70
702
___________________________________________________________________________________
.
.
.
:
-
-
-
-
-
-
-
:
:
--4
--4
--4
2--4
--4
3--4
2--4
4--4
:
-2-4
-2-4
-2-4
--2-4
-2-4
2--2-4
-2-4
3--2-4
-2-4
4--2-4
2-2-4
5--2-4
2-2-4
6--2-4
2-2-4
7--2-4
2-2-4
8--2-4
2-2-4
9--2-4
2-2-4
1--2-4
2-2-4
--2-4
3-2-4
2-2-4
I
:
:
-3-4 -3-4
-3-4
-3-4
2-3-4
-3-4 -3-4
3-3-4 4-3-4 :
-4-4
-4-4
-4-4
2-4-4
2-4-4
3-4-4
2-4-4
4-4-4
3-4-4
5-4-4
3-4-4
:
6-4-4
-5-4
-5-4
-5-4
--5-4
-5-4
2--5-4
-5-4
3--5-4
2-5-4
3-5-4
2-5-4 3-5-4
3-5-4
)(
-3-5-4
6-5-4
)2(
2-3-5-4
8-5-4
)3(
3-3-5-4
9-5-4 9-5-4
4-5-4 )QL(
II
-4-5-4
:
1-5-4
2-4-5-4
1-5-4
)Qt(
3-4-5-4
1-5-4
5-5-4
-5-4
6-5-4
-5-4 -5-4
-6-5-4 2-6-5-4
2-5-4
3-6-5-4
3-5-4
4-6-5-4
4-5-4
7-5-4
4-5-4
8-5-4
4-5-4
9-5-4
5-5-4
1-5-4 :
-6-4 -6-4
-6-4 --6-4
-6-4
2--6-4
-6-4
3--6-4
-6-4
2-6-4
3-6-4
-2-6-4
3-6-4
2-2-6-4
4-6-4
3-2-6-4
4-6-4
3-6-4
4-6-4
-3-6-4
5-6-4
2-3-6-4
5-6-4
3-3-6-4
6-6-4
.
III
4-3-6-4
:
5-6-4
9-3-6-4
6-6-4
4-6-4
7-6-4
5 – 6- 4
8-6-4 8-6-4
8-6-4
6-6-4 7-6-4
8-6-4
9-6-4
9-6-4
9-6-4
-9-6-4
21-6-4 21-6-4
3-9-6-4
2-6-4 2-6-4
2-6-4 22-6-4
2-9-6-4
1-6-4
-1-6-4
2-1-6-4
3-1-6-4
23-6-4
4-1-6-4
IV
:
23-6-4 26-6-4 26-6-4
-6-4
2-6-4 -2-6-4
28-6-4
2-2-6-4
28-6-4
3-6-4
: -7-4
-7-4
2-7-4 3-7-4
2-7-4 3-7-4
3-7-4
-3-7-4
4-7-4
2-3-7-4
5-7-4
)q(
4-7-4
5-7-4
-4-7-4
5-7-4
V
7-7-4
k
V
2-4-7-4
5-7-4
:
8-7-4
6-7-4
8-7-4
-6-7-4
8-7-4
Ch
2-6-7-4
3-7-4 3-7-4
Cv
3-6-7-4 7-7-4
3-7-4
-7-7-4
4-7-4
2-7-7-4
4-7-4
8-7-4 :
-8-4
-8-4
-8-4 -8-4
2-8-4 3-8-4
-8-4 2-8-4
4-8-4
5-8-4 :
-9-4
-9-4
-9-4
--9-4
-9-4
2-9-4
2--9-4
VI
3--9-4
:
4-9-4
4-9-4
4--9-4 2-9-4
5-9-4
-2-9-4
5-9-4
6-9-4 6-9-4
7-9-4
(
2-2-9-4 3-9-4 -3-9-4 2-3-9-4
) 9-9-4
4-9-4
9-9-4
-4-9-4
3-9-4
2-4-9-4
9-9-4
-
3-4-9-4
21-9-4 2-9-4
4-4-9-4 5-9-4
2-9-4
6-9-4
2-9-4
7-9-4
22-9-4
8-9-4
22-9-4
-8-9-4
23-9-4
2-8-9-4
29-9-4
9-9-4
31-9-4
(P-)
3-9-4
32-9-4 32-9-4
)
(
1-9-4 -9-4 2-9-4 3-9-4
35-9-4
4-9-4
VII
:
35-9-4
-4-9-4
36-9-4
2-4-9-4
37-9-4
38-9-4
3-4-9-4
5-9-4
38-9-4
6-9-4
38-9-4
7-9-4
39-9-4
8-9-4
39-9-4
-8-9-4
39-9-4
2-8-9-4
4-9-4
3-8-9-4 ) -9-4(
43-9-4 )
TB
T
( :
-1-4
-1-4
-1-4
-1-4
-1-4 2-1-4
2-1-4 3-1-4 4-1-4
5-1-4
) Underpass ( 2-1-4
6-1-4
2-1-4
7-1-4
2-1-4
8-1-4
3-1-4
3-1-4
9-1-4 1-1-4
VIII
:
3-1-4
-1-1-4
3-1-4
2 -1-1-4
4-1-4
3-1-1-4
5-1-4
-1-4
5-1-4
--1-4
5-1-4
2--1-4
6-1-4
6-1-4
2-1-4
6-1-4 8-1-4 8-1-4
8-1-4 9-1-4
3-1-4
4-1-4
5-1-4 6-1-4
7-1-4 8-1-4
IX
:
-
-
: .
-
.
.
-
(Working Loads)
.(Ultimate Loads) -
-
-
-
.
:
(kg)
kg= 1 9.80665 N
(4-1-1)
:
N
. :
- -
:
10 kg =N 1
(4-1-2)
1t=1000kg=10kN
(4-1-3)
.( )
kN
t
-
.
.
- -
-
:
- -
- - -
. . - - -
: .
-
.
-
.
- - -
.
- - -
.
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:
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. - - -
. - - -
. - - -
. - - -
. - - -
.
- - -
:
- -
:
:
-
. :
-
.( ) - -
:
(
kg, t
( )
N, kN
)
–
( )
– :
a
(
/ )
f0
q
( /
)
Q
(
b
(
D
(
)
)
)
F I L (
QL Qt Qv r
)
( ) ( )
( )( ) (
- -
)
:
W wL
( (
)
C2 -
C1-
a a max
/
b C
( )
d e
(
)
GA
A
GB
B
GM h I L L Lo Qvk or Qv
( (
) )
( )
Qh Qr Qvi qvk
( )
R S S1 S2
- -
(
)
)
:
V
(
/ )
v
/
vi
/
W
( )
α β no
nT
(
)
(first bending natural frequency) (
)
(first torsional natural frequency) (
)
δ0 ystat ydyn
" i ζ m :
Ah
( )
Av
( )
b Ch Cs Cv
Ct
- -
:
dm e*
. Fx
( )
Fv
( )
k q
( / )
V
( /)
Sp
/
,
.
z0 z :
Aeff Ag ag avg as
h
Cu
( / )
ds
de
dg ds ds
- -
Ls
:
dr Ieff Ig Ed
ET E(FX)
X
E(FY)
Y
E(FZ)
Z
Fa F Fi Fi
(i) r
(r)
g H h hi
(i)
HS K Kh Ls
(
Ls1 M M n NEd NSPT
- -
)
:
NS pi
(i )
po R
(
)
Ra Re S Sa Sd (T) Sd (T1)
T1
Se (T) Sve (T) T TB,TC TD Ta Ti T1 VS,30
(
Vi
NS
/
)
i
W Wa wi za
(i)
α ,
- -
W
:
a I i
(i)
v :
Ca Cb V P1 P2
( (MPa) (MPa)
P1
- -
/
)
:
- -
. - ( - - ) .
. - -
– - -
.
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:
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:
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(
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:
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,
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(
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-
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(
)
(
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(
)
(
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:
- -
.(A-
) :
- -
: :( q ) .
( /
-
) / .
(
.
:( Q )
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:
-
)
.
. :
.
( - - )
-
.(
)
-
.(
)
-
. .
- -
,
-
:
( - - ) :
- -
.
:
. - -
-
(q)
%
. - -
% .(Q)
-
.
-
.
(out of plane)
:
- : ( /
) /
(q)
-
% . - -
- -
:
- -
%
- . .
:
- -
(Railings) .
–
:
- -
. )
-
.
(
:
. .
,
,
-
.
-
: a = 0.5
(
/)a
(4-4-1)
f0
.
f0
: -
.
( )
- -
:
- .
…
.(B -
) - - -
-
)
-
(...... . - - -
. - - -
.
- -
:
(
2-5-4 :)
- 4(
.
)W(
.
-1
-2
)
( .) -1-5
.
.) - 1- 5- 4(
-3
WW L
L
.) -1-5-4(
WLW
-4
L
W
W
W
) (
)(
)1-5-4(
2-5-4
:
. . . .
(wL)
:
- -
: :( )
-
:( )
-
.
. .
:( )
-
:( )
- - -
( )
-
( - - ) : :( ) (
-
)
/
( .
) ( /
- -
)
:
. :( ) ( )
/
-
) (
,
)
.
(
/
:( ) ( /
) (
,
)
.
( / ( /
.
) /
,
) -
,
( / .
-
) /
-
,
.
( )
-
.
-
- -
:
/
/
WL
/
WL
(W)
/
WL /
b Va a b le
Variable to verify Variable verify criticalconditions conditions critical
Variableto to verify verify Variable criticalconditions conditions critical
b
/ /
b
( )
( - - ) .
.( - .( - -
-
)
)
-
,
)
,
.
,
.( - . .
( - - )
.
(E - )
- -
–
:
:
( - - )
) ( /
) / (
(
(
)
(
)
)
( )
(
)
( )
(
) ,
( )
(
)
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(
) ,
( )
(
)
( )
(
) ,
( )
( - - ) :( )
- - -
.
( )
. .( - -
)
( , × ,
) -
.
-
- -
:
:
(I)
0.3 (1-D/6) =I
(4-5-1)
: I D
.% ( )
(D = 0) ( )
-
.(Orthotropic decks)
( )
( - - )
- -
:
:( ) /
- - -
,
.
( /
)
. :
- - -
( )
.(
, × , )
( )
-
.( ,
×
, )
-
)
(Composite Bridge) ( .( - - )
(Orthotropic)
:
:
( - - ) (Composite)
- -
:
)6-5-4(
(Orthotropic Deck)
:
4-5-4
:)QL( .
1-4-5-4
-1
-2
.( L (
.) 96( 966 = 360 QL+ 2.7L
(KN)
–3
(4-5-2)
: .) (
) 18( 186
. 2
9-5-4
=
L
–4
:
- - %
(
) . :(Qt)
- - –
. .
( - - ) .(Qt)
–
( – - )
r ≤ 200 m 200 < r ≤ 1500 m
Qt = 0.2 Qv Qt = 40 Qv/r
r >1500 m
(kN) (kN)
Qt = 0
: .(
)
r
.(kN) ( )
Qv
.(
) .(
:
- -
%
- -
, )
....
:
-
)
-
.( . - - - : .
.
- - . (
.
( - -
) )
.
( .(
)
(
)
-
) .
- -
:
-
-
( - -
) - - -
( .
)
.
,
.
,
(
, )
.( - - )
- -
:
45.0°
45.0°
( - - ) - - .
,
.
( F) - )
-
. .
( -
.(F)
( - - )
(
)
(
)
(
)
(
)
- -
:
.
- 7(
) 22,5 ( 225
.
.
-4
)2--3
-3
-5
)Railings(
7-5-4
.
–
:
3
8-5-4
:
-2 -
2
366( /
-1
-
.
.) /
.
2
-
. 9-5-4
.
14-5-4
:
- : – . .
– . .
–
/
– – .
-
)
– .( ..... .
-
–
- -
:
- -
. - - -
. - - -
. - - -
. - Substructures
(
) LM71 ( - - )
- -
:
: )
,
. Qvk
(/
qvk
(
) /
.
.( /
) /
-
(LM71) )
(
( - - ) ) (
,
α
,
. α
. Continuous
SW/0
/
Alternative load
,
bridges
(/ .( - - )
- -
, )
:
LM71
. SW/0
(SW/0)
Stringers
( - - )
Cross Girders
Main Girders
. :
- - -
: .
%
(
)
-
%
% .
:
- - -
.
. .
-
- -
:
-
(LM71 & SW/0)
.( - - - ) -
qvk = 10 KN/m
. .(
- - - ) ( - - - )
:
.SW/0
LM71
-
.( - - - ) :
- - -
(Railings) .
– - - - –
: .(inertial response – impact) ) )
(resonance) (natural frequency)
( .( .
- -
:
. – . - - : . .
-
(influence line)
L
-
.
-
.
-
.
.
(damping)
-
.(vertical irregularities)
-
(Sprung/ unsprung masses)
.(suspension)
/
(supports)
-
. /
.(suspension)
.
- - -
.( - - )
-
(dynamic impact factor) I .( - - - ) .( - - - )
-
- -
:
:
-
.( - - - )
-
.(
-
- - - )
.( - - - )
I
.(
- - - )
I
( - - - ) .
-
/ .
- - -
flow ) ( - - )
(chart : V
/
L no
(first bending natural frequency) .
(
) nT
(first torsional natural frequency) .
(
) .
/ .C1-
- -
v (v/ no) Lim
:
>v /
( )
( )
no
nT >
no
F2 F1 (
)
V/no < (v/no)lim ( )( )( )
( )
- - -
.
.
' φdyn
φ
( - - )
- -
:
: .(rigid supports)
(skew)
.C1-
F2 F1
-
(frequent operating speed of a real train) .C1.(
(
- - - ) \ dyn -
- - - )
(very good standard of passenger comfort) / . ( - - ) . (1)
no
-
no
-
/ .( - - )
: no
(Hz) = 17.75/ √δ0
(4-6-1)
: permanent )
δ0
(actions .
- -
:
] z H [ ˳
n
1
(2)
L
m
: (1) (2)
L
( - - )
n0
(dynamic enhancements)
:
n0 (track irregularities)
n o 94 . 76 L 0 .748
(4-6-2)
- -
:
:
n0
no 80/ L {for 4m ≤ L≤ 20m} (4-6-3) n o 23.58L0.592 {for 20m < L ≤ 100m}
: n0 L
L
.(
)
:(φ)
- - ( - - )
. () (4–6–4b)
(4–6–4a)
I
) .( 0.73
2.16
(4–6–4a)
L 0.2
(4–6–4b)
I 1
I
%
% L
,
:
- -
, L
:
:( – - )
Lφ Lφ :( Orthotropic deck Plate
)
–
(deck plate )
– ,
– –
,
–
(deck plate )
+
–
+
–
, (Open Timber Floor) :
–
(Stringers )
+
–
(End Bracket)
–
(Cross Girders)
–
, (Ballasted Floor) :
–
:
( e 0.5m)
( e 0.5m)
e
(Web)
:( - - )
- -
:
Lφ –
) (
– (Through &Semi-Through) +
–
,
–
,
– :
X( ,
,
,
–
, )
–
/
,
.
,
- - (I)
. - - -
(Ballast) (I)
%
(I)
%
% . ,
(I)
(I)
- -
:
.
- - -
- - - - - .
(Frequency
limits)
-
/
( - - ) .( - - - ) .
- - - -
.
......
.( - - - - )
) .(
/ -
LM71, SW/0
-:
(
.
- - - ) -
.( - - - )
.
- - -
:
-
.
-
.(4–6-4a)
( - - - )
- -
:
( - - )
)
.( ( - - - )
-
Resonance
.
:
.Ballasted track
/
.
,
/
-
,
-
) :
( .
-
Fundamental mode of
.
vibration
. : \ dyn max
(
ydyn y stat
)
1
(4-6-5)
ystat
ydyn
.( Real Train )
: x (1
(
SW/O
LM71
- -
\ dyn
\
\
2
)xΦ
)
:
)
"/2)
(........ )
"
C2 -
.(
.
- - -
(stress range)
: . .(Resonance)
-
.(Resonance)
-
(Frequent Operating Speed)
.
C1 -
( - - ) ( - - )
vi n o xλi
/
≤
(4-6-6) vi ≤
(4-6-7)
: .( / ) .(unloaded) :
vi no
(Frequency of excitation) λi d / i
- -
i
:
: d
(Regular spacing of groups of axles) =
i
.
- – – (C)
: WV 2 C 127 R
KN
(4-6- 8)
: C W
(
/ )
V R
– – :
( - - ) – . – .( I )
- -
:
– % .
%
: :( - - ) ( ( ( ( ( ,
)
(
) Lo
)
,
, )
,
,
)
,
,
– Lo)
+
,
,
( , - ) , + ( ) Lo
,
(
, )
(
, )
,
,
(
)
,
,
( ,
– L o)
( ,
– L o)
,
+ +
,
- -
:
- - - . (
)
. (
)
. . - - (
) .
/ - -
. . . - . , : .
– – .
- -
:
)
– ( .
( /
)
/ :
:
- - - -
.
.( - - )
( - - )
- -
:
: : Qvi .
: :
(
a
- - -
)
. :
-
- - -
-
)
-
- )
( .
( -
.
Load on sleeper
Refrence plane
( - - )
- -
:
- (
- -
) .( - - )
Refrence plane
( - - ) : A
GA
B
GB M R GM e S
- -
:
(
-
- -
-
- -
)
.( - - )
Refrence plane
( - - )
(
)
- ) .(
- -
-
:
Refrence plane
(
(
- - )
-
- -
(
- - )
)
.( - - )
- Clearance
(
,
(
- - )
) .
- -
:
(
( ,
)
)
(
- -
- - )
:
( ,
)
(
- -
- - )
:
( Derailment of trains)
- -
. -
- -
: .
(
- - ) (1.4*α)
(1.4) .
(S1 = 1.5 S) . .
.(
- -
- - )
:
S1
S1
S
S X 0.7 x LM
X 0.7 x LM
S2
S2
S
(
- - ) :
. . .
(
- -
- - )
=
S
=
S2
=
LM
:
-
- -
. . %
-
.(Guard Rails) - ( Loads from R ails- Bridge deck interaction )
. . . ( - - - ) .
EN 1991 - 2 : 2003 (E)
- -
:
- . . .
- - - - .( - - )
:
- - .
.
-
%
- - .( - - ) - - :
. -
.
- -
:
. -
. . . - -
.(
)
(
) -
.
/ . -
.
- -
:
- - - ) .(
( - - ) (X-Direction)
- - -
: Fx
Ch Cs kqAh
(4-7-1)
: .( )
Fx
( / )
q
.( - - ) k
.( - - - )
- -
:
Ch
.( - - - ) Cs
.(turbulence) , .
( - - - )
, ( )
Ah
. - - - -
: Fv
Cv Cs k qAv
(4-7-2)
: Fv
.( ) ( / )
q
.( - - ) k
.( - - - )
Cv
. - - .( - - - )
- -
Cs
:
( )
Av
.( - - ) (q)
:
- -
( / )q
- - -
q 0.5 x10 3 ρ S PV 2 Ct
(4-7-3)
: ( /)
V
( - - ) .
% . /
,
Ct
.( - - ) Sp
-: .
,
=
.
,
=
.( .
- - - ) ( - - )
.
- -
V
- - -
:
( - - )
V
( /) /
/ /
/
/
/
/
/ /
/ /
/
/
/ /
/ /
( - - )
(Ct) Ct
, % : : ,
%
- %
,
%
- %
,
%
- %
,
%
, ,
- -
:
- -
k
- - . - - -
k (ground roughness length) (z0) (open
:( )
exposure)
-
. :( ) .
-
(suburban exposure)
:( ) .
-
(city center exposure)
.( - - )
- - -
k
( - - )
k
,
,
,
k
(z0) z
,
,
,
,
,
,
-
,
,
,
-
, ,
, ,
, ,
-
,
,
,
-
,
,
,
-
,
,
,
-
- -
-
:
k
- - -
z
.( - - )
( - - ) - - - Cv
( - - )
.
Ch
( - - ) - - -
Ch
Ch
( - - )
(d m
b
.( - - )
- -
) ( - - )
:
( - - ) (dm)
( - - )
(dm) d1
-
d2
-
d+3.0 m
-
d+1.8 m
-
d+3.5 m
-
- -
:
b
b
b
b
b
b
b
b
b
b
b
b
b
b
Truss or Plate Truss or Plate
( - - )
- -
:
- - - ( - - )
Ch
.( dm
)
b
( - - )
Ch
b /(dm)
Ch
* 1.30
4≤
1.65
3
1.95
2
2.20
1
2.30
0.80
2.40
≤0.60
-
2.00
4≤
2.20
>4
*
-:
: .
,
Ch
.
,
Ch
. ,
-
Ch
- -
:
- - - ( - - ) ( - - )
Ch
dm
)
b *
.e
( - ( - - )
Ch windward truss
e
0.95 1.00 1.00 0.95 0.95
1.90 1.80 1.70 1.70 1.60
*
0.10 0.20 0.30 0.40 0.50 *
e
. ( - - )
Ch leeward truss
e
0.95 0.93 0.85 0.67 0.57
1.90 1.67 1.45 1.19 0.90
*
0.10 0.20 0.30 0.40 0.50 *
e
.
- -
:
- - -
Cv
( - - ) .( - -
Cv
dm
)
b
( - - )
Cv Cv
b /(dm)
0.90 0.86 0.82 0.78 0.75
4≤ 3 2 1 <1
- - - (Open parapet or barrier) .( – - ) .
Open parapet
Solid parapet Noise barrier Solid safety barrier
open safety barrier
( - - )
- -
:
, .
, . -
Truss bridges
:
(
)
.
-
.
(Open parapet or barrier) .( – - ) . - - )
. (
( )
(
) . . - -
- ) .( - - )
Ch
- -
Cs =1
.( -
:
( - - )
Ch C h for h/b ratios of
40
20
10
6
4
2
1
t/b tt
Wind Wind
b
2.1 1.9 1.7 1.6 1.5 1.4 1.3 <1/4
b
t
1/3 2.2 2.0 1.8 1.6 1.5 1.4 1.3
Wind Wind
to
bb
1/2 tt
2.2 2.0 1.8 1.6 1.5 1.4 1.3
Wind Wind
2/3
b
b
tt
2.0 1.8 1.6 1.5 1.4 1.3 1.2
Wind Wind
1
bb
tt
1.7 1.5 1.4 1.3 1.2 1.1 1.0
Wind Wind
11/2
bb
t
1.4 1.3 1.2 1.1 1.0 0.9 0.8
Wind Wind
2
bb
- -
: t
1.2 1.0 0.9 0.9 0.8 0.8 0.8
Wind Wind
3
bb
tt
1.1 0.9 0.8 0.8 0.8 0.8 0.8
Wind Wind
>4
bb
OCTAGONAL OCTAGONAL
S SQUARE UARE
1.4 1.3 1.2 1.2 1.1 1.1 1.0
Wind Wind
Wind Wind
1.3 1.1 1.0 0.9 0.9 0.8 0.7
0.6 0.6 0.5 0.5 0.5 0.5 0.5
Wind Wind
Wind Wind
12 POLYGON 12SIDE SIDE POLYGON
Circle with surface Circle with smooth smooth surface wherewhere 26m/s tV> tv>6m /s 2
Wind Wind
Circle with surface where Circle withsmooth smooth surface where 2 t V
1.2 1.0 0.9 0.8 0.8 0.7 0.7
.
=h
- -
:
-
-
-
-
-
-
-
-
.
:
.
:
.
:
•
•
. .
•
±
±
.
•
•
±
±
-
: •
.
± •
.
±
: .
- -
•
±
:
.
•
.
•
±
±
-
:
•
•
-
-
•
•
+ +
:
.
- -
-
-
:
- -
Introduction
General
- - ( ,
)
. (Allowabl e/Workin g stress design method) - - -
Scope and General Provisions
. .(
-
- ) -
. .(
- )
( )
(
) -
. . (
) . -
- -
:
. -
(Base Isolation)
. –
. –
. :
-
.
. -
. .
- - -
Definitions
Response Modification Factor
(R) (
. Importance Factor
.
- -
)
:
Non – Structural Elements
.
Response Spectrum
. Return Period
. Shear Waves in Soil
. Artificial Earthquake Records
. Damping Ratio
. (
Mode Shape
.
- -
)
:
Fundamental Period
.
.
(
)
(
)
. Reference Codes
- - – (Eurocode 8: EN 1998-1:2004 - EN 1998-2:2005)
:
-
:
.
.
-
-
-
:
-
-
. :
-
-
.
-
.
-
Global Seismic Hazard Assessment Program (RELEMR, USGS / UNESCO, Prof. Samir Riad et. al.) Seismo-Techtonics & Seismic Hazard Assessment for Egypt, Riad & El-baz, 2002.
- -
-
:
- - - -
Return Period of Earthquake
: No Collapse Requirement
)
-
% .( -
Damage Limitation Requirement
)
% .( –
Increase of Earthquake Safety
(I)
.( - - ) - - - ) :( - Ultimate Limit States
- - - -
:
- -
:
.( -
- - )
.
.(
- - )
R(
) -
.
( - -
- - ) –
.
.
. - - - -
Serviceability Limit State
: . .( - - - )
-
Soil Considerations
- - - -
General
.( - - )
( - - - ) )
.(
- -
:
-
( - - -
)
- .C
( - - )
,
-
(Shear Wave
.
Velocity)
(
)
- - -
Classification of Subsoil Conditions
.( - - )
A
B
( - - ) % . /
- -
VS,30
C
D
E
:
( - - ) NSPT Cu
VS,30*
(
/
) <
( / )
-
A
. ( <
-
<
–
) B
Cu
. ( -
-
-
–
) C
Cu
. –(
) )
>
>
("
>
"
.
Cu
C --
--
D
Vs
–
--
D
E
Vs
.
/ *
. NSPT
- -
:
VS,30
:
VS,30
Hs
(4-9-1)
(h i /Vi )
i 1 ,N s
: i Ns
i
hi Vi
(Hs = hi)
Hs Ns
Vs,30
. - -
Earthquake Actions
- - -
Earthquake Zones
–
:( - - - )
- -
:
(- - - )
(ag) 0.10 g 0.125 g 0.15 g 0.20 g 0.25 g
()
0.30 g
( )
(ag) "
" . ( - - ) ( - - - )
-
.(g=9.81 m/sec2) .
-
- -
:
(cm/Sec2)
( - - ) ( - - -
- -
)
:
( - - - )
-
-
- -
:
- - Basic Representation of Earthquake Action
- - - -
General
."
" . -
( - - ) (Type (1) and Type (2) ) (
)
- - )
Type (1)
.( - - )
( - -
.0.15 g –
–
: . .
- -
:
T
()
Type (1)
T
( )
Type (2)
( - - )
- -
:
- - - -
Horizontal Elastic Response Spectr um
:
Se (T)
( - -
0T
TB
Se
:
(T) =
:
Se (T) = 2.5 agI S ,
TC T TD
:
Se (T) = ag I S
T 4 sec
T
1.0 TB 2.5 η 1.0 ,
ag I S
TB T TC
TD
)
(4-9-3)
TC T
: S e (T) = agI S
(4-9-2)
,
(4-9-4)
TC TD T 2
(4-9-5)
: Se (T) T ag
) ) (I=1.0
(- - ( - -
)
TB , TC
( - ( - ( - -
I
)
)
TD
) ( - -
)
S
Displacement Based Design
( - - )
. A, B , C, D & E
TB,TC,TD & S
.( - - )
- -
:
( - - )
TB,TC,TD & S
:( )
Type (1) SubsoC il lass A B C D
E
S 1.0 1.35 1.5 1.8
T B 0.05 0.05 0.10 0.10
1.6
0.05
TC 0.25 0.25 0.25 0.30
0.25
:(
Type (2) SubsoC il lass A B C D E
S 1.0 1.2 1.15 1.35 1.4
T B 0.15 0.15 0.20 0.20 0.15
η
ηv
, , , ,
TD 2.0 2.0 2.0 2.0 2.0
*
(S)
, v
:( - - )
, , , ,
1.2
)
TC 0.4 0.5 0.6 0.8 0.5
.
ηv
TD 1.2 1.2 1.2 1.2
( - - )
η
Vertical Elastic Response Spectrum
- - - -
Sve (T)
( - - - )
( - - ) .( - - )
0
T
TB
: Sve (T) = avg
T I 1.0 3.0 TB
- -
ηv
1.0 ,
(4-9-6)
:
TB
T
TC
T
TD
T
TC : Sve (T) = 3.0 avg I v ,
TD
: Sve (T) = 3.0 avg
(4-9-7)
I v TC , T
(4-9-8)
4 sec : S ve (T) = 3.0 avg I v TC T2 D T
(4-9-9)
: Sve (T) avg
v
( - - ) ( - - ) Spectrum
avg / ag
TB
TC
Type (1)
0.45
0.05
0. 15
Type (2)
0.90
0.05
0.15
TD
1.0 1.0
(avg)
. - - - -
Peak Ground Displacement
dg
: dg = 0.025 a g
I S
TCTD
(4-9-10)
TD , TC , S , I , ag
.( - - - - )
- -
:
(
)
- - - -
Horizontal Design Spectrum (for Elastic Analysis)
.(
) Sd (T)
-
: 0 T TB
TC
TB T
T
I S 2
: Sd (T) = ag
TC : Sd (T) = ag
I S
TD : Sd (T) = ag I S
T
3
TB
2.5
,
R 2.5 R
2.5 2 , R 3
(4-9-11) (4-9-12)
TC T
,
(4-9-13)
agI 2.5 TC TD
TD
T
4 sec : Sd (T) = ag
I
S R T 2
(4-9-14)
agI
: (
)
Sd (T) ag
I (
- - )
(
)
R
.( - - )
S , TB, TC , TD
-
.
- -
:
(
)
- - - TB
T
TB T
T
( - - )
Sd (T)
.(Participating Mass).% (
( - - )
( - - )
)
- - - -
Vertical Design Spectr um (for Elastic Anal ysis)
(
) .(R = 1.0) -
- - -
Alternative Representation of the Earthquake Action - Time History Input
- - - -
General
. ( (
-
) (
-
)
-
):
. .( - - - - )
- -
:
- - - -
Artificial Earthquake Records
( - - - - ) ( - - - - ) .
I
( - - )
-
.(ag)
. . . :
-
.
-
.
( ag . S )
(2.5 ag S)
-
.
TC
TB
( - - - - )
% T1
2.0T1
0.2T1
. - - Spatial Model of Earthquake Action
- -
:
.( - - - - ) ( - - - - ) - Combination of the Earthqu ake Action with Other Acti ons
. - -
Importance Factors
: :
-
:
-
.(I =1.3) .(I =1.0)
()
- -
Structural Regularity
- - ( - - )
. .
- -
:
( - - )
( ,
)
, -
(Abutments)
(
)
- - ( - - )
.
- -
Structural Analysis
Structural Modeling
- - -
. .
. ) : Ieff = 0.70 Ig Ieff = 0.70 Ig
( -
(
- -
)
-
:
(
Ieff = 0.50 Ig
)
-
(
Ieff = 0.50 Ig
)
-
Aeff =Ag
: : Ieff :
Ig
: Ag : Aeff
. ( - - )
-
. ( - - )
* % %
**
%
* ( /
)
/
** - - -
Methods of Analysis
: Uniform Load Method ( - - - -
( - - - -
) )
Simplified Modal Response Spectrum Method
- -
() ( )
:
( - - - -
)(
)
( )
Multi–Modal Response Spectrum Method Time History Method ( - - - -
)
()
.
( - - ) . ( - - )
() ()
()
()
( )
( )
( )
( )
( ) ( )
()
()
()
( ) ()
( ) ( )
( )
( )
( )
() ()
() ()
( ) ( )
. -
*
*
-
( ) () .
() ( ) - - - -
Uniform Load Method
: (
)
(
) .()
- -
-
:
)05-9-( K
(K)
Ls
-2
(4-9-15)
Δ
: )06-9-( T1 2 M
Ls
T1
M K
-3
(4-9-16)
W g
: )
(
.)7-9-(
+
M
+
(F)
-
)07-9-( F = Sd(T1) W/g
(4-9-17)
:
)
)T1(
(
+
)6-2--9-(
)5-2--9-( +
.)7-9-(
25-9-4
Sd(T1)
W
:
2-2- 8-9-4
Simplified Modal Response Spectrum Method
:
(po)
)
(
(Fundamental mode period)
(n)
n
T1 2π
-0
. )08-9-(
T1
)i)
-2
2
w δ i i
i 1
(4-9-18)
n
g pδ i 1
i i
:
× po= (i)
.
( )7-9-(
pi
)
(i)
.(i) . .(po)
26-9-4
(i)
wi
g i
:
( - - ) Fi
-
β S (T ) δ w γ
1
d
i
i
/g
(4-9-19)
(i)
Fi
(
)
(T1)
Sd(T1)
( - - - - )
( - - - - )
: n
β w iδi i 1 n
γ w i δi
2
i 1
n
i
(i) (i)
wi
(
) .( - - ) (
)
- - - -
Multi-Modal Response Spectrum Method
()
.(Modal Analysis) Fi
T
r
(r)
( - - - - )
(r)
Sd(T)
.( - - - - ) (modes)
.
.
(%
) - -
:
.(CQC)
(SRSS)
Time History Method
- - - - - - - . - - - - -
(Actual earthquake records) (Artificial accelerograms)
. ( - - - )
I
( - - -
- - - - -
) .( - - ) - - - - .
. - - - - % .( - - - - ) - - - - .( , )
R(
- -
)
:
- - - (Pot bearings) (Elastomeric bearings)
. - - : :
.
-
( - -
)
.
(Kh, Kv)
( K
h
α.Sγ R
I
,
K
v
0.5K
- - )
h
(4-9-20)
: (g)
(ag)
( - - - ) ( - - ) ( , )
(
)
S R
( , )
- -
:
(Anchored or braced walls)
.
I - - . .
,
(Kh)
, .
Secondary Effects
(P-∆)
- -
(P-)
( ΔM
- - )
1 R Ed 2 .ds .N
(4-9-21)
: ds
ds =
R
de
(4-9-22) de
. η
( - - ) (piers and substructure) .(deck) (
- - )
(
R
) .( - - ) ds
- -
:
.( - - ) NEd
.( - - )
- Combination o f the Co mponents of the Earthquake Actions
- - ) :
( (% (%
ET = E (Fx)
) =(
)
-
- -
-
- -
)
+
0.30 E (Fy)
+
0.30 E (Fz)
-
ET = 0.30 E
(Fx)
+
E (Fy)
+
0.30 E (Fz)
-
ET = 0.30 E
(Fx)
+
0.30 E (Fy)
+
E (Fz)
: E(Fx)
X E(Fy) Y E(Fz) Z ET
.
. ET
2 E (Fx)
2 2 E (Fy) E (Fz)
(4-9-23)
- -
:
Displacement Analysis
- -
ds
:(
- - )
ds = η R de
(4-9-22)
: de
.( - - - - ) .(
- - )
( - - - - )
(
(
) R
)
( - -
)
(piers and substructure) .(deck) ds
-
.( - - - - ) (
)
-
(
R
)
. (
)
- -
Response Modification Factor (R)
( - - )
(R) (
)
-
.(
)
- -
- -
:
-
- -
-
- -
-
- -
-
- -
-
- -
(Plastic hinges)
.(Stable plastic mechanism) . - - - ) (
(R)
.
(R)
.( , )
(R) (R)
.
.
) %
(
(R)
(
R
) .
( , ) ( - - - )
- - -
(R)
.( , ) (R)
( , )
- -
- -
:
. ( , )
R
.
-
( , )
:
. -
(R)
- -
( - ) . %
R
.( , )
.
- - -
- -
:
( R) (
)
( - - )
:
Reinforced Concrete Piers
)
:
3.0)
-
Inclined piers in bending (as 3.0)
-
1.0)
-
* ,
,
Vertical piers in bending (as
* , * ,
, ,
Squat piers (as
* ,
,
Inclined piers in bending (as
,
Piers with elastomeric bearings (in absence of seismic buffers/ stoppers)
,
(
1.0)
(
:
Steel Piers
(
)
)
:
,
,
Vertical piers in bending
–
,
,
Inclined piers in bending
-
,
,
Piers with normal bracing
-
,
-
Piers with eccentric bracing
,
Piers with elastom eric bearings (in absence of seismic buffers/ stoppers)
, ,
,
= Ls h
( (
–
) )
:
Arches
(as = Ls/ h) :
(
)
*
= )
: )
= (R)
(1.0
.(
as /3
)
as 3.0)
( (( )
( ) - -
Non-Structural Elements
General
)
(
- -
- -
:
. . -
Analysis
- -
. –
(Fa)
: Fa =
( Sa Wa
a ) / Ra
(4-9-24)
: Wa
( ) ( (
Sa
a
- - )
- - )
Ra
: S
a
-
Sa
3(1.0 z a /H) α.S 0.50 2 1.0 (1.0 Ta /Ti ) )
(4-9-25)
: g
(ag)
α S
- -
:
Ta Ti za H
-
- -
Importance Factors and Respon se Modifica tion Factors for NonStructural Elements
:
a
( , )
-
.
.
(I)
.(
(a)
- - )
.
–
( - -
)
(
- - )
Ra
Ra
-
Ra
1.0
-
2.0
-
- -
:
- Pier Width under Movable Supports at Expansion Joints
( - - - - )
- - -
-
: . -
(restrainer)
- -
. - Seismic Effects on Bridges during Construction
. (%
)
- -
Special Bridges
(
)
.
- -
:
Safety Verifications
- -
General
- -
( - - )
.( -
- - ) ( -
Ultimate Limit State General
(
- - ) -
- -
- -
- -
)
. - -
Resistance Conditions
- -
Ed
.( )
( -
- - )
Re
(4-9-26)
: Ed
Re
Ductility Conditions
- -
- -
. – (Capacity Design Provisions)
- -
:
.(brittle failure mode)
- -
Equilibrium Conditions
.(Overturning and Sliding)
- ( - - )
- -
Resistance of Foundations
- -
.
:
-
-
- )
.(
- - )
-
( -
- -
Seismic Requirements at Movem ent Join ts
-
- -
.(
- - ) -
:
-
.
(
- - )
.
- -
:
Serviceability Limit State (SLS)
General
-
- -
- -
- -
. :
-
ds
ds = ds *
(4-9-27)
: ( (
ds
- - )
) (
- - )
( - - ) (
ν
0.5
0.4
- - ) () -
ds
.( - - )
- -
:
( - - )
Annex (4-9-A)
Alternative Method for Estimating the Drift at Serviceability Limit State (SLS)
( - - -
( - -
- - ) )
– ()
.
–
TB
. 0 T TC : Sdrift (T) = Se = () 2.5 a g I S
T
TC T TD : Sdrift (T) = Se = () 2.5 a g I S C T
T
C
TD T 4sec
:S
drift
(T) = Se = () 2.5 a g I S
- -
TD
T
2
:
( - - )
Annex (4-9-B)
(
) TB
TB
T
T (T)
- - )
d
.
0 T TC : Sd(T) = ag I S
2 .5
TC T TD : Sd(T) = ag I S
2 .5
TD T 4sec
S (T)
( - - )
R
R
T T [0.20] Iag
:S d(T) = a g I S
C
2.5 R
T T T 2 [0.20] Iag
- -
C
D
(
:
-
-
-
-
.
: (
)
(
)
-
. . .(
–
-
,
) -
(
-
-
-
-
) .
,
: .
: .
.
-
-
:
.( - - ) ( Underpass )
-
-
. : ( )
-
:
: .( - - ) -
.(
- - )
( - - ) -
-
-
-
-
-
.( - - )
.
–
( )
.( - - -
(
)
) % -
.( - - -
-
-
)
:
.(
)
% . -
-
-
-
-
-
-
-
-
-
- -
-
-
.
( /
) / .
( )
.
.
( /
) /
-
.
- .
-
-
-
-
:
( -
- )
(
)
(
)
. .
( -
- ) -
-
-
Abutments
.( /
) /
-
Surcharge
/
)
α
.( - -
-
-
:
-
-
-
-
-
. . -
.( /
)
-
/
-
.
.
%
.
.
-
.
%
-
(Cantilever Method)
( /
)
- -
-
-
/
,
-
-
/ .
( /
)
(Deck Pushing Method)
- -
.
-
-
%
:
(Piers)
-
)
( .
-
)
(H. W. L.)
(
:(Piers)
-
( - : P1 5.14 *10
( 4
CaV
2
-
)
)
–
P1
MPa
: ( - -
)
(
)
Ca
/
: P 2 5.14 *10
4
CbV
2
P1
V
–
P2
MPa
: ( -
-
)
Cb
(
)
-
-
: . .
-
-
-
:
. ( –
Drag coeff.
- )
Ca
(
0.7
)
0.8
º
1.4
Lateral drag coeff. ( – Cb
- ) Angle
θ
0.0
0
0.5
5
0.7 0.9
10 20
1.0
≥30
-
-
:
( -
- ) -
-
. (Spill through abutment)
-
-
-
-
. (Reinforced – Earth) ( - ) .(
)
-
-
–(
–
)
:
- (Uplift or Buoyancy Forces)
.(Pile caps)
-
-
A
:
A-
Foot Bridges Permanent Actions Comb Type
Comb No.
DL
SDL
C&S
SETT
LL EP
PREST
1
q
Q
s n o ti a in b m o C s d a o L te a m it l U
l ta n e d i c c A
1.35
3
s n o it a n i b m o C s d a o L e c i v r e S
s c tis i r e t c a r a h C
e u q t e n r F
QuasiPermanent
VEH IMP
WL
1.35
0.45
1.35
1.35
0.45
7
1.35
1.35
1.35 1.35(DL+SDL+C&S)+1.2SETT+1.5EP+1.0PREST
1.35
0.54
0.54
9
0.54
0.54
10
0.40
11
0.40
13
1.00(DL+SDL+C&S+SETT+EP+PREST)
1.00 1.00 0.40
1.00
0.40
1.00
0.40
1.00
1.00(DL+SDL+C&S+SETT+EP+PREST)
1.00 1.00
1.00
2
1.00
1.00
4
1.00(DL+SDL+C&S+SETT+EP+PREST)
1.00
1.00
1.00
1.00
5
0.40
0.40
6
0.40
0.40
0.40
0.40
7 8
0.30 0.60 0.30 0.60 1.00 1.00 0.50
1.00(DL+SDL+C&S+SETT+EP+PREST)
0.60
9 10
0.9
1.50 1.00
1
3
EQ
1.50
0.40
14
16
RUPT
0.9
8
12
EXPL
1.35
6
5
TEMP
1.35
4
15 EQ
HLE FORCE 1.35
2 s ic t is r te c a r a h C
SERV VEH
1.35
0.20 1.00(DL+SDL+C&S+SETT+EP+PREST)
0.50
-A-
CONST
A
:
During Construction (Ultimate Load Combinations) 1
1.35
1.35
1.50
1.00
1.50
1.50
Combinations for Global Equilibrium Checks 1
1.35
1.35
1.50
1.00
1.50
1.35
2
1.00
1.00
1.50
1.00
1.50
1.35
Notes: 1- In case the Permanent Action are on the Favorable side, the service load comb. factors 0.9, 0.9, 0.9, 0.9 &0.9 are used for DL, SDL. C&S, SETT and EP, respectively 2- In case the Permanent Action are on the Favorable side, the ultim. load comb. factors are 1.15, 1.15, 1.15, 1.0 &1.28 are used for DL, SDL. C&S, SETT and EP, respectively 3 Notations DL De adL oa d q U ni f or mL i v eL oa d T EM P T em p er a t ur eL oad s SDL Sup e r i m p o s e d D e a dL o a d Q C o n c e nt r a t e dL i v e L o a d EQ E a rt h q ua ke C&S C r ee pa ndS h r i nka ge SE R VV E H Se r v i c e V e h i c l e C ON ST C o ns tr uc t i o nL oa d SETT Di f fe r e nt i a l Se t tl e me nt H L E F OR C E H o r i z o nt a l F o r c e E XP L E x pl o s i o n EP Ea rth Pr essure VE H IMP Vehi cl e Impact (A ccid ent alSho ck ) RUPT Ca bl e Rupture Ef fe ct PREST Prestressing WL Wind Load
-A-
A
:
.
(A- ) : .Characteristic
.Accidental
.EQ
.Characteristic
:
.Deflection .
-A-
Frequent
.Quasi- Permanent
B
:
BRoad Bridges Permanent Actions Comb Type
s n o ti a in b m o C s d a o L te a im tl U
s c tis i r e t c a r a h C
l ta n e d i c c A
Comb No.
DL
SDL
C&S
SETT
LL EP
PREST
LM1 VEH UNI
1
1.35
1.35
2
1.00
0.54
1.35
1.35
1.35
1.35
3
LM2
7
s n o ti a
in b m o C s d a o L e c i v r e S
s c tis i r e t c a r a h
8
1.00
0.54
9
1.00
0.54
10
0.75
0.40
11
0.75
0.40
12
0.75
0.40
13
C
t n e u q e r F
1.35
1.35
1.35
RUPT
EQ
0.9 0.90 0.90
1.00
1.00(DL+SDL+C&S+SETT+EP+PREST)
1.00
0.75
1.00
0.75
1.00
0.75
1.00 1.00
0.75 1.00(DL+SDL+C&S+SETT+EP+PREST)
1.00
0.20
0.20
1
1.00
1.00
1.00
1.00
2
1.00
1.00
1.00
1.00
1.00
5
0.75
0.40
6
0.75
0.40
0.75
0.40
0.60 0.60
1.00
1.00(DL+SDL+C&S+SETT+EP+PREST)
4
0.60 1.00
7
11
EXPL
1.00
0.75
9
TEMP
1.50
17
8
WL
1.00
16
3
VEH IMP
1.50
1.00(DL+SDL+C&S+SETT+EP+PREST)
0.60 1.00 1.00 0.50
0.75
0.50 0.60
10 QuasiPermanent
1.35
0.75
15
19
1.35
1.35
18 EQ
CENT &LAT
1.35 1.35(DL+SDL+C&S)+1.2SETT+1.5EP+1.0PREST
6
14
BR 1.35
1.35
4 5
LM3
0.20 1.00(DL+SDL+C&S+SETT+EP+PREST)
0.50
-B-
CONST
B
:
During Construction (Ultimate Load Combinations) 1
1.35
1.35
1.50
1.00
1.50
1.50
Combinations for Global Equilibrium Checks 1
1.35
1.35
1.50
1.00
1.50
1.35
2
1.00
1.00
1.50
1.00
1.50
1.35
Notes: 1- In case the Permanent Action are on the Favorable side, the service load comb. factors 0.9, 0.9, 0.9, 0.9 &0.9 are used for DL, SDL. C&S, SETT and EP, respectively 2- In case the Permanent Action are on the Favorable side, the ultim. load comb. factors are 1.15, 1.15, 1.15, 1.0 &1.28 are used for DL, SDL. C&S, SETT and EP, respectively 3 Notations DL De adL oa d LM 1 L i v eL oa dm od el1 C EN T& LA T C ent ri f ug a lan dL a te ra lL o ad SDL Sup e ri m p os e dDe adL oad V EH V e h i cl e V E HIM P V e h i c l eI m pa c t( A cc i d e nta lS h oc k ) C&S C r ee p a nd S h r i nka g e UN1 U ni f o r m L oa d WL W i nd L o a d SETT Di f fe r e nt i a lSe t tl e me nt LM 2 L i veL oadm od e l2 TEM P T em p e ra t ur eL oa d s EP E a rt h P r e s s ur e LM 3 L i vL e oad m ode3l EQ E a r t h q ua k e P R EST P r e s t r e s s i ng BR B r a k i ng C ON S T C o ns tr uc ti onL oa d EXPL Explosion RUPT Cable Rupture Effect
-B-
:
B
.
,
)B-4(
: .Characteristic
.Accidental
.EQ
.Characteristic
: .Deflection
Frequent
.Quasi- Permanent . ) .)1 ( . .
3-B-
(
C
:
C1-
Table c1.1 – Maximum value of (v/ n0 ) lim for a simply supported beam or slab and a maximum permitted acceleration of a max< 3.50m/s Mass m 3
10 kg/m Span L ζ
2
>5,0 <7,0
>7,0 <9,0
>9,0 <10,0
>10,0 <13,0
>13,0 <15,0
>15,0 <18,0
>18,0 <20,0
>20,0 <25,0
>25,0 <30,0
>30,0 <40,0
>40,0 <50,0
>50,0 -
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
v/n 0
% 2
m 1,71
m 1,78
m 1,88
m 1,88
m 1,93
m 1,93
m 2,13
m 2,13
m 3,08
m 3,08
m 3,54
m 3,59
4
1,71
1,83
1,93
1,93
2,13
2,24
3,03
3,08
3,38
3,54
4,31
4,31
2
1,94
2,08
2,64
2,64
2,77
2,77
3,06
5,00
5,14
5,20
5,35
5,42
4
2,15
2,64
2,77
2,98
4,93
5,00
5,14
5,21
5,35
5,62
6,39
6,53
1
2,40
2,50
2,50
2,50
2,71
6,15
6,25
6,36
6,36
6,45
6,45
6,57
2
2,50
2,71
2,71
5,83
6,15
6,25
6,36
6,36
6,45
6,45
7,19
7,29
1
2,50
2,50
3,58
3,58
5,24
5,24
5,36
5,36
7,86
9,14
9,14
9,14
2
3,45
5,12
5,24
5,24
5,36
5,36
7,86
8,22
9,53
9,76
10,36
10,48
1
3,00
5,33
5,33
5,33
6,33
6,33
6,50
6,50
6,50
7,80
7,80
7,80
2
5,33
5,33
6,33
6,33
6,50
6,50
10,17
10,33
10,33
10,50
10,67
12,40
[17,5,20,0) [20,0,25,0) [25,0,30,0)
1 1 1
3,50 5,21 6,25
6,33 5,21 6,46
6,33 5,42 6,46
6,33 7,08 10,21
6,50 7,50 10,21
6,50 7,50 10,21
7,17 13,54 10,63
7,17 13,54 10,63
10,67 13,96 12,75
12,80 14,17 12,75
12,80 14,38 12,75
12,80 14,38 12,75
[30,0,40,0)
1
10,56
18,33
18,33
18,61
18,61
18,89
19,17
19,17
19,17
>40,0
1
14,73
15,00
15,56
15,56
15,83
18,33
18,33
18,33
18,33
m
a
[5,00,7,50) [7,50,10,0) [10,0,12,5) [12,5,15,0) [15,0,17,5)
a
L [a,b) means a < L < b
NOTE 1 Table F.1 includes a safety factor of 1.2 on (v/ n0 ) lim for acceleration, deflection and strength criteria and a safety factor of 1,0 on the (v/ n0 ) lim for fatigue. NOTE 2 Table F.1 includes an allowance of (1+ φ ‘ /2) for track irregularities.
: L m critical damping
ζ
/
v n0
/ ( -C-
a max
- - - )
Ф"/2
C
:
Table F.2 – Maximum value of (v/ n0 ) lim for a simply supported beam or slab and a maximum permitted acceleration of a max< 5.0m/s Mass m
2
>5,0 <7,0
>7,0 <9,0
>9,0 <10,0
>10,0 <13,0
>13,0 <15,0
>15,0 <18,0
>18,0 <20,0
>20,0 <25,0
>25,0 <30,0
>30,0 <40,0
>40,0 <50,0
>50,0 -
ζ
v/n
v/n
v/n
v/n
v/n
v/n
v/n
v/n
v/n
v/n
v/n
v/n
% 2
m 1,78
m 1,88
m 1,93
m 1,93
m 2,13
m 2,13
m 3,08
m 3,08
m 3,44
m 3,54
m 3,59
m 4,13
4
1,88
1,93
2,13
2,13
3,08
3,13
3,44
3,54
3,59
4,31
4,31
4,31
2
2,08
2,64
2,78
2,78
3,06
5,07
5,21
5,21
5,28
5,35
6,33
6,33
4
2,64
2,98
4,86
4,93
5,14
5,21
5,35
5,42
6,32
6,64
6,67
6,67
1
2,50
2,50
2,71
6,15
6,25
6,36
6,36
6,46
6,46
6,46
7,19
7,19
2
2,71
5,83
6,15
6,15
6,36
6,46
6,46
6,46
7,19
7,19
7,75
7,75
1
2,50
3,58
5,24
5,24
5,36
5,36
7,86
8,33
9,14
9,14
9,14
9,14
2
5,12
5,24
5,36
5,36
7,86
8,22
9,53
9,64
10,36
10,36
10,48
10,48
1
5,33
5,33
6,33
6,33
6,50
6,50
6,50
7,80
7,80
7,80
7,80
7,80
2
5,33
6,33
6,50
6,50
10,33
10,33
10,50
10,50
10,67
10,67
12,40
12,40
[17,5,20,0) [20,0,25,0) [25,0,30,0)
1 1 1
6,33 5,21 6,46
6,33 7,08 10,20
6,50 7,50 10,42
6,50 7,50 10,42
7,17 13,54 10,63
10,67 13,75 10,63
10,67 13,96 12,75
12,80 14,17 12,75
12,80 14,38 12,75
12,80 14,38 12,75
12,80 14,38 12,75
12,80 14,38 12,75
[30,0,40,0)
1
18,33
18,61
18,89
18,89
19,17
18,89
19,17
19,17
19,17
>40,0
1
15,00
15,56
15,83
18,33
18,33
18,33
18,33
18,33
18,33
10
3
kg/m
Span L m
a
[5,00,7,50) [7,50,10,0) [10,0,12,5) [12,5,15,0) [15,0,17,5)
a
0
0
0
0
0
0
0
0
0
0
0
0
L [a,b) means a < L < b
NOTE 1 Table F.2 includes a safety factor of 1.2 on (v/ n0 ) lim for acceleration, deflection and strength criteria and a safety factor of 1,0 on the (v/ n0 ) lim for fatigue. NOTE 2 Table F.2 includes an allowance of (1+ φ ‘ /2) for track irregularities.
: .(rigid supports) )
half through complex
structures
.(
-C-
C
:
Neutral axis
-
. , . ≥
.
-
no
-
. nT > 1.2 no
-
.( – - ) .
-C-
C
:
C2-
-
( - - -
)
.
.
(fatigue)
-
(Ф " + Ф ’ + ) (Ф"/2 + Ф’ + )
.
φ ’
K
for K < 0.76
1 K K 4
} =1.325
(C2 – 1)
for K >0 .76
v
K
2 L n0
φ"
β 100
2
[56e 4 j 50(
Lφ n0
80
2
1)e j ] > 0.0
(C2 – 2)
j Lφ / 20
β
v
22 =1
for v < 22m/sec forv>
22m/sec
: .
β L
.( – - ) ) . .
/
(
no v
-C-
C
:
(4-C2-1) .
Ф’
.(
Ф’
/
( – - )
- - - ) (4-C2-2)
Ф"
.( - - )
Ф"
. no
Ф" + Ф’
.( - -
-C-
)
D
:
D -4
%055 , %5 .
.
:
.
. .
6
2
. .
6
2
)deflectometers) .
. .
/
25
1- D-
:
E
E
- - -
-
( )
Influence Lines and )
.(4-E-1)
(Influence Surfaces
(4-E-1) ( )
(Skew bridges) .(4-E-2)
(Torsion)
(4-E-2)
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EGYPTIAN CODE OF PRACTICE FOR PLANNING, DESIGN & CONSTRUCTION OF BRIDGES AND ELEVATED INTERSECTIONS Part 6 - Analysis & Design of Steel Bridges MEMBERS
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