 .0000108 .0000117 .0000105 .0000105 .0000117 .0000105 .0000099 .0000117 .0000108 .0000105
.03610 .05740 .06700 .09130 10670 : 11520 .14520 18310 : 23090 .29110 14900 : 25410 .27660 .33600 .39680 .44140 .47630 .52750 .34240 .28940 .36730 .41270 .36530 .46300 .52710 .43160 .51210 .54690
.06600 .08333 .08567 .10533 .10833 .11833 .13267 .14900 .16733 18767 : 12233 .15367 .16033 .17667 19200 : 20233 .21033 .22100 .21100 .20300 21400 : 22667 .22800 .24033 .24700 .24767 .25733 .26100
.07523 .10119 .10876 .13939 .15206 .16515 19668 : 23606 .28516 .34635 19279 : 29695 .31971 .37961 .44081 .48556 .52067 .57192 .40219 .35350 .42509 .47085 .43061 .52166 .58210 .49761 .57312 .60599
Table C-4.-Conductor
Code word LARK PEL I CAN FLICKER HAWK HEN OSPREY PARAKEET DOVE EAGLE PEACOCK SQUAB TEAL KINGBIRD ROOK GROSBEAK EGRET SWIFT FLAMINGO STARLING REDW I NG CUCKOO DRAKE MALLARD COOT TERN CONDOR RUDDY
Size, AWG or kcmil 397.5 477.0 477.0 477.0 477.0 556.5 556.5 556.5 556.5 605.0 605.0 605.0 636.0 636.0 636.0 636.0 636.0 653.9 666.0 715.5 715.5 795.0 795.0 795.0 795.0 795.0 795.0 900.0
’ Does not include NESC constant.
Stranding .luminum steel 30/ 7 18/ 1 24/ 7 26/ 7 30/ 7 18/ 1 24/ 7 26/ 7 30/ 7 24/ 7 26/ 7 30/19 18/ 1 24/ 7 26/ 7 30/19 36/ 1 18/ 3 24/ 7 26/ 7 30/19 24/ 7 26/ 7 30/19 36/ 1 45/ 7 54/ 7 45/ 7
and overhead ground wire data (U.S. customary&Continued
Diameter , in
Area, in2
.806
.3850 .3954 .4232 .4356 .4620
.814 .846 .858 .883 .879 .914 .927 .953 .953 .966 .994 .940 .977 .990 1.019 .930 .953 1 .ooo 1.051 1.081 1.092 1.108 1.140 1.040 1.063 1.093 1.131
.4614 .4938 .5083 .5391 .5368 .5526 .5835 .5272 .5643 .5809 .6134 .5133 .5321 .5914 .6535 .6901 .7053 7261 : 7668 .6416 .6676 .7053 .7555
Ultimate strength, lb 20,300 11,800 17,200 19,500 23,800 13,700 19,800 22,600 27,800 21,600 24,300 30,000 15,700 22 ) 000 25,200 31,500 13,800 14,800 23,700 28,400 34,600 27,900 31,500 38,400 16,800 22) 100 28,200 24,400
Coeff. of linear expansion, per OF .0000099 .0000117 .0000108 .0000105 .0000099 .0000117 .0000108 .0000105 .0000099 .0000108 .0000105 .0000115 .0000117 .0000108 .0000105 .0000115 .0000122 .0000121 .0000108 .0000105 .0000115 .0000108 .0000105 .0000115 .0000122 .0000115 .0000107 .0000115
Weight, lb/ft .62280 .51800 .61450 .65700 74700 : 60400 .71700 76600 : 87200 .78000 .83300 .94000 .69100 .81900 .87500 .98800 .64370 .67620 .85900 .98500 1.11100 1.02400 1.09400 1.23500 .80470 .89600 1.02400 1.01500
4-lb/ft2 wind, Ib/ft
Resultant weight,’ Ib/ft
.26867 .27133 .28200 .28600 .29433 .29300 .30467 .30900 .31767 .31767 .32200 .33133 .31333 .32567 .33000 .33967 .31000 .31767 .33333 .35033 .36033 .36400 .36933 .38000 .34667 .35433 .36433 .37700
.67828 .58476 .67612 .71655 .80290 .67132 .77904 .82598 .92806 .84221 .89307 .99669 .75872 .88137 .93516 1.04476 71446 : 74710 .92141 1.04545 1.16797 1.08677 1.15466 1.29214 .87620 .96352 1.08688 1.08275
Table @I.-Conductor
Code word CANARY CATB I RD RAIL CARDINAL ORTOLAN CURLEW BLUE JAY FINCH BUNT I NG GRACKLE B I TTERN PHEASANT D I PPER MART I N BOBOLINK PLOVER NUTHATCH PARROT LAPW I NG FALCON CHUKAR BLUEBIRD KIWI THRASHER JOREE
Size, AWG or kcmil 900.0 954.0 954.0 954.0 1,033.5 1,033.5 1,113.0 1,113.0 1,192.5 1,192.5 1,272.0 1,272.0 1,351.5 1,351.5 1,431.0 1,431.0 1,510.5 1,510.5 1,590.o 1,590.o 1,780.O 2,034.o 2,156.0 2,167.O 2,300.O 2,312.0 2,515.0 3,064.O
’ Does not include NESC constant.
Stranding .luminum, steel 54/ 7 36/ 1 45/ 7 54/ 7 45/ 7 54/ 7 45/ 7 54/19 45/ 7 54/19 45/ 7 54/19 45/ 7 54/19 45/ 7 54/19 45/ 7 54119 45/ 7 54/19 84/19 721 7 84/19 72/ 7 96/19 76119 76/19 84/19
and overhead ground wire data (U.S. customary&Continued
Diameter. in 1.162 1.140 1.165 1.196 1.213 1.246 1.259 1.293 1.302 1.338 1.345 1.382 1.386 1.424 1.427 1.465 1.466 1.506 1.502 1.545 1.602 1.681 1.762 1.737 1.857 1.802 1.880 2.101
Area, in2 7985 : 7702 .8011 .8464 .8678 .9169 .9346 .9849 1 .OOlO 1.0550 1.0680 1.1260 1.1350 1.1960 1.2020 1.2660 1.2680 1.3370 1.3350 1.4070 1.5120 1.6669 1.8310 1.7760 2.0359 1.9144 2.0826 2.6028
Ultimate strength, lb
Coeff. of linear expansion, per OF
31,900 19,800 25,900 33,800 27,700 36,600 29,800 39,100 32,000 41,900 34,100 43,600 36,200 46,300 38,300 49,100 40,100 51,700 42,200 54,500 51,000 46,800 60,300 49,800 80,000 56,700 61,700 85,700
.0000107 .0000122 .0000115 .0000107 .0000115 .0000107 .0000115 .0000108 .0000115 .0000108 .0000115 .0000108 .0000115 .0000108 .0000115 .0000108 .0000115 .0000108 .0000115 .0000108 .0000115 .0000120 .0000115 .0000120 .0000108 .0000117 .0000117 .0000115
Weight, lb/ft
4-lb/ft2 wind, lb/ft
Resultant weight,’ lb/ft
1.15900 .96600 1.07500 1.22900 1.16500 1.33100 1.25500 1.43100 1.34400 1.53300 1.43400 1.63500 1.52200 1.73700 1.61300 1.84000 1.70200 1.94200 1.79200 2.04400 2.07400 2.16200 2.51100 2.30300 2.96800 2.52600 2.74900 3.57000
.38733 .38000 .38833 .39867 .40433 .41533 .41967 .43100 .43400 .44600 .44833 .46067 .46200 .47467 .47567 148833 .48867 .50200 .50067 .51500 .53400 .56033 .58733 .57900 .61900 .60067 .62667 .70033
1.22201 1.03805 1.14299 1.29204 1.23317 1.39430 1.32331 1.49450 1.41234 1.59656 1.50245 1.69866 1.59057 1.80069 1.68167 1.90370 1.77076 2.00583 1.86063 2.10788 2.14164 2.23343 2.57878 2.37467 3.03186 2.59644 2.81952 3.63804
Table C-4.-Conductor
Wire type and size
and overhead ground wire data (U.S. customary&Continued
Diameter, in
Area, in2
Ultimate strength, lb
Coeff. of linear expansion, per OF
I
Weight, lb/ft
4-lb/ft2 wind, lb/ft
Resultant weight ,l lb/ft
STEEL STRAND OVERHEAD GROUND WIRE (7 WIRE) 3/8 3/8 7/16 7/16 l/2 i/2
HIGH STRENGTH INCH INCH EXTRA HIGH STRENGTH INCH HIGH STRENGTH INCH EXTRA HIGH STRENGTH INCH HIGH STRENGTH INCH EXTRA HIGH STRENGTH
.360 .360 .435 .435 .495 .495
.0792 .0792 .1156 .1156
1497 :1497
10,800 15,400 14,500 20,800 18,800 26.900
.0000064 .0000064 .0000064 .0000064 .0000064 .0000064
ALUMOWELD STRAND OVERHEAD GROUND WIRE 8M
10M 12.5M 14M
7 7 7 7 7 7 7 7
16M 18M 20M 25M NO. 12 NO. 11 NO. 10 NO. 9 NO. 8 NO. 7 NO. 6 NO. 5
AWG AWG AWG AWG AWG AWG AWG AWG
* Does not include NESC constant.
.272 .306 .343 .363 .386 .417 .444 .519 .242 .272 .306 .343 .385 .433 .486 .546
.0455 .0572 .0714 .oco5 .0901 .1062 .1204 1645 : 0359 .0453 .0571 .0720 .0908 .1145 .1443 .1820
8,000 10,000 12,500 14,000 16,000 18,000 20,000 25,000 6,301 7,945 10,020 12,630 15,930 19,060 22,730 27.030
.0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072 .0000072
.27300 .27300 .39900 .39900 .51700 .51700
.12000 .12000 .14500 .14500 .16500 .16500
.29821 .29821 .42453 .42453 .54269 .54269
.13100 16500 :20800 .23200 .26200 .30600 .34700 .47500 .10360 .13060 16470 :20760 .26180 .33000 .41630 .52490
.09067
.10200 .11433 .12100 .12867 .13900 .14800 .17300 .08067 .09067 .10200 .11433 .12833 .14433 .16200 .18200
.15932 19398 :23735 .26166 .29189 .33609 .37724 .50552 .13130 .15899 19373 :23700 .29156 .36018 .44671 .55556
Table C-5.-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (metric)
Code word TURKEY SWAN SWANATE SPARROW SPARATE ROBIN RAVEN QUAIL PIGEON PENGU I N GROUSE PETREL M I NORCA LEGHORN GUINEA DOTTEREL DORK I NG COCH I N OWL WAXW I NG PARTR I DGE OSTR I CH MERLIN L I NNET ORIOLE CH I CKADEE BRANT IBIS
F
NATIONAL LIGHT
Force with no ice .5268 .8377 .9778
1.3324 1.5572 1.6812 2.1190 2.6721 3.3697 4.2483 2.1745 3.7083 4.0367 4.9036 5.7909 6.4417 6.9511 7.6983 4.9970 4.2235 5.3603 6.0229 5.3312 6.7570 7.6924 6.2987 7.4735 7.9814
’ Includes 0.7297 NESC constant. * Includes 2.9188 NESC constant. 3 Includes 4.3782 NESC constant.
ELECTRICAL
SAFETY
T
LOADING
MEDIUM
0.43 1-kPa Resultant wind force’
7orce with 6.35-mm ice
2.1672 2.7364 2.8130 3.4588 3.5573 3.8856 4.3563 4.8926 5.4946 6.1623 4.0170 5.0458 5.2647 5.8011 6.3046 6.6439 6.9066 7.2568 6.9285 6.6658 7.0270 7.4429 7.4867 7.8917 8.1106 8.1325 8.4499 8.5703
2.5602 3.1070 3.2789 3.9013 4.1669 4.4271 5.0601 5.8356 6.7828 7.9382 4.9749 6.9353 7.3545 8.4437 9.5398 10.3314 10.9497 11.8421 9.0046 8.1222 9.4089 10.2439 9.5703
2.9600
3.5914 3.7078 4.4362 4.6129 4.9634 5.5740 6.3045 7.1753 8.2144 5.2975 6.9916 7.3639 8.3256 9.2902 9.9837 10.5286 11.3092 9.2721 8.6208 9.5678 10.3042 9.9205 11.1189 11.9080 11.0161 12.0104 12.4409
11.1641
12.1903 10.8057 12.1121
12.6699
CODE
T
LOADING
0.192-kPa wind 3.3955
3.6485 3.6825 3.9695 4.0133 4.1593 4.3684 4.6068 4.8744 5.1711 4.2176 4.6749 4.7722 5.0106 5.2343 5.3851 5.5019 5.6576 5.5116 5.3949 5.5554 5.7403 5.7597 5.9397 ‘6.0370 6.0467 6.1878 6.2413
1977
Resultant force2 7.1713 7.7110 7.8495 8.4845 8.7041 8.9932 9.6037 10.3536 11.2714 12.3928 9.4409 11.2826 11.6859 12.7373 13.8003 14.5694 15.1730 16.0430 13.4763 12.6694 13.8453 14.6614 14.0886 15.5646 16.5220 15.3012 16.5199 17.0425
ALL VALUES
1
EDITION HEAVY
Force witk 12.7-mm ice 6.8629
7.6457 7.8494 8.7396 9.0460 9.4424 10.2705 11.2684 12.4653 13.8976 10.0446 12.4317 12.9416 14.2533 15.5581 16.4904 17.2176 18.2553 15.2817 14.2903 15.7267 16.7342 16.0788 17.8405 18.9575 17.5819 19.0200 19.6277
LOADING
0.192~kPa wind 5.8278 6.0808 6.1148 6.4019 6.4456 6.5916 6.8008 7.0391 7.3067 7.6034 6.6500 7.1072 7.2045 7.4429 7.6667 7.8175 7.9342 8.0899 7.9439 7.8272 7.9877 8.1726 8.1920 8.3720 8.4693 8.4791 8.6201 8.6736
Resultant force3 13.3816 14.1472 14.3283 15.2116 15.4857 15.8937 16.6962 17.6645 18.8271 20.2197 16.4246 18.6981 19.1900 20.4577 21.7227 22.6278 23.3360 24.3457 21.6013 20.6717 22.0172 23.0014 22.4236 24.0854 25.1415 23.8979 25.2604 25.8370
ARE IN NEWTONS PER METER.
Table C-S.-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (metric&Continued
NATIONAL
Code word -LARK PEL I CAN FLICKER HAWK HEN OSPREY PARAKEET DOVE EAGLE PEACOCK SQUAB TEAL KINGBIRD ROOK GROSBEAK EGRET SWIFT FLAM I NGO STARLING REDWING CUCKOO DRAKE MALLARD COOT TERN CONDOR RUDDY
L I GHT
ELECTRICAL
SAFETY
T
LOADING
MEDIUM
T
LOADING
9.0891 7.5596 8.9680 9.5882 10.9016 8.8147 10.4638 11.1789 12.7259 11.3832 12.1567 13.7183 10.0844 11.9524 12.7697 14.4188 9.3941 9.8684 12.5362 14.3750 16.2138 14.9442 15.9657 18.0235 11.7437 13.0761 14.9442 14.8128
1 Includes 0.7297 NESC constant. ’ Includes 2.9188 NESC constant. 3 Includes 4.3782 NESC constant.
0.43 1-kPa wind 8.8220 8.9096 9.2598 9.3912 9.6648 9.6210 10.0041 10.1464 10.4310 10.4310 LO. 5733 LO.8798 LO.2887 LO.6937 10.8360 11.1534 LO. 1792 10.4310 10.9454 11.5036 11.8320 11.9524 12.1275 12.4778 11.3832 11.6350 11.9633 12.3793
Resultant force’ 13.3962 12.4142 13.6203 14.1509 15.2986 13.7782 15.2064 15.8266 17.1843 16.1694 16.8412 18.2385 15.1364 16.7676 17.4773 18.9588 14.5813 15.0890 17.3717 19.1409 20.8017 19.8657 20.7792 22.6509 17.0849 18.2328 19.8726 20.0342
1by; .
;Nll -
ice
13.8820 12.3888 13.9424 14.6171 16.0440 13.9389 15.7469 16.5210 18.1859 16.8433 17.6758 19.3644 15.4854 17.5214 18.3977 20.1784 14.7498 15.3285 18.2095 20.2798 22.2548 21.0351 22.1293 24.3323 17.5986 19.0355 21.0396 21.0808
0.192-kPa wind
Resultant force2
6.3532 6.3921 6.5478 6.6062 6.7278 6.7083 6.8786 6.9418 7.0683 7.0683 7.1316 7.2678 .7.0051 7.1851 7.2483 7.3894 6.9564 7.0683 7.2970 7.5450 7.6910 7.7445 7.8223 7.9780 7.4915 7.6034 7.7494 7.9342
18.185516.8594 18.3221 18.9594 20.3163 18.3879 20.1025 20.8389 22.4300 21.1851 21.9790 23.6021 19.9150 21.8562 22.6928 24.4076 19.2267 19.7984 22.5359 24.5567 26.4651 25.3342 26.3899 28.5256 22.0456 23.4166 25.3402 25.4432
ALLVALUES
EDITION HEAVY
L
L
Force with no ice
1977
CODE
I Torte
LOADING
with 12.7-mm ice
0.192~kPa Resultant force3 wind
20.9442 19.4874 21.1861 21.9153 23.4557 21.3325 23.2993 24.1324 25.9154 24.5727 25.4642 27.2799 23.1558 25.3597 26.2950 28.2074 22.3748 23.0579 26.1523 28.4540 30.5652 29.3954 30.5622 32.9104 25.7229 27.2641 29.4045 29.6181
8.7855 8.8244 8.9801 9.0385 9.1601 9.1406 9.3109 9.3741 9.5006 9.5006 9.5639 9.7001 9.4374 9.6174 9.6806 9.8217 9.3887 9.5006 9.7293 9.9774 10.1233 10.1768 10.2546 10.4103 9.9239 10.0357 10.1817 10.3665
ARE IN
27.0904 25.7704 27.3889 28.0842 29.5591 27.5865 29.4690 30.2673 31.9801 30.7236 31.5791 33.3313 29.3833 31.5003 32.3985 34.2466 28.6429 29.3166 32.2816 34.5308 36.5762 35.4853 36.6149 38.8958 31.9490 33.4307 35.4955 35.7580
D : 2 0 x 0
E7NTONS PER METER. 2
Table C-5.-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (met&)-Continued
NATIONAL
Code word CANARY CATB I RD RAIL CARDINAL ORTOLAN CURLEW BLUEJAY FINCH BUNT I NG GRACKLE B I TTERN PHEASANT D I PPER MART I N BOBOL I NK PLOVER NUTHATCH PARROT LAPW I NG FALCON CHUKAR BLUEBIRD KIWI THRASHER JOREE
LIGHT
Force with no ice 16.9143 14.0977 15.6884 17.9359 17.9019 19.4245 18.3153 20.8839 19.6142 22.3724 20.9277 23.8610 22.2119 25.3496 23.5400 26.8528 24.8388 28.3414 26.1523 29.8299 30.2677 31.5520 36.6453 33.6098 13.3147 36.8642 10.1186 52.1002
’ Includes 0.7297 NESC constant. ’ Includes 2.9188 NESC constant. 3 Includes 4.3782 NESC constant.
SAFETY
ELECTRICAL
T
LOADING
MEDIUM
CODE LOADING
0.43 1-kPa Resultant wind force’
Force with 6.35-mm ice
0.192-kPa wind
12.7186 12.4778 12.7514 13.0907 13.2768 13.6380 13.7803 14.1524 14.2509 14.6450 14.7216 15.1266 15.1704 15.5863 15.6191 16.0350 16.0460 16.4838 16.4400 16.9107 17.5346 18.3993 19.2858 19.0122 20.3257 19.7237 20.5774 22.9963
23.3230 20.4065 22.1107 24.4989 23.6420 26.2144 25.1642 27.8871 26.6583 29.5799 28.1669 31.2682 29.6372 32.9474 31.1514 34.6367 32.6272 36.3113 34.1041 37.9769 38.6734 40.3162 45.7772 42.6282 52.8777 46.1776 49.7861 62.7707
8.0850 7.9780 8.0996 8.2504 8.3331 8.4936 8.5569 8.7223 8.7661 8.9412 8.9752 9.1552 9.1747 9.3596 9.3741 9.5590 9.5639 9.7585 9.7390 9.9482 10.2255 10.6098 11.0038 10.8822 11.4659 11.1984 11.5778 12.6529
21.8923 19.5563 20.9467 22.9347 22.3014 24.4638 23.6502 25.9572 24.9744 27.4692 26.3166 28.9815 27.6278 30.4876 28.9801 32.0058 30.3006 33.5161 31.6201 35.0196 35.7097 37.2545 42.1401 39.3442 48.5763 42.5387 45.8178 57.6794
1
1977
T
1
EDITION HEAVY
LOADING
Resultant force2
Force with 12.7-mm ice
0.192-kPa wind
Resultant force3
27.6034 24.8294 26.4663 28.7696 27.9864 30.4748 29.4981 32.1381 30.9813 33.8205 32.4811 35.4997 33.9436 37.1698 35.4500 38.8503 36.9188 40.5185 38.3862 42.1770 42.9212 44.6077 49.9999 46.9140 57.0254 50.4348 54.0333 66.9520
32.0010 28.9847 30.8023 33.3312 32.5515 35.2736 34.2825 37.1597 35.9717 39.0567 37.6755 40.9447 39.3319 42.8145 41.0321 44.6899 42.6850 46.5506 44.3252 48.3932 49.3485 51.3498 57.1784 53.9159 64.7101 57.7604 61.7229 75.7106
10.5173 10.4103 10.5319 10.6827 10.7654 10.9260 10.9892 11.1546 11.1984 11.3735 11.4076 11.5876 11.6070 11.7919 11.8065 11.9913 11.9962 12.1908 12.1713 12.3805 12.6578 13.0421 13.4361 13.3145 13.8983 13.6307 14.0101 15.0852
38.0631 35.1756 36.9313 39.3794 38.6636 41.3052 40.3789 43.1759 42.0526 45.0572 43.7428 46.9310 45.3870 48.7869 47.0751 50.6489 48.7168 52.4986 50.3441 54.3300 55.3241 57.3584 63.1140 59.9138 70.5640 63.7251 67.6711 81.5770
ALL VALUES
ARE IN NEWTONS PER METER.
Table C-5.-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (metric)-Continued
NATIONAL
Wire type and size
0.43 l-kPa wind
3.9841 3.9841
mm HS mm EHS mm HS mm EHS mm HS mm EHS
5.8230 5.8230 7.5450 7.5450
3.9404 3.9404 4.7613 4.7613 5.4180 5.4180
Resultant force’
1.9118
8M 12.5M 14M 16M 18M 20M 25M 7 NO. 7 NO. 7 NO. 7N0. 7N0. 7N0. 7N0. 7N0.
2.4080 3.0355 3.3858 3.8236 4.4657 5.0641
6.9321 1.5119 1.9060
12
11 10 9 8 7 6 5
/
2.4036 3.0297 3.8207 4.8160 6.0754 7.6603
1 Includes 0.7297 NESC constant. ’ Includes 2.9188 NESC constant. 3 Includes 4.3782 NESC constant.
2.9772 3.3493 3.7543 3.9732 4.2249 4.5642 4.8598 5.6807 2.6488 2.9772 3.3493 3.7543 4.2140 4.7394
5.3195 5.9762
FtT
STRAND
4.2678 4.8548 5.5576 5.9498 6.4279 7.1152 7.7484
9.6921 3.7796 4.2647 4.8522 5.5540
6.4179 7.4866 8.8048 .0.4454
GROUND
OVERHEAD
4.2810
4.. 9315 5.7270 6.1680 6.7102 7.4930
8.2139 10.4224 3.7450 4.2752
4.9271 5.7211 6.7028
7.9159 9.4159 11.2731
EDITION HEAVY
0.192-kPa wind
WIRE
4.3101 4.4609 4.5922 4.9571 3.6096
~~.~~~” ice
LOADING
0.192-kPa wind
Resultant force3
(7-WIRE)
11.7907 11.7907 14.3103 14.3103 16.5771 16.5771
6.6159 6.6159 6.9807 6.9807
8.6136 9.2190 9.9626 10.3799 10.8940 11.6392 12.3293 14.4599
8.9196 9.7244 10.6878 11.2196 11.8662 12.7897 13.6332 16.1820
6.1878 6.3532 6.5332 6.6305 6.7424 6.8932 7.0245 7.3894
8.1201 8.6092
8.2474
GROUND
3.7555 3.9209 4.1009 4.1982
3.7555 3.9209 4.1009 4.3052 4.5387 4.7965 5.0884
Resultant force2
10.8625 10.8625 12.9422 12.9422 14.8693 14.8693
4.1836 4.1836 4.5484 4.5484 4.8403 4.8403 STRAND
1977
LOADING
OVERHEAD
6.3332 6.3332 8.2514 8.2514 10.0185 10.0185 ALUMOWELD
10M
CODE
MEDIUM
STEEL I.525 I.525 I.11 I.11 12.7 12.7
SAFETY
LOADING
LIGHT
Force with no ice
ELECTRICAL
7.2726 7.2726
17.8982 17.8982 20.3004 20.3004 22.4804 22.4804
WIRE
9.2156 9.9579 10.8851 12.0436 13.4860 15.2871
8.9137 9.7200 10.6819 11.8542 13.2852 15.0258 17.1553
6.0419 6.1878 6.3532 6.5332 6.7375
6.9710 7.2288 7.5207
15.2339 15.9940 16.9046 17.4105 18.0261 18.9072 19.7146 22.1675 14.6018
15.2291 15.9903 16.8996 18.0133 19.3812 21.0524 23.1096
ALL VALUES ARE IN NEWTONS PER METER.
Table C-&-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (U.S. customary)
Code word TURKEY SWAN SWANATE SPARROW SPARATE ROBIN RAVEN QUAIL PIGEON PENGU I N GROUSE PETREL M I NORCA LEGHORN GUINEA OOTTEREL DORK I NG COW I N OWL WAXWI NG PARTR I DGE OSTR I CH MERLIN L I NNET ORIOLE CH I CKADEE BRANT IBIS
F
NAT LIGHT
IONAL
ELECTRICAL
r
LOADING
SAFETY MEDIUM
Weight with no ice
9-lb/ft2 wind
Resultant weight’
Weight with l/4-in ice
.0361 .0574 .0670 .0913 .1067 .1152 .1452 1831 : 2309 .2911 1490 : 2541 .2766 .3360 .3968 .4414 .4763 .5275 .3424 .2894 .3673 .4127 .3653 .4630 .5271 .4316 .5121 15469
.1485 .1875 1928 : 2370 .2438 .2663 .2985 .3353 .3765 .4223 .2753 .3458 .3608 .3975 .4320 .4553 .4733 .4973 .4748 .4568 .4815 .5100 .5130 .5408 .5558 .5573 .5790 .5873
.2028 .2461 .2541 .3040 .3161 .3401 .3819 14320 .4917 .5629 .3630 .4791 .5046 .5705 .6366 .6841 .7214 .7749 .6353 .5907 .6556 .7061 .6798 .7619 .8160 17548 .8230 .8525
1754 : 2129 .2247 .2673 .2855 .3034 .3467 .3999 .4648 .5439 .3409 .4752 .5039 .5786 .6537 .7079 .7503 .8114 .6170 .5565 .6447 .7019 .6558 .7650 .8353 .7404 .8299 .8682
1 Includes 0.05 NESC constant. ’ Includes 0.20 NESC constant. 3 Includes 0.30 NEW constant.
1977
CODE
EDITION
T-
LOADING
4-lb/ft2 wind
Resultant weight’
.2327 .2500 .2523 .2720 .2750 .2850 .2993 .3157 .3340 .3543 .2890 .3203 .3270 .3433 .3587 .3690 .3770 .3877 .3777 .3697 .3807 .3933 .3947 .4070 .4137 .4143 .4240 .4277
.4914 .5284 .5379 .5814 .5964 .6162 .6581 .7094 .7723 .8492 .6469 .7731 .8007 .8728 .9456 .9983 1.0397 1.0993 .9234 .8681 .9487 1.0046 .9654 1.0665 1.1321 1.0485 1.1320 1.1678
HEAVY
Weight with
l/2-in ice .4703 .5239 .5379 .5989 .6199 .6470 .7038 .7721 .8541 .9523 .6883 .8518 .8868 .9767 1.0661 1.1300 1.1798 1.2509 1.0471 .9792 1.0776 1.1467 1.1017 1.2225 1.2990 1.2047 1.3033 I 1.3449
ALL VALUES
LOADING
4-lb/ft2 wind .3993 .4167 .4190 .4387 .4417 .4517 .4660 .4823 .5007 .5210 .4557 .4870 .4937 .5100 .5253 .5357 .5437 .5543 .5443 .5363 .5473 .5600 .5613 .5737 .5803 .5810 .5907 .5943
ARE IB POUNDS
Resultant weight3 .9169 .9694 .9818 1.0423 1.0611 1.0891 1.1441 1.2104 1.2901 1.3855 1.1254 1.2812 1.3149 1.4018 1.4885 1.5505 1.5990 1.6682 1.4802 1.4165 1.5087 1.5761 1.5365 1.6504 1.7227 1.6375 1.7309 1.7704
ER FOOT
Table C-k-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (U.S. customary)-Continued
Code word LARK PEL I CAN FLICKER HAWK HEN OSPREY PARAKEET DOVE EAGLE PEACOCK SQUAB TEAL KINGBIRD ROOK GROSBEAK EGRET SWIFT FLAMINGO STARLING REDWI NG CUCKOO DRAKE MALLARD COOT TERN CONDOR RUDDY
F
NATIONAL LIGHT
Weight with no ice
.6228 .5180 .6145 .6570 .7470 .6040 .7170 .7660 .8720 .7800 .8330 .9400 .6910 .8190 .8750 .9880 .6437 .6762 .8590 .9850 1.1110 1.0240 1.0940 1.2350 .8047 .8960 1.0240 1.0150
’ Includes 0.05 NESC constant. * Includes 0.20 NESC constant. 3 Includes 0.30 NESC constant.
ELECTRICAL
T
LOADING
9-lb/ft* wind
Resultant weight’
.6045 .6105 .6345 .6435 .6623 .6593 .6855 .6953 .7148 .7148 .7245 .7455 .7050 .7328 .7425 .7643 .6975 .7148 .7500 .7883 .8108 .8190 .8310 .8550 .7800 .7973 .8198 .8483
.9179 .8506 .9333 .9696 1.0483 .9441 1.0420 1.0845 1.1775 1.1080 1.1540 1.2497 1.0372 1.1489 1.1976 1.2991 .9991 1.0339 1.1903 1.3116 1.4254 1.3612 1.4238 1.5521 1.1707 1.2493 1.3617 1.3728
SAFETY MEDIUM
Weight with l/4-in ice .9512 .8489 .9554 1.0016 1.0994 .9551 1.0790 1.1320 1.2461 1.1541 1.2112 1.3269 1.0611 1.2006 1.2606 1.3827 1.0107 1.0503 1.2478 1.3896 1.5249 1.4414 1.5163 1.6673 1.2059 1.3043 1.4417 1.4445
CODE LOADING
4-lb/ft* wind .4353 .4380 .4487 .4527 .4610 .4597 .4713 .4757 .4843 .4843 .4887 .4980 .4800 .4923 .4967 .5063 .4767 .4843 .5000 .5170 .5270 .5307 .5360 .5467 .5133 .5210 .5310 .5437
1977
HEAVY
Resultant weight* 1.2461 1.1552 1.2555 1.2991 1.3921 1.2600 1.3775 1.4279 1.5369 1.4516 1.5060 1.6173 1.3646 1.4976 1.5550 1.6725 1.3174 1.3566 1.5442 1.6827 1.8134 1.7359 1.8083 1.9546 1.5106 1.6045 1.7364 1.7434
ALL VALUES
1
EDITION
Weight with l/2-in ice 1.4351 1.3353 1.4517 1.5017 1.6072 1.4617 1.5965 1.6536 1.7758 1.6838 1.7449 1.8693 1.5867 1.7377 1.8018 1.9328 1.5332 1.5800 1.7920 1.9497 2.0944 2.0142 2.0942 2.2551 1.7626 1.8682 2.0148 2.0295
LOADING
4-lb/ft* wind .6020 .6047 .6153 .6193 .6277 .6263 .6380 .6423 .6510 .6510 .6553 .6647 .6467 .6590 .6633 .6730 .6433 .6510 .6667 .6837 .6937 .6973 .7027 .7133 .6800 .6877 .6977 .7103
Resultant weight3 1.8563 1.7658 1.8767 1.9244 2.0254 1.8903 2.0193 2.0740 2.1913 2.1052 2.1639 2.2839 2.0134 2.1585 2.2200 2.3466 1.9627 2.0088 2.2120 2.3661 2.5063 2.4315 2.5089 2.6652 2.1892 2.2907 2.4322 2.4502
ARE IN POUNDS PER FOOT.
Table C-&-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading (U.S. customary)-Continued
Code word CANARY CATB I RD RAIL CARDINAL ORTOLAN CURLEW BLUEJAY FINCH BUNT I NG GRACKLE B I TTERN PHEASANT D I PPER MART I N BOBOLINK PLOVER NUTHATCH PARROT LAPW I NG FALCON CHUKAR BLUEBIRD KIWI THRASHER JOREE
F
NATIONAL LIGHT
Weight with no ice
1.1590 .9660 1.0750 1.2290 1.1650 1.3310 1.2550 1.4310 1.3440 1.5330 1.4340 1.6350 1.5220 1.7370 1.6130 1.8400 1.7020 1.9420 1.7920 2.0440 2.0740 2.1620 2.5110 2.3030 2.9680 2.5260 2.7490 3.5700
’ Includes 0.05 NESC constant. 2 Includes 0.20 NESC constant. 3 Includes 0.30 NESC constant.
l-
LOADING
9-lb/ft2 wind .8715 .8550 .8738 .8970 .9098 .9345 .9443 .9698 .9765 1.0035 1.0088 1.0365 1.0395 1.0680 1.0703 1.0988 1.0995 1.1295 1.1265 1.1588 1.2015 1.2608 1.3215 1.3028 1.3928 1.3515 1.4100 1.5758
SAFETY
ELECTRICAL
Resultant weight l 1.5001 1.3400 1.4353 1.5715 1.5281 1.6763 1.6206 1.7786 1.7113 1.8822 1.8033 1.9859 1.8931 2.0891 1.9858 2.1931 2.0763 2.2966 2.1667 2.3996 2.4469 2.5527 2.8875 2.6959 3.3285 2.9148 3.1395 3.9523
MEDIUM
Weight with l/4-in ice 1.5981 1.3983 1.5151 1.6787 1.6200 1.7963 1.7243 1.9109 1.8267 2.0269 1.9300 2.1426 2.0308 2.2576. 2.1345 2.3734 2.2357 2.4881 2.3369 2.6022 2.6500 2.7625 3.1367 2.9210 3.6233 3.1642 3.4114 4.3012
1977
CODE
l-
LOADING
4-lb/ft2 wind .5540 .5467 .5550 .5653 .5710 .5820 .5863. .5977 .6007 .6127 .6150 .6273 .6287 .6413 .6423 .6550 .6553 .6687 .6673 .6817 .7007 .7270 .7540 .7457 .7857 .7673 .7933 .8670
Resultant weight2 1.8914 1.7014 1.8135 1.9713 1.9177 2.0882 2.0213 2.2022 2.1229 2.3174 2.2257 2.4325 2.3259 2.5469 2.4291 2.6621 2.5297 2.7764 2.6303 2.8900 2.9410 3.0566 3.4261 3.2146 3.9075 3.4559 3.7025 4.5877
ALL VALUES
1
EDITION HEAVY
LOADING
Weight with l/2-in ice
4-lb/ft2 wind
Resultatlt weight’
2.1928 1.9861 2.1106 2.2839 2.2305 2.4170 2.3491 2.5462 2.4648 2.6762 2.5816 2.8056 2.6951 2.9337 2.8116 3.0622 2.9249 3.1897 3.0372 3.3160 3.3814 3.5186 3.9180 3.6944 4.4341 3.9578 4.2294 5.1878
.7207 .7133 97217 .7320 .7377 .7487 .7530 .7643 .7673 .7793 .7817 .7940 .7953 .8080 .8090 .8217 .8220 .8353 .8340 -8483 .8673 .8937 .9207 .9123 .9523 .9340 .9600 1.0337
2.6082 2.4103 2.5306 2.6983 2.6493 2.8303 2.7668 2.9585 2.8815 3.0874 2.9973 3.2158 3.1100 3.3430 3.2257 3.4706 3.3382 3.5973 3.4497 3.7228 3.7909 3.9303 4.3247 4.1054 4.8352 4.3666 4.6369 5.5898
ARE IN POUNDS PER FOOT.
Table Cd.-Conductor
and overhead ground wire values for NESC light, medium, and heavy loading f U.S. customary&Continued
I Wire type and size
NATIONAL I. I GHT
Weight with no ice
ELECTRICAL MEDIUM
LOADING
9-lb/ft2 wind
Resultant weight l STEEL
3/8 3/8 ‘/I6 ‘46 l/2 y/2
INCH INCH INCH INCH INCH INCH
HS EHS HS EHS HS EHS
.2730 .2730 .3990 .3990 .5170 .5170
.2700 .2700 .3263 .3263
.3713 .3713
.1310
8M
16M 18M 20M 25M 7 NO. 7 NO. 7 NO. 7N0. 7N0. 7N0. 7N0. 7N0.
12
11 10 9 8 7 6 5
1650 : 2080 .2320 .2620 .3060 .3470 .4750 .1036 .1306 1647 : 2076 .2618 .3300 .4163 .5249
’ Includes 0.05 NESC constant. 2 Includes 0.20 NESC constant. 3 Includes 0.30 NESC constant.
.2040 .2295 .2573 .2723 .2895
.3128 .3330 .3893 1815 : 2040 .2295 .2573 .2888 .3248 .3645 .4095
Weight with l/4-in ice
STRAND
.2924 .3327 .3808
.4077 .4405 .4875 .5309 .6641 .2590 .2922 .3325 .3806 .4398 .5130 .6033 .7157
1977
CODE LOADING
4-lb/ft2 wind
OVERHEAD
.4340 .4340 .5654 .5654 .6865 .6865 ALUMOWELD
10M 12.5M 14M
SAFETY
GROUND
HEAVY
Resultant weight’ WIRE
.3117 .3117 .3317 .3317 OVERHEAD
.2933 .3379 .3924 .4226 .4598
.5134 .5628 .7142 .2566 .2929 .3376 .3920 .4593 .5424 .6452 .7725
.2573 .2687 .2810 .2877 .2953 .3057 .3147 .3397 .2473 .2573 .2687
.2810 .2950 .3110 .3287 .3487
Weight with l/2-in ice
4-lb/ft2 wind
Resultant weight”
.8079 .8079 99806 .9806
.4533 .4533 .4783 .4783 .4983 .4983
1.2264 1.2264 1.3910 1.3910 1.5404 1.5404
.4240 .4353 .4477 .4543 .4620 .4723
1.0439 1.0959 1.1583 1.1930 1.2352 1 h2956 1.3509 1.5190 1.0005 1.0435 1.0957 1.1580 1.2343 1.3280 1.4425 1.5835
1.1359 1.1359
GROUND
LOADING
(7-WIRE)
.2867 .2867
STRAND
EDITION
WIRE .5902
.6317 .6827 .7113 .7465 .7975 .8448 .9908 .5564 .5899 .6315 .6823 .7459 .8252 .9241 1.0475
ALL VALUES
.6112 .6663 .7323 .7688 .8131 .8764 .9342 1.1088 .5651 .6108 .6660 .7319 .8123 .9103 1.0296 1.1755
.4813 .5063 .4140 .4240 .4353 .4477 .4617 .4777 .4953 .5153
ARE IN POUNDS PER FOOT.
<
Barometric pressure, 426 Basic impulse insulation level, Broken conductor, 56 sags and tensions, 29 thesis, 307 unbalanced condition, 67 Building clearances, 274
104
California safety code (see Safety codes) Carroll, J. S., 284 catenary curve. 14, 17, 22, 25, 28 charts azimuth, 342
pyiw.
127
structure limitation, 127 Circumference tables for wood Class of poles, 156 by pole lengths, 273 Clayton, J. M.. 111 Clearance patterns. 103, 111 construction of, 121
poles,
351
Clearances air-gap, 103, 109, 112 at conductor transposition, 7 between conductors, 51 climbing, 2 conductor to building, 274 conductor to ground, 34, 38, 266 conductor to guy, 130, 131 (Calif.) conductor to steel structure, 112 conductor to wood structure, 129, 131 (Calif.) crossings, 273 curves for spotting, 266 midspan, 110 models for, 6 NESC, 34 patterns, 103, 111 right-of-way, 274 Codes (see Safety codes) Concentrated loads, 29, 99 Conductor broken, 29, 56, 307 clearance patterns, 103, 111 clearances (see Clearances) creep, 9, 13, 26, 442, 452 data tables, 430, 442, 452, 462, 466, 470, 474 effect of temperature change, 30 elastic limit, 13 electrical conductivity, 9 elongation, 10 galloping, 50, 284 ice and wind load, 27, 470, 474 lightning protection, 103 loading conditions (see Loading conditions) loading constants, 27 mechanical strength, 9 modulus of elasticity, 13 proportional limit, 13 sags and tensions (see Sags and tensions) sag template, 32 selection of, 9 stress-strain curves, 10 ultimate tensile strength, 13 uplift, 268 vibration, 282 working limit, 13 yield strength, 13 Cone of protection, 108 Construction single wood-pole, 4 type of, 4, 128 Copperweld sag charts, 29 Corona, 284 loss, 9 with armor rods, 282 Cost estimates, 2 Creep, 9, 442, 452 defdtion, 13 in final loading condition, 26 Crossings, 273
Dancing conductors (see Galloping Data summary form. 23 Davison, A. E., 50
479
conductors)
480
TRANSMISSION
Den Hat-tog, J. P., 50 Density, 426, 427 Department of Energy, iii Design instructions, 21 Design tensions (conductor), 128 Distance between low points, 128 Double-circuit steel structures. 6 Douglas fir pole circumferences, 351 Drawings guying chart, 209 plan and profile, 32, 266 project, 4 sag template, 32, 266 standard, 4 steel structure limitation chart, 147 wood structure limitation chart, 205
clearance to conductor, 130, in poor hearing soil, 274
Factor of safety California, 13 1 insulation withstand, 105 steel construction, 127 wood construction, 129 Farr. Holland H., iii Field data, 1 Final loading condition, 26 Final modulus of elasticity, 13, 26, 442, 452 Flashover, 103 characteristics of insulators and air gaps, 423 critical impulse, 120 lightning, 107 60-He wet, 120 surge, 104 switching values of air gaps, 424 Flattop construction, 4 Footing resistance, 103, 111 surge resistance, 111 Fortescue, C. L., 106
GUYS calculations
for,
169
131 (Calif.)
H-frame wood-pole structures, 4 guying, 169 maximum design tensions, 128 maximum low-point distance. 153 maximum sum of adjacent spans, 156, stresses, 213
Effective span, 8 Ehrenburg, D. O., 40 Elastic limit, 13 Electrical conductivity, 9 Ellipses, 130, 184 Elongation, 10, 26 Engineers cost estimate, 2 Equations (survey), 300
Galloping conductors, 50 half- and full-sag ellipses, 130 vibrations, 284 Grading the transmission line, 268 Graphic method for sag-tension calculations, Ground clearances, 34, 38 on side slopes, 273 Ground resistivity. 111, 344 Guying chart. 127 eonstrnction of. 186
LINE DESIGN MANUAL
30
162
Ice loading, 27, 470, 474 Impulse insulation level (value), 104, 112, 423 Inclined spans, 38 sags and tensions, 28 stringing, 292 Initial loading condition, 26 Initial modulus of elasticity, 13, 26, 442, 452 Insulation, 103 air-gap, 103, 112, 423 basic impulse level, 104 safety factors, 106 selection tables, 107 withstand, 105 Insulator effect, 77 extra units, 106 factor of safety, 128 flashover characteristics, 423 impulse insulation value, 104, 112. 423 offset, 292 sideswing, 51, 268 strength requirement for steel structures, 135 swing angle, 105. 112, 129, 131, 133, 142 vertical force, 141 Isoceraunic level. 103
Kientz,
H. J., iii
Land sections, 340, 341 Level spans sags and tensions, 28 Lightning direct-stroke theory, 106 impulse voltages, 103 protection, 103, 106 Line deflection angle, 128 near a substation, 274 resultant force, 169 Loading conditions, 2, 128 ACSR, 27 California, 3, 27, 130 final, 26 for galloping, 50 full load, 132 initial. 26 NESC. 9.26 overhead ground wire, 28 Loading constants, 27
INDEX Locating structures (see Structure Long-span construction, 7 Losses corona, 284
Martin, J. S., 29 Martin’s Sag Calculating Tables, Mass per volume (wood species), Metric conversions, 431 Midspan clearances, 110 Models for clearances, 6 Modulus of elasticity, 13, 26 Mohr, R. D., iii Moment of resistance ANSI standard, 348 formula, 343 USBR standard, 345
spotting)
29 427
NESC, 2.93 clearances, 34, 273 loading conditions, 27, 132 Nomenclature steel structures, 5, 133 wood-pole structures, 4, 149 Normal span, 7
Oscillations (see Galloping conductors) Outages lightning, 111 Overhead ground wires, 108 data tables, 462, 466, 470, 474 loading conditions, 3, 27 midspan clearances, 110 Overvoltage6 causes, 105 liihtuing, 103 power frequency, 103 switching surges, 103
Parabola. 14, 25, 28 Peek, F. W., 284 Permanent set, 10, 26 definition, 13 values for ACSR, 442, 452 values for Alumoweld strand, 419 values for steel strand, 420 Peterson, W. S., 284 Pole circumferences Douglas fir, 351 southern yellow pine, 351 western red cedar, 385 Pole ground wire. 128 Power frequency operating voltages, 103 causes of overvoltages, 105 Power loss. 284 Pressure due to wind, 429 Priest, F. F.. iii, 99 Proportional limit, 13
Protection lightning, 103 Proximity effect, 104
Relative air density, 426 Relative mass density (wood), 427 Resistance maximum moment of, 343 Resistivity, 111, 344 Restriking, 104 Right-of-way, 274 Rockwell, M. M., 284 Ruling span definition, 8 for stringing, 292
Safety codes, 2, 28 California, 2, 26, 35, 130, 273 NESC, 2,26, 132, 273, 275 Safety factor (see Factor of safety) Sags and tensions, 25, 29 calculation form, 33 calculations for, 30, 38 catenary versus parabola, 14, 25, 28 Copperweld charts, 30 Ehrenburg’s method. 40 inclined spans, 28, 38, 292 initial and final loading conditions, 26 insulator effect on, 29, 77 level spans, 28 loading conditions, 2, 27 loading constants, 27 Martin’s tables, 29 maximum tensions, 3, 27 spans adjacent to a broken conductor, 29, 56 spans with concentrated loads, 29, 99 stringing, 292 temperature for loading conditions, 3, 27 Sag template, 32 broken conductor, 67 for structure spotting, 266 inclined span, 38 Scale factors for structure limitation charts line deflection angle, 141 (steel), 151 (wood) low point, 140 (steel), 149 (wood) sum of adjacent spans, 141 (steel), 152 (wood) Section numbering, 340 Selection of conductor, 9 ruling span, 8 type of construction, 4 Sheaves for stringing, 292 Shield angle, 103, 108 Sideswing, 51, 268 angle, 105, 112, 129, 131, 133, 142 SI metric, 431 Single-circuit steel structure, 5, 133 Single span limits on structures, 183 Single wood-pole structure, 4 Southern yellow pine pole circumferences, 351
481
482
TRANSMISSION
Spacing between conductors, 51 SpaDS adjacent to broken conductor, 29, 56 effective, 8 inclined, 28, 38 level, 28 maximum permissable, 51 normal, 7 ~lins, 8 substation approach, 273 with concentrated loads, 29, 99 with unbalanced loads, 29, 67 Standards for preparing structure limitation chart, 127 Station equations, 300 Steel strand, 7-wire data tables, 465. 469 ice and wind load. 27,473,477 initial and foal modulus, 13, 26, 422 loading conditions, 2, 26 loading constants, 27 loading tables, 473, 477 permanent set, 420 sags and tensions (see Sags and tensions) stress-strain mtrves, 14 Steel structures (see Structures) Strength basis for calculation, 128 determining low-point distance, 153 determining span length, 183 determiniq sum of adjacent spans, 156, 162 limitation of single insulator string, 166 requirements of insulator string, 135 (steel) Stresses conductor, 10 voltage, 103, 112 wood-pole structures, 213 Stress-strain curves, 10, 15 Stringing, 25 sag data, 292 Stroke current, 103 Structure limitation chart, 127 angle of bias lines, 142 (steel), 152 (wood) angle of bias lines for insulators, 168 basis for strength calculations, 128 clearance patterns, 111 conductor calcuhxtions, 135 (steel), 150 (wood) conductor clearances, 129, 131 (Cahf.) construction of, 145 (steel), 185 (wood) data required for construction of, 132 (steel), 146 (wood) effect of hold downs, 156 full-load conditions, 132 guying, 169, 176, 179, 182 insulator swing angles, 142 (steel) insulator swing limits, 129, 131 insulator vertical force, 141 (steel), 150 (wood) line deflection angle scale, 141 (steel), 151 (wood) loading conditions, 3, 128 low-point distance, 153 low-point scale, 140 (steel), 149 (wood) maximum design tensions, 128 safety factors, 128, 131 single span limits, 183 standards to follow, 127
LINE DESIGN MANUAL strength of insulators, 105 (wood), 135 (steel) structure design, 130 (Cahf.) sum of adjacent spans, 156, 162, 164 sum of adjacent spans scale, 141 (steel), 152 (wood) wind force on pole, 156 Structures adjacent to substation. 273 basic types of, 4 double-circuit steel, 6 for special conditions, 4, 6 functional classes of. 4 gr0”miing of, 111 H-frame wood-pole, 4, 149 insulation for, 103 liihtning protection, 103 single-circuit steel, 5. 133 single wood-pole, 4 spotting, 266 stresses in wood-pole, 213 Structure spotting, 29, 266 sag template, 32 uplift, 268 Substations, 29, 273 Summary form, 23 Sum of adjacent spans, 128 (steel), 156, 162 (wood) Survey equations, 300 Suspension clamp, 292 Suspension insulator string flashover characteristics, 423 switching surges, 103 Switchyards (see Substations)
Taps, 29, 99 Temperature coefficients of expansion, 428 for loading conditions, 3, 27 Template (see Sag template) Tensile testing, 10 Tension (see also Sags and tensions) calculation of, 29 conductor, 3, 25 maximum design. 128, 130 overhead ground wire, 28 Tie-downs, 29, 99 Township, 340 Transmission lie data summary form, 23 equations, 300 grading the line, 268 Transpositions, 6 Triangular construction, 4 Types of construction double-circuit steel, 6 H-frame wood-pole, 4 selection of, 4 single-circuit steel, 5 single wood-pole, 4
ultimate tensile strength, defhtion, 13 Uplift (upstrain). 268
422,
462,
466
INDEX USBR standards augle of protection, 110 clearance patterns, 111 conductor and overhead ground wire design criteria, 3 conductor clearance to buildiugs, 275 conductor clearance to guy wire, 130, 131 (Calif.) conductor clearance to structure, 129, 131 (Calif.) wowings, 273 ellipses, 50 factors of safety for wood construction, 129, 131 (Calif.) full-load conditions. 132 insulation coordination, 105 insulator swing limitations, 129 (wood) maximum moment of resistance for wood poles, 345 structure limitation chart, 127 structures and spans near substations, 273
Vibration dampers, 282 Voltagc stress, 112 lightning impulse, 103, 105 power frequency, 103, 105 switching surge. 103
Wave shape, 103 Western Area Power Administration, iii Western red cedar pole circumferences, 385 Wind force on ~004 pole, i56 loadiug on conductor, 3 pressure on projected area, 429 Wiieauckas, G. R., 29, 56, 307 Wood-pole structures basis for strcugth calculation, 128 classes of poles, 156, 273
483
climbii clearance, 2 conductor calculations, 149 conductor clearance to guy wire, 130, 131 (Calif.) conductor clearance to structure, 129, 131 (Calif.) designations and types, 149 effect of hold downs, 156 full-load conditions, 133 guying, 169;171, 176, 179, 182 H-frame, 4, 128, 149 insulator string strength, 166 insulator swing limits, 129, 131 insulator vertical force, 150 loading conditions, 3, 128 low-point distance, 153 mass per volume of wood, 427 moment of resistance, 343 pole circumferences, 351, 385 relative mass density of wood, 427 safety factors, 129, 131 (Calif.) single, 4 single span limits, 183 stresses in, 213 structure limitation chart, 146, 185 sum of adjacent spans, 156, 162, 164 tensions (design), 128 type of construction, 128 wind force on pole, 156 Wood species mass and density of, 427 Working limit, 13
X-braces,
4
Yield strength, 13 Young, F. S., 111
