..
,.-
SSC-222
CATAMARANS-TECHNOLOGICAL TO SIZE AND APPRAISAL DESIGN INFORMATION
This document for
public
OF STRUCTURAL
AND PROCEDURES
has
been
approved
release
and
sale;
distribution
LIMITS
its
is unlimited.
SHIP STRUCTURE COMMITTEE 1971
/.
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——— -.—---- ---
—-
..
SHIP
STRUCTURE AN INTERAGENCY COMMITTEE DEDICATED THE STRUCTURE
COMMITTEE ADVISORY TO IMPROVING OF SHIPS
MEMBER AGENCIES:
ADDRESS CORRESPONDENCE
UNITED STATES COAST GUARD NAVAL. SHIP SYSTEMS COMMAND
SECRETARY
MILITARY SEALIFT COMMAND MARITIME ADMINISTRATION AMERICAN BUREAU OF SHIPPING
U.S. COAST GUARD HEADCIUARTERS WASHINGTON, D.C. 20594 20590
TO:
SHIP SIRUCTURE COMMITTEE
SR 192 1971
The Ship Structure Committee has completed a project that assesses the present state of the art for designing Catamarans, large platform, twin hulled ships. The purpose of the project was to collect and analyze design techniques and data presently available and assess their usefulness for catamarans approaching 1000 feet in length. This report contains procedure for the initial design of a large catamaran and indicates where additional tests should be made before the final design stage is completed.
W. l?. REA III Rear Admiral U.S. Coast Guard Chairman, Ship Structure Committee
—————
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SSC-222
Final Report on Project SR-192, “Catamaran Designs” to the Ship Structure Committee
CATAMARANS - TECHNOLOGICAL LIMITS TO SIZE AND APPRAISAL OF STRUCTURAL DESIGN INFORMATION AND PROCEDURES
by Naresh M. Maniar and Wei P. Chiang M. Rosenblatt & Son, Inc.
under Department of the Navy Naval Ship Engineering Center Contract No. NOO024-70-C-5145
This doeuvwnt haz been approved for public ?elease and sale; its distribution is unlimited.
U. S. Coast Guard Headquarters Washington, D. C. 1971
-.
ABSTRACT
Existing United States shipbuilding facilities can handle 1000foot catamarans with up to 140-foot individual hull beams on the premise that the hulls would be joined afloat. Major harbors and channels of the world suggest an overall beam limit of 400 feet and 35-foot draft. Drydocking for catamarans over 140-foot in breadth will require new faciliScantlings of a ties or extensive modification to existing facilities. 1000-foot catamaran cargo liner can be expected to be within current shipbuilding capabilities. The uniqueness of the catamaran design lies in the cross-structure and the important facets of the cross-structure design are the prediction of the wave-induced loads and the method of structural analysis. The primary loads are the transverse vertical bendDesigners have reing moments, axial force, shear, and torsion moment~. lied heavily on model tests to obtain design loads and have used general structures principles and individual ingenuity to perform the structural analysis in the absence of established guidelines. Simple semi-empirical equations are proposed for predicting maximum primary loads. A structural analysis method such as the one proposed by Lankford may be employed for conceptual design purposes. The Lankford method assumes the hulls to be rigid and the cross-structure loads to be absorbed by a group of bulkheads and associated effective deck plating. This procetransverse dure in general should provide an overall conservative design and not necessarily an economic or optimized design. Additional research and development work including systematic model test programs are necessary for accumulating additional knowledge in areas of uncertainty and for the establishment of reliable design methods for catamaran structure.
ii
CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . ...1 ANALYSIS OF FEATURES THAT MAY IMPOSE SIZE LIMITS . . . . . . . . 2 EXISTING STRUCTURAL DESIGN METHODS 3.1 3.2 3.3
GENERAL. . . . . . . . . . . . . . . . . . . . . . . .4 CROSS-STRUCTURE LOADS . . . . . . . . . . . . . . . . . 4 SURVEY OF EXISTING DESIGN METHODS . . . . . . . . . . . 7
MODEL TEST DATA ANALYSIS 4.1 4.2 4.3
. . . . . . . . . . . . . . . 4
. . . . . . . . . . . . . . . . . . . .17
TEST BACKGROUND . . . . . . . . . . . . . . . . . ...17 DATA CONSOLIDATION AND COMPARISON . . . . . . . . . . .21 DISCUSSION OF THE PLOTS . . . . . . . . . . . . . . . .26
CONDITION FOR MAXIMUM RESPONSE AND RECOMMENDED METHOD FOR DESIGN LOADS ESTIMATE . . . . . . . . . . . . . . . .27 5.1 5.2 5.3 5.4
CONDITION FOR MAXIMUM RESPONSE IN BEAM SEAS DEVELOPMENT OF DESIGN LOAD EQUATIONS. . . . COMPARISON OF LOADS CALCULATED BY PROPOSED EQUATIONS AND BY OTHER METHOD . . . . . . . METHOD FOR DESIGN LOADS ESTIMATE. . . . . .
HULL FLEXIBILITY AND CROSS-STRUCTURE STRESSES.
. . . . . .27 . . . . . .30 . . . . . .35 . . . . . .35
. . . . . . . . .38
DESIGN SHIP. . . . . . . . . . . . . . . . . . . . . . . . . . .40 7.1 7.2 7.3
7.4 7.5
PURPOSE. . . . . . . . . DESIGN DESCRIPTION. . . . EXPLANATION FOR EFFECTIVE CROSS-STRUCTURE LOADS AND DESIGN CONCLUSIONS. . . .
. . . . . . . . . . STRUCTURE STRESSES. . . . . .
. . . . .
. , . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
.40 .43
,43 .45 .45
TOPICS FOR FUTURE RESEARCH AND DEVELOPMENT PROGRAM . . . . . . .47 CONCLUSIONS. . . . . . . . ., ACKNOWLEDGEMENTS.
. . . . . . . . . . . . . . . . .50
. . . . . . . . . . . . . . . , , . . . . , .50
REFERENCES.
. . . . . . . . . . . . . . . . . . . . . . . . . .52
APPENDICES.
. . . . . . . . . . . . . . . . . . . . . . . . . .
1. 2.
3.
CATAMARAN RESISTANCE . . . . . . . . . . . . . . . . . .54 REPRODUCTION OF PORTIONS OF REFERENCE (8), THE STRLICTURAL DESIGN OF THE ASR CATAMARAN CROSS-STRUCTURE” BY BENJAMINW. LANKFORD, JR. . . . . . . . . . .56 REPRODUCTION OF “SUMMARY AND DISCUSSION” OF REF~R: . . ENCE (13), “AMETHOD FOR ESTIMATING LOADS ON CATAMARAN CROSS-STRUCTURE” BY A. L. DISENBACHER, . . . .62
iii
-—,
—
LIST (IFTABLES Table
Page
1
CATAMARAN LOAD AND STRUCTURE ANALYSIS . , . . . . . . . . . . 7
2
PROTOTYPE CHARACTERISTICS OF MODEL TEST VESSELS . . . . . . .19
3
PARTICULARS OF “E. W. THORNTO~l” SERIES SHIPS. . . . . . . . .20
4
PARTICULARS OF “ASR” SERIES SHIPS . . . . . . . . . . . . . .20
5
PARTICULARS OF THE UNIVERSITY OF MIAMI SERIES SHIPS . . . . .20
6
RATIOS OF MAXIMUM LOADS IN BEAM SEAS AND OBLIQUE SEAS . . . .25
7
WAVE-INDUCED TRANSVERSE VERTICAL BENDING MOMENTS IN BEAMSEAS. . . . . . . . . . . . . . . . . . . . . . . . . .36
8
WAVE-INDUCED SHEAR IN BEAM SEAS . . . . . . . . . . . . . . .36
9
WAVE-INDUCED TORSION MOMENT IN OBLIQUE SEAS . . . . . . . . .36
10
DESIGN LOAD SCHEDULE . . . . . . . . . . . . . . . . . . . . .37
11
T-AGOR16 CATAMARAN STRESS SUMMARY . . . . . . . . . . . . . .40
12
DESIGN SHIP PARTICULARS . . . . ... . . . . . . . . . . . . .41
13
DESIGN SHIP WAVE-INDUCED CROSS-STRUCTURE LOADS. . . . . . . .46
14
DESIGN SHIP, CROSS-STRUCTURE STRESS SUMMARY . . . . . . . . .47
iv
LIST OF FIGURES Figure 1 2
Paae CATAMARAN RESPONSE IN A REGULAR BEAM SEA . . . . . . . . . . 15 M *VERSLIS M
3 *
VERSUS L, BEAM SEAS . . . . . . . . . . . . ...23 M
4
VERSUS b3 BEAM SEAS . . . . . . . . . . . . ...23
* 5
F VERSUS A, BEAM SEAS . . . . ... . . . . . . ...23
A;; 6
7 8 9
A, BEAM SEAS . . . . . . . . . . . . ...23
F
so
Ab Zmcw
VERSUS A, BEAM SEAS . . . . . . . . . . . . ...24
To/T1
VERSUS A, OBLIQUE SEAS....
VERSUS AL, OBLIQUE SEAS. . . . . . . . . . . . . 24 ADDED MASS FOR SWAY DIRECTION, SERIES 60, FROM REFERENCE ... . . . . . . . . . . . ... . . . . ...25
10
CATAMARAN IN BEAM WAVES OF DIFFERENT LENGTH. . . . . . . . . 28
11
LOADING CONDITION FOR MAXIMUM VERTICAL BENDI!JG MOMENT INBEAMSEAS. . . . . . . . . . . . . . . . . . . . .30
12
T-AGOR16 STRUCTURAL CO!iFIGURATION. . . ... . . . . . . . . . 39
13
STRUCTURAL MODEL OF T-AGOR16 FOR IBM-1130 “STRESS’’pROGRAM. . . . . . . . . , . . . . . . . . . . . .3g
14
DESIGN SHIP PROFILEANDPLAN.
15
DESIGN SHIP TYPICAL BULKHEAD STRUCTURE . . . . . . . . . ... 42
16
DESIGN SHIP SECTION MODUL1 . . . , . . . . . . . . . . , . . 44
. . . . . . . . . . . . . . . 42
v
.“..
. . . . . . ...24
SHIP STRUCTURE COMMITTEE The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research program to imprmm the hull structures of ships by an extension of knowledge pertaining to design, materials and methods of fabrication. RADM W. F. Rea, III, USCG, Chairman Chief, Office ofhlerchant Marine Safety U. S. Coast Guard Headquarters Mr. E. S. Dillon Chief Office of Ship Construction Maritime Administration
Capt. J. E. Rasmussen, USN Naval Ship Engineering Center Prince Georges Center Capt. L. L. Jackson, USN Maintenance and Repair Officer Military Sealift Command
Mr. K. Morland, Vice President American Bureau of Shipping
SHIP STRUCTURE SUBCOMMITTEE The SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committee on technical matters by providing technical coordination for the determination of goals and objectives of the program, and by evaluating and interpreting the results in terms of ship structural design, construction and operation. YAVAL SHIP ENGINEERING CENTER
U. S. COAST GUARD
Mr. Mr. Mr. Mr. Mr.
LCDR C. S. Loosmore, USCG - Secretary CDR C. R. Thompson, USCG - Member CDR J. W. Kime, USCG -Alternate CDR J. L. Coburn, USCG - Alternate
P. J. G. H. I.
M. Palermo - Chairman B. O’Brien - Contract Administrator Sorkin - Member S. Sayre - Alternate Fioriti - Alternate
NATIONAL ACADEMY OF SCIENCES MARITIME ADMINISTRATION Mr. Mr. Mr. Mr.
F. A. R. R.
Mr. R. W. Rumke, Liaison Prof. R. A. Yagle, Liaison
Da.shnaw- Member Maillar - Member Falls - Alternate F. Coombs - Alternate
SOCIETY OF NAVAL ARCHITECTS & MARINE ENGINEERS Mr. T. M. Buermann, Liaison
AMERICAN BUREAU OF SHIPPING Mr. S. G. Stiansen - Member Mr. F. J. Crum - Member OFFICE OF NAVAL RESEARCH
BRITISH NAVY STAFF
Mr. J. M. Crowley - Member Or. W. G. Rauch - Alternate NAVAL SHIP RESEARCH & DEVELOPMENT CENTER
Dr. V. Flint, Liaison CDR P. H. H. Ablett, RCNC, Liaison
Mr. A. B. Stavovy - Alternate WELDING RESEARCH COUNCIL MILITARY SEALIFT COMMAND Mr. R. R. Askren - Member Lt. j.g. E. T. Powers, USNR - Member
vi
Mr. K. H. Koopman, Liaison Mr. C. Larson, Liaison
LIST
Where also
equations
provided.
are
reproduced
Each appendix
SYMBOLS
from
of their
symbols
are
list of symbols.
Definition
qh
Aggregate
B
Beam of each
b
Hull
horizonta
centerline
Block
I acceleration
hull spacing
coefficient
CLA Cw c
Waterplane Oblique
wave
c
Midship
coefficient
Do
Draft
d
dl-0.65Do
Centerplane
area
coefficient
coefficient coefficient
d]
Distance
of cross-structure
F Sc
Vertical
shear
Fsl
Maximum
shear
F so
Maximum
waveinduced
total
9
Gravitational
H
Wave
neutral
at iuncture
cross-structure
weight
above
base I ine and
hul I due
to
weight of cross%ructure
at iuncture
shear
I ess cross+
axis
of cross-structure
at iuncture
and
hu I I
of cross-structure
and
hul 1,
ructure
acceleration
height
RI/~
Significant
HL
Side
hydrostatic
force
on outboard
HR
Side
hydrostatic
force
inboard
h
Horizontal
L
Length
Ml
Maximum
wave
shift
between
and M=
definitions
references,
has its own
Symbol
Cb
OF
Moment
height
of center
shel I
shel I
of buoyancy
of one
hul I
perpendicular
vertical
bending
moment
at iuncture
of cross-structure
hull at iuncture
of
cross-structure
and
hul I due
to weight
of
cross-structure M.
Maximum
P
Maximum
s
Clear
wave-induced
bending
1ess cross-structure
hull
axia I force spacing
vii
moment
on cross-structure,
weight-
Definition
Symbol
T1 Tc
Maximum
torque
on cross-structure
abut
its twist
center,
t # o
To
Maximum
torque
on cross-structure
about
its twist
center,
t = o
t
Longitudinal
distance
between
axis
and
cross-structure
Centroid
of HR below neutralaxis of cr~ssstructure
width
neutral
LCG
of HL
Total
below
ship
Centroid
of cross-structure
of catamaran
Wave
surface
above
stil I waterline
at outboard
Wave
surface
below
still
at
Total
(both
g x added Wave
hulls)
waterline
displacement
mass in sway
of both
length
LCA Mass
density
Circular
wave
of water frequency
viii
—.
-.
hulls
inbcard
shell shell
twist
center
1.
INTRODUCTION
The history
of catamarans
it is only
in the
resulting
in the construction
Except
last decade
for one
pipe-laying
cargo
in Iengthl
except
(Russian). were
barges.
vessel
transverse
stabi I ity,and
research
good
However,
that
(Dutch)
for the
special advantage
I ity
these
ships,
to tuke
maneuverabi
all
to note
Duplus
that mainly
(2).
of serious
for use on the Volgar
the 400-foot
monohulls
a revival
in this
interest
century,
in catamarans
vessels.
it is pertinent
be recognized
over
(1) and
has been
oceanographic
Also,
for two,
It may
selected
references
there
of some sixteen
pose vessels , such as ferries, and
is old,
that
fishing these
and
boats,
large
under
purrigs
315
Kyor
feet
Ogly
catamarans
deck
offered
special
drilling
ships are
in question,
of the speeds
are
the 425-foot
purposes
at low
vessels
area,
by the
high
catamaran
configuration.
The question cial
sector
for low with
density
the
taken
has been
the
Navy.
pay
load .
Catamaran
Study
a comprehensive
Industries (6),
and
claim
and
for the
proiect tions
trade
obstacle
information
reported
here
of catamarans,
structural
knowledge
The features
the
catamarans?”
interest the
by General
of catamaran
prepared
- both
is related Maritime
technology
(2),
design
commervessels
Administration and
the
(3) and
catamaran
a preliminary
in the
to high-speed
Dynamicsr
of a semi-submerged
began
Navy (4).
Litton
container
of a catamaran
has under-
ship
(~) and
container
ship
(7).
in assessing
the desirability
to establish
the structural
was to investigate
into
appraise
existing
required
to insure
examined
that
the
design their
could
scant! ings , construction
cross structure
not large
this question,
performed
design
have
et al,
A SOI ient
To answer
assessment
Trans-Atlantic
of technical
“why groups,
(1)1
an actual
Fisher,
raised, In both
of large
structural
size
problems,
limits
and
has been
The purpose
technological
procedures,
impose
catamarans
requirements.
to size
determine
the
lack
of the and
propor-
the additional
adequacy.
limits
repair
were
powering
facilities,
and
and propulsion, harbor
and
pier
limitations.
In order at by
least
to estimate
the first
considerations
The maior design and
of the
comparison
Evaluation ture
other
effort
the
cross-structure
of the prel iminary than
of the
cross-structure. of al I available
of the analytical
analysis
Numbers
cycle
cross-structure
proiect
scantl design
scantl
was centered
methods
test data for estimate
methods.
in parentheses
refer
to references
I isted.
catamaran
to accomplish of a size
indicated
ings.
around
The task was divided model
ings it was necessary
of a large
into
on the
the procedure three
loads
parts,
on the
of cross-structure
for the viz:
structural
(a) Assembly
cross structure; load
and
(c)
(b) Struc-
2 New rnomentf tion
equat ions are proposed
axial
force
Modifications
and shear force .
of wave-induced
vertical
bending
are proposed
to an existing
equa-
for torsion. The project
scope was limited
semi-submersible
catamarans
made to analyze
the influence
Of all tion
and model
of catamaran
Appendix
1.
as well
of catamaran
Recommendations large
work
test measurements, aspects
or strut-stabilized)
of symmetrical
Considerable
important
catamarans .
as opposed
No attempt
hulls or non-symmetrical
hulls
to
was
on the size
of catamarans.
the aspects
in the past.
surface
to conventional
(column-stabilized
I imit or the cross-structure
2.
for the estimate
design,
resistance
has been done as their
resistance
has received
correlation.
as gathered
are made for the future
the most atten-
in the areas of theoretical A brief
from the I iterature
research
prediction
statement
on the most
is provided
in
program
for
and development
catamarans.
ANALYSIS
OF FEATURES
It appears, would
in principle,
preclude
that
the design that
wil I not be special
problems
development
necessary
dertaken force
effort
strongly
favor
without
The features a.
IMPOSE
the facilities
are no insoluble
exist
to build
to build or that
termincltioh
considered
considerations
catamaran is no need
vessel .
What
to design
some unknown
which
in the United
many ships immediately,
the venture
that
technical
there
an efficient
catamaran,
LIMITS
of a 1000-foot
to overcome,
a large
SIZE
that
for future
is meant and build
technological
States. there
research
is that
and
if eco-
one may be un-
problem
wou id
of the venture.
in reaching
the foregoing
conclusion
are as follows:
Resistance-Powering-Propulsion: Main
,, situation
and propulsion
in large
may require
limit
designed
machinery
not found
catamarans upper
there
a strong reservation
the premature
MAY
and construction
This does not imply
nomics
THAT
monohull
system for a large Depending
designs.
more than one propeller
to the catamaran
to accommodate
size,
assuming
per hull .
that
hull
catamaran
beam
However,
very
a
large
this need not set an
is sufficient,
Machinery
more than one propel Ier.
does not present
on speed and draft,
and form can be
weight
and volume
should
be acceptable. b.
Wave
Loads,
Cross-Structure
The hydrodynamic cwrse, Design
the differential checks
ing show that loads.
With
conservative thickness
unique
loading
for up to approximately cross-structure full
transverse
estimate
is 1-1/4
to be stee 1.
effect
wave
with
There
and
Structural
to catamarans
Material:
and of prime
on the hul Is to be absorbed 1000-foot
practical
bulkheads
of effective
inches.
$cantling
catamaran
IOO-foot
scantl ings can be designed
at approximately
flange,
with
consideration
the maximum
is no doubt
that
50-foot steel
is, of
by the !cross-ktructure. clear
to absorb
spacing
the wave
and making
(100,000 psi yield)
the cross-structure
hul ~
material
the
plate
would
have
3 c.
Drafts: depths at existing
Water approximately d.
United
140’ monohulls. measure
Northern larger
the world
suggest draft
Ireland
Company’s
cun build
new drydack
y 1965’
of the available hul Is afloat.
dock would
equal
at Sparrows
have
Point,
construction
Catamarans
of
1050’ Maryland
in Japan
with
x
and
overal I beam
to have the hulls and the center-
technique
depth,
up to approximately
under
x 329’.
The latter
Twin docks with
may be an answer,
e,
facilities
One mil I ion ton drydocks
wi II be approximate with
construct ion.
Steel
x 200’,
than the width
width,
States drydock
Bethlehem
1200’
body assembled
was used in the E.W.
iust the correct
depth
Thornton
and iust the correct
if available.
Drydocking: Drydocking
poses a problem
dock sizes mentioned construction floating
in the previous
of new facilities
will
if the desired paragraph.
be required.
catamarans
are too large
Modification
of existing
From a technical
for the dry-
facilities
viewpoint,
or
use of two
docks may be feasible. One
problem.
must not underestimate
Evidently
struction
the ingenuity
no serious reservation
of the 250-ft
wide
Mohole
of shipyards
was held
k Iatform
regarding
to solve
drydocking
the drydocking when the con-
was initiated. I
~
I The Livingston Shipbuildi~g Company has Chydockdd the 10~-fi wide E.W. o n a single floating dry~ck split into two longitudinal hlalv$s held together I beams. \~ ;
Thornton I
1imitation
Construct ion: Existing
will
cargo piers around
35 feet.
by spacer
I
i’
It is beli~ved smal I catamarans !,
I
I
11
tha~ the Rus~ians have a scheme
for maintenance
and repairs.
1
I
for’ dismantling 1
I
their
relatively
1:1’1 )
f’ .~
Cargo
H6ndlirig
,,
and Piers: \
I
,,
The problems of cargo handling and piers are economic probllems. They can be I at a p~ice, if the ecolnornicsof catamarans we r e so attractive~. Use of twin
solved,
piers or di+chqrge
Channels
9.
‘1
Certain
c~n ~cckpt ‘1,
have possibi I ities.
and Harbors:
,,
I world
o~ cargo offshore
that the maiority
ur!publ ishe~ st~dies ‘claim 1000’
x 400’
I
ca~@narans.
‘,1
!
I
I
h . Economics:
of maior ,!
I
‘1
!,’
harbors around 1’
I
/,
I I
,’
Dynami ~s study (1 )and certairl 1
nomics of catamarans most marginal
.
as compared
Captain
M.
to economics
-Eckhart,
Jr.
,.
unpublished
studies
claim that the eco-
of mbnohul Is are unfavorable
reporting
I
1:
I
‘1
The General
the
on the Navy’s
findings
or at the
to date
(3)
4 states “No multihull
3.
compelling or catamaran
EXISTING 3.1
reason
STRUCTURAL
exception
of existing hulls
the classification
criteria
structural
or guidelines
engineering
Ship design
the ASR Catamaran 3.2
METHODS
determination
A.
nor the governmental
Calm
water
i .
have
16 Catamaran
“ The Structural
Design of
(8) as guidance.
there are two phases to the cross-structure of the structure
by the cross-structure
load due to the weight
to alxorb
design,
the loads.
are:
(lightship
weight
and dead-
loads due to differential
wave
loads on the indi-
hulls.
Transverse vertical as iust the Bending
Bending
Moment,
Moment
or sometimes
usual I y referred
to
even as the Rol I
Moment. I
ii.
estab-
must follow
of the cross-structure.
Wave-induced vidual
agencies
design and designers
In the case of the T-AGOR
by Lankford
since
Loads
experienced
weight) B.
societies
to the cross-structure
as monohul Is.
for cross-structure
of the loads and the design
The lads
is I imited
been treated
did suggest the use of the paper
Construction”
Cross-Structure
design procedures have
techniques.
the Navy
As for any structure, the
to the
.“
DESIGN
individual
Neither
Research
shift from the monohull
General
lished design general
in sight for a general
configuration
The coverage withou~
is yet
Vertical
Shear Force,
usual Iy referred
to as iust the Shear
Force.
t’1
C1--p3 !
I
namely,
5
iii.
Torsion Moment,
sometimes
referred
to as the Pitch
Moment.
iv.
Transverse
v.
Horizontal
in-plane
in-plane
Horizontal
Moments
I
Force or Side Force ,
or Yaw
I
Moment.
b
c.
vi.
Longitudinal
vii.
Water
sidered
i,
impact
Grounding
The controlling numbered
ii,
a design hulls.
bending
moments Earlier
model
test (9) (report
which
designers
appear
tended
to neglect
unpublished)
were
Impact bottom
loads are treated and
in causing
to be included
them and only the side forces
and docking inboard
as local
shell
the maximum
in the direct
of the in-
vertical
stress calcula-
in one conventional measured.
loads is con-
catamaran
Loads (v) and (vi)
stresses.
However, conclusions
rise to the muximum appear
is devoted
at this point
investigators’ load estimate
loads.
are the wave-induced
(if grounding
to be instrumental
magnitude
likely
to give
water
design
loads
of the cross-structure
The rest of this section sign methods.
Loads
and docking
and the calm
are of sufficient
tion.
cause negligible
and Docking
reinforcement
Side forces
loads.
grounding
criteria)
dividual
Force.
loads in the cross-structure
and iii,
loads and require
in-plane
to the survey of the existing
it may be desirable
as to the vessel positions
in Section
5.
response
with
to point respect
and the recommended
out that
structural
to the waves method
de-
the proiect *hat are
for design
7
Table 1 - Catamaran Load and Structure Analysis
Areas of Contribution
c-s
Wave
Steel Ref. —.
B.W.
Lankford,
H .A.
Schade
—
Bending
Shear ——
Torsion
15
Table tests to provide
for wave any
cluded in tables of Section
3.3.1
1-
+
+
+
Structure
Description
of Univ.
of Miami
Catamaran
5.
Design
Structure
Methods analysts
loads.
actual
and their Iy built
Model
These tables
published
have
test data
on the work of each
calculations
and calculations
performed compare
relied analysis
structure
to assess their model
by new equations
contributions. heavily
is covered
in Sec-
analyst
listed
methods
are in-
test predictions,
presented
It
on model in
calculations
in this report.
R. SCOTT While
Scott proposed
+
Thornton
and discussion
Howeverf
methods
+
of E i W.
of catamarans
the numbers
1 follow.
by existing
Design
designers
Brief description
+
Description
1 lists load and structure
that
i-
+
Survey of Existing
is emphasized
-+
1-
14
Michel
3.3
maran
Moment —
+
Michel
Table
Strwc~ure Analysis
Torsion
Force
-1--
4
Livingston
and W.H.
tion 4.
Shear
i ng Mom. .—
13
J .L. Glaeser
W,H.
Loads
Bend-
12&13
Thomas
C .W.
Est.
8
Jr.
. Dinsenbacher
G. O.
i ng
10
R . Scott
A.L
Ground-
Wt
Loads
expressions
cross-structure
still
a Naval
Architectural
student
for the stresses due to torque
(10).
at the University
and transverse
bending
of Michigan, of a cata-
They are as fol lows:
Torsion: To obtain vessel
was poised
obliquely
the torsional on a trochoidal
bending wuve,
moment, a fine-1 ined 300-foot 170’ x 1(3’ . The crest coincided
long with
8 the forward
quarter
point
of one hull
the trough at the extremities. vessel or the basis for selecting the center percent
of buoyancy
high wave.
,A = Total
)
of the other
Under
hull,
information
this attitude
of O .04L
was given
displacement
the wing structure
S, was given
point additional
with
on the of the vessel,
the crest by an amount
hul I had a torque
on the cross-structure
Assuming the stress,
a 10-foot
Thus, each
torque Where
sion,
has not provided
of The hulls moved toward
of the length.
hull and the total
and the aft quarter
(Scott
equal
to 4
times the displacement
per
by T = O .04LA
of catamaran
as a thin wal led rectangular
tube in tor-
by
S.-L 2 At where
A =
Area
t
Tube thickness
=
of the tube and
The approach be,
has merit
have
been compared
where tive
for application with
the test value
to obtain
in early model
the total
test results
is 16°\0 higher,
moment,
in all
in Table other
9.
cases,
as simple
Torque as given
Except O .04LlJ
as it may
by O .04LA
in the case of one vessel would
provide
conserva-
estimates. Little
catamarans
have
as a single
tube.
application
longitudinally
Transverse
can be found for the stress expression
discontinuous
cross-structure
partially
emerged
where
severe
one-half
Hull Stress
=
—
separation
Section
(W-2
A portion than
(Note:
SL
/4
Here
available while
model
for other
S = clear
Under
displacement
modulus of cross-structure
B)~/4
Section
with
x 1/2
rolling
of the entire
cantilevered from the end of the cross-structure. cross-structure is expressed as
/4
which
as al I known
can not be idealized
Bending: [t was assumed that during
can become
S2
torque
stages of the design.
=
7 is
test results. vessels S L
this assumption
of one hul I is the stress orI the
of one hull on centerline
s6/4 Sect ion modu I us
modulus
of Table
in beam seas one of the hulls displacement
a comparison
of bending
moments given
by
[t shows that the test value for ASR is higher /4 is higher than the test values.
hull spacing)
..—
9
Even though higher
than the model
ship-wave
relationship
generates
cussion on the condition
3.3.2
Lankford’s
operators
(8) includes
approach
of the design sea loads
11[.
Drydocking
and grounding
iv.
Structural
to sea lwd
v.
The design procedure
configuration
occurrence
tests (1 1),
The ~rt above,
together
with
such a manner aft at station considered wave
overly
induced
no buoyancy
support
assume that the hull
torque
which
used response amplitude derived
from data on 12
(Great
Britain),
in Appendix
and wave
forward
is given
at station
by bd/4
can occur
with
LA .
which
docking
in
is supported
This criteria condition Further,
can force
.
weight
are much higher
only .
is not such that the vessel weight
criteria
maximum
The assumed loading
during
(v) mentioned
4 and the other
= 0.175
values
9.
through
2 of this report.
loads as design
or grounded
and it gives torque
is available
moments were obtained
covers points (ii)
and grounding
as can be seen in Table flexibility
spectrum
of Oceanography
uses drydocking
conservative
torque
wave
that the vessel is docked
the design
bending
calculations
, is reproduced
that one hul I is supported 18,
Design
prediction
vertical
ocean
of the paper
Lankford
“The Structural
At[antic.
the references
Based on the assumption
dis-
5.
of the ASR
lnst itute
in the North
in Section
loads
The prediction
storms at the National
of the
the fol lowing:
Distribution
by model
values
A more detailed
paper,
ii.
provided
frequency
appears
Analytical
a long term prediction.
most severe
moment
and valuable
The design wave-induced by making
moment.
i.
. ..
moment
assumption
JR.
well-known
Cross-Structure”
bending
the particular
bending
bending
LANKFORD,
provides
whether
the maximum
for maximum
B.W.
of ASR Catamaran
Scott’ s assumption
tests it is questionable
is than where
one must the keel
down to the blocks.
The Lankford designers
for two reasons, i. ii.
method
of cross-structure
ana Iysis is likely
to attract
viz:
It is neatly
stated and simple
It is the only available vessels actually
built,
and quick
method namely
which
to apply. has been applied
the ASR and the T+GOR
to 16,
10 However, the readers must be cautioned against of this method as it appears to oversimplify the structure
acceptance questionable
assumptions.
servat ive structure.
Further,
The primary assumption
the cross-structure
at the iunction
H.A.
does not assure
oversimplification
mary questionable
3.3.3
the method
is that there
since
forces,
vertical
SCHADE
moment,
the information
and A.L.
The Ship Structure
graphs are taken
equations
developed
Appendix
The ,pri -
the hul Is and
proiect
reported
and Analysis
made to Schade’s
are reproduced
equations
in Appendix
methods,
para-
of Dinsenbacher’s
and the assumption which
3 of this report.
in the paper
from
The fol lowing
(from the same paper)
refer to the references
devel-
here benefited
section
to-
for axial
of methods
in these two references.
The Summary and Discussion
bers in the quotation
to develop
moment are refinements
from the Introduction
paper and they state the refinements the methods.
between
works (12) and ( 13) are considered
Committee
of presentation
directly
rotation
DINSENBACHER
by Dinsenbacher
shear and torsion
and style
nor a con-
of the hul Is and the cross-structure.
the methods employed
oped by Schade.
an economic
is that the hulls are rigid.
is no relative
.Schade’s and Dinsenbacher’s gether
the unreserved and make some
which
include
of
the
(The reference
num-
are also included
in
3.) “In
1965 Professor H .A.
going
catamaran
cross-structure forms acted
relates
higher
but to modify
only
to employ
in an effort
loads measured “The resulting
waves.
design
empirical
tudinal
strength,
ship hull girder
equations
design
A procedure
(Quotation
“For this study,
Imds.
Imds,
lengths Also,
Schade’s
method
length.
It method
waves are substituted are related
the wave
to the ship
amplitudes
relationship
are
and to the
”
herein
height-length
are simple
relationship
evaluations primary
and quick
of a more realistic
and loads measured
for estimating
loads to be some-
Also,
Sinusoidal
model.
devised
to compare
aspects of Schade’s
height-length
model and full-scale design
test.
on a combination
wave
gross loads is also included.
wave
used for longi-
of current
surface-
on a catamaran
stresses resulting
model from the
‘“
Continued) in a manner
ized as two rectangular rectangular
wave
the
test of an
and not to wave
The wave
to optimize
They are founded
the current
Assumptions:
Schade’s
many of the general
on the ASR catamaran
shape,
in waves.
showed
used in his study.
Iy fronted
to the current
to employ.
It was decided
to ship dimensions,
the waves
for the vertical related
The comparison
height
was thus decided
dimensions
waves.
to results from a model
than those found from the model
wave
for estimating
assumed the hulls to be prismutic
Iy fronted
from this method
(2).
study of an ocean-
were developed
The author
upon by vertical
ASR catamaran
made a feasibility
equations
loads (1).
the loads resulting what
Schade
in which
similar
to that of Schade,
prisms (representing
box (the cross-structure)
.
the ship is ideal-
the hul Is) connected
The longitudinal
by a
and transverse
dis-
11 tributions
of weight
structure. tation
are taken
The length,
as uniform
beam,
of the hulls are taken
draft,
box has t-he same length
weightr
clearance
above
forces
displaced
between
fluid
produce
,
Also,
vertical
These heave
maxima
to expect
than vertically Inertia
are ignored.
structure
Figures
on the equations
force
contribution
Bendina
discussion
Moment i.
celeration
idealiza-
are not unrealistic
Sinusoidal
waves
rather
in calculating produced
loads.
Slamming
that relative the highest
posicross-
in the worst conditions. 1 and 2 will
There-
be considered
,“
3. associated
assumptions
fol low:
1 (see Appendix is the same. ii.
dix 3,
for maximum
values
in 40-knot
in beam seas does not account acceleration,
which
conditions
and available
not stated
3,
specifically
side hydrostatic for the relative
Figure
for the pos-
can be substantial
for maximum
test data
,
loads as
is covered
1).
the bending
in Section
moment equations
force and maximum
vertical
wave and ship position
ac-
of Loading
Alsa that the sense of the acceleration
The second term on the right
shear is obtained
wind
by relating
side of equation
(75),
the shear and bending
on
Appen-
moment
RMS
beam seas for the ASR catamaran.
that shear and moment
sult of the particular
force
and Shear:
occur at the same time
both hulls
Intrinsic to this operation IS are in phase or that the particular shear is the re-
moment. The validity
do play a very
ing moments and shear. tion 5.
(3) .
and their
on the prohble
maximum
Condition
assumptions
and these accelera-
assumed herein
in Appendix
analysis
Although
assume that
the assumption
in the com-
Pressures are assumed hydrostatic.
result
developed
for axial
from some independent
development
life
shown in Figures
due to the horizontal
Detailed concluded
in
forms as
Force: The equation
sible
work will
conditions
hull
is not modified
of * 0.4g
to those which
1 and 2 are included
Comments
Axial
amplitudes
It is further
loads in Schade’s
only the loading
axis
for the difference
the loads on the prismatic
forces on the ship mass are included and ship similar
of neutral
used for the computa-
of ~0 .4g,
waves are used.
tions of wave fore,
density
for the ship’s service
and whipping
depth,
blocks and the actual
accelerations
acceleration
fronted
width,
location
density
represen-
The intercon-
the drafts are found for the prismatic
tions and drafts are used in computing tion.
hul Is),
here to compensate
the fluid
loads.
hulls.
and vertical The fluid
the rectangular
however,
of transverse
forms which
stil I water,
is modified
was done by Schade; putation
(span between
cross-structure
tion of vertical
of the prismatic
as those of the actual
necting
as does the actual
in the hulls and in the cross-
and weight
of the foregoing
irnportan~
The reasoning
two assumptions
part in the resulting behind
equations
the objections
will
is doubted.
The two
for maximum be found
bend-
in Sec-
5.
12 Torque,:, Equation occurs
in oblique
TO =
ter of gmvity,
which
by relating weightless
sion.
gravity
cross-structure)
over
without
beginning
ployed
of Catamarans”
with
Analysis
and Design” lecture
for torque.
THOMAS
G.0.
Thomas delivered
at the University
[n developing tories
to refer
to some very recent
(unpublished)
tion on structural and slamming
The clearance ance
loads which
to note that designed
the design
formula
C=3+
1.1
of Miami the forward
“Structural
in September strike
criteria
criteria
Analysis
of Ship Structural 1970.
[t was a gen-
platform
for which
con-
developed.
was as presented
for aircraft
at the British formulas
to catamarans
for cross-structure
{~)
by this formula
carriers, National
and Development
contained
by
Thomas was Physical
Center.
for cross-structure
in general
.
clearance
above
LakraThe secclearance
load waterline
but C<20 compared
and the ASR but it gave
design
and preas possible
The first term is em-
Techniques
of a naval
Ship Research
selection
Thomas’
Thornton
in as many details
load derivation
work performed
are applicable
as calculated
for the E .W.
the University
criteria
of
in this report.
and at the Naval design
that the term
of center
is large.
(4) entitled
and design
on design
earlier
tor-
moment
4).
a lecture
design
was collected
The m@erial
able
to the fact
of motions.
of California
on the conceptual
bending
is found to be logical
of a short course on “Modern
and discussed
causes the maximum
from center
It seems to take equations
(for a catamaran
I isted under
is drawn
of the ship,
term is ob-
moment
which
equation
(which
the ship’s cen-
The latter
of twist of the cross-structure,
ize :he test data (Section
information
of gravity through
bending
tr the distance
G.O.
bed
design
the hulls. wave
torque
is
t/s
the center
Attention
unless
the fundamental
as one prt
eralized
Dinsenkmcher
also.
to be large
to nondimensional
siderable
Iy heave
in the same oblique
is doubted
expression
3.3.4
hAQ
due to shear acting
of the first term in the torsion
Scott’s
for maximum
is the same as the second assumption
is not I ikely
The development
0.14
shear to the maximum
of the ship to the center
ferred
I
the .tcmsion about
tends to differential
and shear and its validity in question
developed
of the cross-structure +
the torsion
the maximum
This assumption
3,
center
BAL 2/2~
represents
the second term represents
tained with
the twist
SCbg
The first term on the right while
(79) Appendix
seas) about
and the Ridgely
quite
closely
much higher
Warfield.
to the actual
values
in this respect
clear-
than actual
b
it is pertinent
end of the Ridgel y Warfield’s cross-structure is lmw shaped and It is suspected that for very large catamarans the crossfor low cl *rance.
is
13 structure
clearance
may be controlled
for the individual additional
hul Is.
clearance
Also,
by the minimum
the designer
is I ikely
depth and freelward
requirements
to pay some penalty
if the ends of the cross-structure
are within
in terms of
approxirrwtely
L
0.15
of the ends of the hulls. Thomas provides cross-structure as local
slamming.
areas since
The following
He elects
a fairly
lengthy
to treat
the relatively
they are of minor
discussion
Region 2) is quoted
importance
on the slamming
directly
“In Region 2,
lecture
strictly
the easer
Wave
buildup
slamming oratory
but lacking
within
aft.
specific
cally
in the lateral duration
bent and overall “The highest
report
(a) short-term
pressures for short-term
The equation
which
could
p is the flat
for sea water. forward
slamming
_. .-
S. L.,
pile-
slamming deadrise
insufficient
“Experiments
bottom
”
can be taken
appearance
as for flat
that welding
dis-
to the cross-structure crests as a flat
bottom.
is from Chuang*
pressure
in pounds per square
ship and fluid
station
in feet per second,
for relative
since
impact
motion
on top of the wav~, pitch of hull
motion.
on Flat-Bottom
Slamming,
impact
at
velocities
as transients
to fluid. to affect
and
to those
was taken
Pressures greater However,
to the water-structure momentum
inch,
pressures are assumed to
can be experienced
angles
localized
lo-
64/62.4
and,
the ship descends
shallow
in Region 2 can be
pressures from those for fresh water
on design maximum
sumed to carry
1966)
Lab-
water
pressures acting
by considering
slamming
The slamming of amidships
are usual Iy very
(March
with
and on the edges of floors and
slamming
between
converts
from flat-bottom
*Chuang,
bottom
motion
64/62.4
bottom
then slam on wave
used for flat-battom
V is the relative
tively
effects
Physical
less than at the forward
high-impact
This can be iustified
p =4.5V
when
by the National.
bottom gril Iage design.
plating
ksed
to be so.
it primarily
pressures used for cross-structure
bottom
were
platright
it was taken
since
for lower
cross-structure
can cause a s! ightl y concave
occur
to as
This may not be
for ~nels
tortion
O .46L
(referred
Imttom
direction
impact.
the value
flume.
information,
fins were a little
bottom
where
areas
weight.
of the cross-structure
on the cross-structure
into two kinds:
(b) longer
for
”
“Loads from slamming divided
areas
pressures aft for a catamaran
anti-pitching
point.
middle
of cross-structure
was neglected
A second unpublished
up and without
smal I forward -cmd-aft
the catamaran
the tunnel
shows that high-impact
quarter
area
by the descent
passing through
criteria
notes ( 4).
of the largest
ing was assumed to be caused on top of a wave
on the design
to the overal I cross-structure
loads on the large
from Thomas’
slamming
discussion
than those
for relathese pressures
interface
and were as-
the design
of the plating.
” Journal
of Ship Research
”
14 “ The
first mentioned
cross-structure a given
severity
Pritchett**
The general
sea conditions
short-term,
80 and fell
(Beaufort
120 psi, (within
within
impact
of bottom
flat-bottom
tanks,
and to floors and double local
“Following
slamming which
~ V2 where
P is the flat
pressures were applied
were then designed bottom
of the wave.
ship and fluid velocity
the orbital
sures were
bottom
might
then applied
for the conceptual
limitations
it to nonaircraft 3.3.5
carrier
JOHN While
pared an undergraduate
is extremely
L.
carriers.
i .e.,
ship and fluid
of particles ranged
in the wave
below
the crest
from 600 to 900
series studied.
These pres-
bottom grit Iage
for the cross-structure
of involving
large
errors when ap-
GLAESER
at the Webb
thesis entitled
calculated
test results (1 1) . Figure
equation
restricted. Actual Iy, it was developed llm equation is not presented here due
and high prokbility
were heave,
Glaeser
a weight
type structure.
Institute
of Naval
“A Theoretical
and the Shear and Bending
responses considered model
between
to the overal I cross-structure
design on aircraft
to its acknowledged
on his theory,
to that
of sea water,
”
but its application
of a Calamaran
of the cross-
now be well
Pressures from this equation
Thomas has also developed
plying
of
to design
in feet per second .“
velocity
pounds per square foot for the catamaran
of a catamaran
girders
pressure in pounds per square foot and V
the relative
to include
the cross-structure
design.
over single
0.994V2
between
“For this relationship can be taken
equation
as for boundaries
longitudinal
? is the mass density
bottom
motion
is the relative
since
of the cross-
of the series. ”
slam on the bottom plating
P= where
7 sea in another),
the pressure can be assumed to drop very rapidly
by 1/2
at
most prob-
.“
the initial
structure, given
collapse
testing
pressures from the Chuang
catamarans
“High
plating
in more recent
pressures can be assumed to be between
Slamming
for all
the
of slams of
when they did occur.
6 in one case and State
panels against
the intensity
of the size of the ship or height
reason).
this range
raising
the freque~cy
so far is that for the higher
slamming
regardless
showed that
reduced
this conclusion
concensus
high-impact
structure
NPL report model
but did not reduce
has confirmed
NSRDC. able
unpublished
on a catamaran
Moments
Architecture,
Investigation
on its Cross-Structure”
rol 1, shear and vertical
bending
moment.
the responses for the ASR and compared
1 (taken
Glaeser
pre-
Into the Motions (14).
The
As a check them with the
from the summary of the thesis) shows the compari-
son. ** Pritchettr Structure, (January
C., ” Naval
1970).
“Model
Studies of ASR-Catamaran
Ship Research and Development
Impact Center
Pressures on Between T&E
Report 340-H-01
Hull
15
HEAVE R E5PohJ5~
I
Ill
s
I
I
4
ROLL
I
,4
,2
I
,6
,5
, \/
1
1,0
I
1,2
1.4
1
I
I
,4
I
.Co
i
.6
1
1.0
FREQ~EtJCY
CF.055
5TIWCT
1
1
1.t3 Z,O
THEOL?Y (V= O RT5) MODELTEST (V=\5 KTS)
~E5mhJsE
.2
1
l.~
1
l-z
1.4
1
I
I
l-~
1.8
2.0
(~ADjsEc)
U IZE
13EMDI MG MOMENT (V=
O KTS)
TEST
( V=O
T
~,,,,
1 .2
1 .4
]000
Fig.
1 -
I
I
,6 FREQti8EhIcJ
1
W5)
(V’ 15 KT5)
1
!
1
1.4
1.6
1.8
,I 2.0
“~RAd j3Ecj
W%;OE LE !dG?I! Catamaran
I
E5T
Response
.50
100 ~FT)
In
a Regular
.
Beam Sea (Reproduced
from
Ref.
14)
16 To permit ing a catamaran
the
most basic analysis
the prablem
at zero speed in a two-dimensional
maximum
roll and vertical
sumptions
of the theory Motion
moments appear
cosine
to occur
WS simplified
wave.
by tak-
T his is reasonable
in beam seas.
Other
primary
as
as-
are as follows:
Calculations:
1.
The hulls are thin enough, the wave sides.
2.
All
a point
hydrostatic
The catamaran
is not pitching heave
between
Moment
is the same as at the
and inertial of each
and there
forces act
hul 1. is no cross coupling
and rol 1.
Calculations:
hydrodynamic
of buoyancy
of a hull
so that
sided.
on the centerline
effect
All
2.
is wall
the hydrodynamic,
Shear and Bending
1.
at the center
The catamaran
through 3.
height
and the roll small enough
and hydrostatic
of each
The cross-structure
forces act through
the center
hull as it moves. is weightless
(in accordance
with
the model
test), The catamaran
3.
First, and rol 1. were
Then knowing
calculated,
Gltieser
The constants
Grim’s
coefficients. Comments
being
is nearly
theory
identical
. .
mass and damping
Although
far heave
individual
hull
differential
were
equa-
calculated
using
Calculation
the shear response
in the principle
to the roll
motion
occurs at
point.
@ z
comparison However,
in identifying,
~
in magnitude at least,
is not in-
the shear com-
are verY respectable except that the 2 hull centerline spacing) while the 2 overall
width).
It is suspected
that *he hulls are thin and that the vertical
The agreement
and shear force.
1 ( A
thesis.
comparison.
The rol I and shear correlations 1.2(>= occurs at @ ~
maximum
has succeeded
1.
it is included
this i$ due to the simplification
rol I m~tion
made up the original
of Theoretical
parison
a single
equations
sided.
Test Results for the ASR See Figure
through
and is wall
the differential
on the Comparison
in the summary,
experimental
those which
of gravity
the forces on each
added
eluded
maximum
and solved
of proportionality,
and Model
theoretical
wrote
its center
the motions of the vessel,
the forces
tions.
rolls about
leads one to conclude
the principle
parametem
that
force acts that the
which
influence
17 Figure valuable
1 does not show the model
to note that the theoretical
test curve
in which
when roll,
heave/wave
shear and bending
heave
height
curve
test heave.
In this respect
it is
the Thornton
model
is very much like
is approximately
moment are maximum
zero at that wave
and approximately
frequency
unity
at low fre-
quencies. The bending theory. static
As Glaeser
himself
and hydrodynamic
moment
suspected
side forces.
correlation
is poor casting
it is most likely It will
a doubt on the
due to neglecting
be observed
that
locations
both the hydroof maximums
are the same as for roll motion.
4.
MODEL
TEST DATA
As mentioned induced nize
earlier
model tests have assisted greatly
loads on the cross-structure
is that they will
have been proven This section imposed
ANALYSIS
continue
to do so until
to a high degree consolidates
of catamarans.
by sea waves on the catamaran
test programs and the consequent The purpose of the comparison and the major parameters 4.1
theoretical
of confidence
and compares
to this project,
the data plots appearing
mode[
cross-structure.
test data on the loads
Limitations
of the various
comparison
are enumerated.
the gross relationship
between
the loads
design and waves.
characteristics
as reported,
extrapolation
are amenable
was most valuable The portion
submersible
platforms
4.1.2
Vessel
of the Mohole
~’Undisclosed
range
around
the “Thornton”
of sea conditions
in estimating
were
that within Series. ”
catamaran.
.
and the
The amenability
loads on large
and the Livingston
were useable
the data
6-column
to
catamarans. semi-
for the ocean
tow con-
lines are below the top of the lower longitudinal surface catamarans. Test program for the University
Design was quite
I imited
.
Loads Compared The loads compared
test with
marked
be observed
and comparison
as it was helpful
In this condition the water hul Is and the vessels are essentially Research
a large
to extrapolation
.
It will
has been centered
included
test data which
2.
of a conventional
The bulk of the analysis
test data
of the vessels whose model
in Table
are data points
test report
and the “ASR” whose test programs
in each
methods
takes time).
the available
are provided
in the report
These are from an unpublished
of Miami
to recog-
Test Vessels The prototype
were available
dition
(which
was to determine
of wave-
and semi-empirical
1imitat ions of the data
of the catamaran
in the estimation is more important
Test Back~round 4.1.1
data,
What
model
at zero
speed,
were the two moment and one force viz:
measured
18
0 Vertical
Bending
e Vertical
Shear Force
aI Torsion Moment The crucial vertical data
moment
were measured
for the various
4.1.3
All
in Beam Seas
in Beam Seas
in Oblique
Seas
side forces which
are the malor
in the Livingston
test only.
tests are inadequate
Pertinent a.
Moment
Notes
to attempt
of the catamaran
simulated
a meaningful
acceleration
comparison
.
on the Tests
the test models simulated
radii
cause of the maximum
The reported
the total
as a rigid
the structural
weight,
body.
rigidities
centers
None
and gy -
of the models
of the centerbody
or the cross
members. b.
The ASR report
(11) provides
terms of response amplitude
random
wave
operators
test results
(only)
in
and response spectral
energy. The other oratory
tests which
reports
However,
were all
both regular
the random
wave
performed
wave
at the Davidson
and random wave
Lab-
test results.
test results are in terms of averages
only. c.
The all
important
various
loads and the wave
Livingston d.
Each test was performed
e.
dynamometers portional rangement
Load measurement
on two rigid
measure
loads.
Laboratory differential
have a core mounted
between
of the core.)
was not the same for every
“The hulls were
frames which inches
forward
connected
by a rigid
and
one forward
force
gages
and one aft to
measurement
to measure
dyna-
loads.
(The
the fol lowing
structure
which
The bridge
to linear
force
The bridge
arpara-
of the system.
system.
the hulls at the L.C .G.
aft of the L. C.G.
test,
is pro-
instrumentation
of the principle
bridge
moments measuring hul 1.
the actual
Laboratory
is informative
spanned
and one load-
two springs and the VOI tage output Although
Davidson
in the starboard
bars,
transformers
to the port hul I and was connected
dynamometers
configuration
used Schaevitz
Report (17)
part of the force and fixed
the
and the
The ASR test used four strain
aluminum
are I i near variable
to the displacement
for a specific
system:
mounted
graph from the “ Thornton”
between
for the Mohole
only.
The Davidson which
on phase relationship are available
tests only.
ing condition
mometers
information
was a was
measurement-
wws made up of three and at two points
The frame at the L .C .G.
12 was
19 Table 2 - Prototype Characteristics of Model Test Vessels
Reference
15,
Number
17
11,18
16,
19
20,21
22
Test Facility
Davidson
NSRDC
Davidson
Davidson
IMvidson
Hul I Symmetry
U nsym
Unsym
Unsym
Sym
Sym
1~1+11
390’-0”
260’ -0”
136’-6”
* 355! -Oil
Length
Overall
Length
Bet.
Perp,
Beam Overall,
Spacing,
Clear
Hull
Test Draft, Total
B b
Spacing,
s
Do
Displacementfb
z~ol-o~l 86141
501-511
250’-0”
371@
241-011
16’-10”
35’-0”
361-011
681+,1
621-011
331-7”
215’-0”
1641-011
311-ofl
*1-O,,
16’-10”
180’-0”
128’-0”
171-oil
18’-0”
6700 T
2797
0.73
0.54
0.84
105’-0”
W
Beam Each Hull, Hull~,
255’-0”
L
91-5,1 T
695 T
200’ -0”
161-OU
28 ‘ -7” 16,800
T
7700
0.75
0.90
0.737
1.0
1.0
0.92
0.92
1.0
1.0
L/b
3.75
3.37
1.163
1,220
L/D.
15.00
11.67
14.44
13.64
16.25
B/’Do
2.18
1.33
1.78
1.24
2.25
L/B
6.89
8.75
8.13
11.14
7.22
b/W
0.648
0.721
0.667
0.860
0.820
0.47
0.51
0.46
0.77
0.78
Block Coef, Waterplane Centerplane
Oblique
Cb Coef,
Cw
Coef,
Wave
Coef,
CLA
CA
* Assumed vu Iue
.
0.56
4.063
T
20 Table
3 -
Particulars
of
TABLE 3 -PARTICULARS
“E.
OF “E. W.
Ship A Scale
1,1
607.47
510.0’
325.89 ‘
255.0’
BeamOverall, W
250.22’
210.0’
134.19’
105.0’
88.17’
74.0’
47.29’
37.0’
73.87
42.0’
39.62’
31.0’
162.05’
12.5.0’
86.9’
‘s3 .0’
40.51’
34.0’
21.73’
17’-
Spacing, s
Draft,
Spacing, b DO
90,800 T
Displacement,A d 2 (W-B)
=2b
Particulars PARTICULARSG+
m
of
44.0’
324.10
272.0
“ASR” Series
“ASR”
14,000T
53, LOOT
52.43’
173.8
YES
ASR
1!3.19
1:2.675
1:1.71
1,1
669.90’
561.75’
359.1’
210.0’
8e.m Ovemll, W
274.34’
230.05’
147.06’
86.0’
41.04’
24.0’
Hull ~Spacing, Draft, Do Displacement, A d 2 (W-B) =2b
b
.64.20’
121.22’
110.65’
64.98’
33.0’
197.73’
165.85!
106.02’
62.0’
57.42’
4$..15’
30.7a’
90,800 93.79’ 395.54
T
53,600
124.0
Ships
Scale
Hull Spacing, S
22.0’
SERIES SHIPS
&!.!&
76.56’
0“
6r7@l T
2a.12’
LBP, L
Ekm Each Hull, B
Thornton
E.W.
LBP, L
Hull~
TABLE 4-
Ship C
m
1,1 .27a
B
Ships
SERIES SHIPS
1,2
Hull
4 -
THORNTON”
Series
1,2.3S3
Beam Each Hull,
Table
W. Thornton”
T
14,000T
Table
2,797T
50 .27s
73.65’ 331.70
1s .0’
29,4’ 124.0
212.04
5 -
Particulars
of
5- PARTICULAR50F TABLE
the
University
THEuNtVER51w
OFMIAMI
of
Miami
Series
SERIESSt+IPs
Univ. of Miami M
Ship C
=
Ships
Sc.alc
I;5. IXO
1,3.339
1:1,143
1:1
LBP, L
693.#
455.8
156.0’
136.5,
256.0’
168.3’
57.b’
50.4’
B5.3’
56.1,
19.2’
16.8’
85.3
56,1’
19.2,
16.8’
170.7’
112.2’
3.4’
33.6’
48.0’
31.5’
Beam Over. [1, VI B,nm Each Hull,
B
Hull Spucing, S Hull~
Spacing,
ila?t,
b
DO
Displacement,
A
91,1139T
25,827 T
10,81
9,45’
1,042T
495 T
23.9’
20.9’
d
106.2’
2 (W-B) = 2b
341.4
224.4
76.8
67<2
45.7
30.0
10.3
9.0
Signijicnnt HI T
Wave Ht,
69.8 ‘
Ships
21
attached other
to two dynamometers
frames were attached
terline tive
plane
spaced
to single
of the starlmard
hull .
shear force and the relative
the two dynamometers
moments , i .e. , primary
bending
whereas
the Ikvidson
4.2
Data
Laboratory
Consolidation
As mentioned and the ASR tests. prototypes ment.
were
operators
the R. A. O.S*
while
should be clarified state 5
(~ 1/3
the pierson-Moskowitz
the rela-
the outputs
relative
primary
of
rol I moments. ”
the ASR System measured
the data
analysis
the total
ver-
moments due to shear,
bending
is centered
data extrapolation,
moments only.
the particulars
expanded
S were
condition. spectrum
7 (E 1/3
from the report
= 30’)
represented
displace-
loads response
The ASR test report
The response of each
sea state
The wave
based on the regular
s picked
the “Thornton”
and the ASR
ships up to 90,800-ton
of the series.
by Froude sealing. R. A.O.
around
the “ Thornton”
into a series of geometric
the Thornton
= 10’),
on the cen-
gave
while
moments and secondary
that the ASR R .A .0.
of two runs for each sea
previously
were
dynamometers
registered
whi Ie the two
located
and Comparison
Tables 3 and 4 provide
amplitude
that
inches apart
moment,
System measured
To accomplish
expanded
All
pitch
at the L .C .G.
It should be clarified tical
three
dynamometers
provided
wave
data.
It
were the mean values
ship in the series was obtained
and sea state 8 (~1/3
= 50’)
in
using
as fol lows:
33.56 S (W), ft2 sec2 = ~8
@
R1/3
ti4
W5 Area
The University deduce
response amplitude
sponse information it was expanded
under curve
of Miami
to three
Research
vs ti
Vessel
equals
design
~ ,/3/2
.832
test data
was too I imited
to
operators.
For the one random wave test, the wave and rein terms of averages only . To make the most of the data,
is reported
feet
of S (w)
prototype
lent to
10.3
(sea. state 5),
ticulars
of these ships appeur
ships which
30.0
feet
in Table
5.
had test significant
(sea state
7) and 45.7
The Undisclosed
wave feet
height
equiva-
(sea state 8).
Series was devel~ped
Par-
in the
same manner. The semi-submersible
platform
data was used “as is. ”
All the test data assembled are for zero speed. In case of the ASR model tests (1 1),. the load measurements were made in forward speeds up to 20 knots and it was found that the maximum cable
to all
craft,
* Response Amplitude
loads occurred
particularly
Operators
very
at zero
speed.
high speed craft ,
This finding
need not be appli-
22
There is general induced
bending
moment
occur
relation equal
in oblique
between
available,
agreement
seas (45°
the “Thornton”
is that the maximum
to approximate
Non-dimensional
ized
2:
Figure
3:
is presented
vert.
bend.
vert.
test data that seas while
A significant
mom.,
bend.
mom.
cor-
R. A.O. with
S are
length
plots:
Versus A
)/2 mom.
in waves
wavetorsion
I beam.
in the fol lowing
bend.
maximum
the maximum
the two tests for which
moment and shear occur
times the overal
d(A+A, Max.
in barn
off 0° or 180° heading).
to 60°
bending
data
the different
occur
and the A5R tests,
y 1 .8 to 2.0
Max.
Figure
among
moments and shear force
, km
SWS
Versus L,
Beam Seas
Versus b,
Beam Seas
d(A+At)/2
Figure
Max. vert.
4:
d(A+A1
Figure
5:
Figure
6:
)/2
Max. shear force A/2
Max.
Versus A , Ekam Seas
shear force
Versus A , Beam S,eas
Abc Tvw
Figure
7:
Figure
8:
torsion mom. T1
Max.
Max.
torsion
Versus A
mom.
, Oblique
Versus AL,
Oblique
Seas
Seas
T1 Each fiaure
includes
plots fo~ the vurious
data
from all
the tests in three
Thornton
—+-+—i—-”””””” .~e.%
. . . . . . ●
6 @ ●
sea states.
tests are as fallows:
. ...*
Series
ASRSeries Univ. of Mimmi Catamaran
. .. . . .
Undisclosed
.. *.**
Mohole
. . . . . .
Livingston
Series
Platform Platform
Series
The symlmls used in the
b“’w’so
‘*A
I Fia..
2 - Max.
Vertical d(A+Al
B.hl.
vs.
\ \
\
\
G4=t0’
A.
)/2
Beam Seas Fig.
3 - Max.
Vertical d(A+A1
B.M.
vs.
L,
)/2
Beam Seas-
03
i
J,,.,. ,% A
b,
Fig.
4 -
Flax.
ma
t.?o
m
,60
Vertical d(A+A1
B.M.
2b
‘m,
Fr
.
vs.
b,
)/2
Fig. 5 -
Beam Seas
The plots are for loads in terms of maximum
single
amplitudes
Max Shear Beam Seas
where
Force/$
maximum
fol lows: Thornton
and A5R:
Average
of the 1/1 000 highest
the Pierson Moskowitz All
Other
Tests:
Maximum
measured
(obtained
from significant
erage
values),
calculated
for
spectrum.
or average
whichever
1/1 000 highest
or 1/10 is greater.
highest
av-
vs.
is taken
A,
as
24
;7e&=:*. ——— ——– ———+—
k’e-
H4=2&a
----
:
\ \
@
., —~’’c5___+_+
--—
SEASTATE8 ––—–e.–___+_/&ae,
___ ‘-0
Fig. 6 - Max. Shear Force
Fig. 7 - Max. Torsion Tl Oblique
o
=,,
vs.
Moment
A,
vs.
Beam
A,
Seas
=-’
Fig. 8 - Max. Torsion Moment vs. AxL, TI Oblique Seas
Seas
25 The reported column
phase relationships
platform
(in towing
between
condition)
cross-structure
loads for Levingstcm
in both beam seas as well
as oblique
6-
seas are as
follows: a Maximum
shear 90°
e Maximum
side force
e Maximum
yaw
e Maximum
torsion
~
out of phase with in phase with
moment
90°
moment
bending
bending
out of phase with 180°
moment
moment bending
out of phase with
moment
bending
moment
,;—=f=ll o
0,2
0,8
0,6
044
.
(Q)’H 9 Fig,
Table and oblique able
6 gives
9 -
Added Series
the ratios
seas for the Thornton,
in deducing
Mass For 60 (Ref.
of maximum
Swa Di recti 23 Y
magnitude
of each
ASR and the Livingston
the load schedule,
Table
on,
load
Platform,
in beam seas They were
Table 6 - Ratios of Maximum Loads in Beam Seas and Oblique Thornton Bending
Moment,
Oblique
Seas
Beam Seas
Oblique
Shear,
ASR
Beam Seas Oblique
It. was real ized tailed material
added
bending
and Crane
that
to calculate
Seas
added
moments.
mgss calculation
on the added
was decided
Livingston
Mean
0.36
0.55
0.48
0.52
0.55
0.53
0.53
0.55
0.36
0.55
0.49
Seers
Moment,
to the vertical
Seas
0.54
Beam Seas
Torsion
valu-
10.
mass (
However,
for each
‘l/g)
test vessel .
mass in sway of unsymmetrical the added
(23) and reproduced
mass tused
in Figure
wasa n important
the scope of the proiect
9 here.
Also, vessel
a I iterature was futile.
on Series 60 coefficients
term contributing would search
not permit
de-
for reference
In view provided
of this it by Eda
26
4.3
Discussion
of the Plots
4.3.1
Vertical a.
are large
are consistently
enough b.
ing in addition
test data,
plying should
to experimental against
do not help to explain
It is recognized
that
be pointed
of secondary
length
out that the Livingston
Platform
hull spac-
.
ASR test data together the bending
maximum
the Livingston
Platform
the dif-
alone.
distribution
out of phase with
with
is that the
and that
and centerline
moments to the total
is in accordance
series,
inaccuracies
the data
in plotting
it is assumed that shear is 90°
This assumption
can be made of the plots
than the Thornton
The plots of coefficient
that the contribution
is zero.
that
higher
not to be attributed
to displacement c.
other
Moments
The first observation
ASR series coefficients ferences
Bending
with
the
moment
im-
bending
moment
tests results.
hul Is are much more widely
It
spaced
than the ASR hulls (see Table 2), and that this assumption may be inaccurate for the ASR. Further, that the inaccuracy of this assumption may be one of the reasons why the ASR bending
moment d.
coefficients
coefficient The data
on the difference
it is not possible
to develop
is much higher is too insufficient
noted abve a better
than for other to deduce
or the general
representation
ships.
the influence
trends.
of form
For the same reason
of size than iust displacement
to
the first power. e. cant wave
height.
There is a plausible enced
The bending
explanation
in waves with
A
Now,
shifts to longer
waves and wave 1y resulting
4.3.2
for waves with
the maximum
A=l
for ves-
spectral
energy
.8 to 2.0 W does not in-
of items (a),
(d),
and (e) under Vertical
Bending
Mo-
to shear force also.
was in the hope of explaining
for the semisubmersible
platforms.
the other
could
vessels which
hull centerline the introduction ficients
moments are experito 548 feet
Shear Force
The purpose of using both force
bending
to signifi-
in vessel size.
in the non-1 i near load response.
Discussions ments apply
respect
decrease
from 100 feet
as the sea state rises,
height
with
with
Maximum
for this trend.
on the plot) .
proportional
increases
= 1 .8 to 2 .OW (2 W range
sels represented crease
moments are non-linear
Also that the non-linearity
spacing,
The apparent
particularly
to nondimensionalize
~
differe~ces
influence
b, and high vmterplane
sea states.
and $
the reason for the high values
of Cw tends to increase
in the higher
A
~
of MAX
between
Fso/ ‘/2
the platform
the shear force are their
coefficients,
the differences
Cw.
and
very wide
It is realized
that
in the ASR and Thornton
coef-
27 4.3.3
Torsion Moment a.
the ASR series, the opposite
The Thornton
whereas,
ments are no nlinear
Just as the vertical
with
respect
c. representing
coefficient
although
(ii)
CONDITION
develop
implying
FOR MAXIMUM
point
similar
to the
RESPONSE
the correlation
AND
be-
moment
used to nondimensional
ize the
moments.
RECOMMENDED
ESTIMATE to determine the probble motions and cross-structure
and (iii)
in nearly
A L scale
suggest a design
wave and ship posiloads are caused,
load schedule.
in items (i) and (ii)
the same form as developed
]t is in-
since
it is proposed
by Dinsenbacher
(Ap-
3).
5.1
Condition Figure
waves.
In Figure the wave
for Maximum
10 depicts length
times bigger
drostatic,
inertial
By inspection tude.
Res~onse in Beam Seas
a catamaran
1O-I , the wave
be several
equals than
length
2b,
poised
in several
equals
b, the centerline
and in Figure
it can be seen that when
and damping) the Imds
the cross-structure
be high and roll magnification When
structure
wave
loading unity.
should
the wave
A=
different
length
in Figure
is supposed to
b, the wave-induced
are due to the differential
due to the mass of the cross-structure),
dition
the differential
in three
hul I spacing;
on both the hulls have the same direction
should
10-III,
10-III,
locations
b.
Since the loads on the cross-structure
two hulls (besides
roughly
mo-
design are much higher
in sea state 8 the torsion
torsion
on the beam sea condition
equation
and
maximum
LOADS
load equations
to concentrate
to use the torsion
1O-II,
the torsion
as to why the data
catamarans
that the expression
to estimate
FOR DESIGN
simple
A
Further,
series is good.
The purpose of this section is (i), in which the maximum catamaran
pendix
than
but not to the same degree.
is available
they are both conventional
unity
is most promising
tended
height,
design and the Undisclosed
At the upper end of the
approaches
METHOD
tion
are higher
and shear force,
and ASR,
d.
5.
moment
moment and shear,
wave
explanation
of Miami
the ASR and Thornton
moment
coefficients
bending
bending
to significant
No apparent
the University
than the other ships,
tween
moment
is true. b.
Thornton
series torsion
in the case of the vertical
loading
length loading
should be small .
Intuitively,
forces
loading
on the
in this particular the heave
con-
magnification
small .
is much bigger
than the catamaran
width,
as in Figure
on the hulls should be small and consequently
be smal 1.
(hy-
and magni-
Also,
the roll and heave
magnification
the cross-
should be
L=
ACCf=LEEAT\ON
v= VELOCITY
k? 1t-
{1
I
I
I
L‘
MA%
& MAX I
t —
V
MAY * MAY V
II A=2b I
I
Fig.
10-
Catamaran
in
Beam Waves
of
Different
Length
29
Waves
of
>
zz 2b,
tions for high differential other
in the trough
erating
loading
maximum
dependent
to be small .
sible,
then the rol I and shear should on the catamaran
juncture
Further,
terline
the particular
valuable
wave
be maximum,
that a catamaran
heave
paragmphs,
results wi I I be inspected
for the same purpose.
The principal
i.
result
equal
in maximum
moment on
have the same sense as the
when the trough
sense.
and oppo -
the moment at the
Figure
is on the cen-
1O-I I makes another
be smal I when
conclusions
~
=
2b because
were reached
response are caused.
clues from the model
There is general with width
Now
test results regarding
agreement
among
the different
rol 1, shear force and vertical
vessel at zero to 2.0
forward
bending
speed in beam wave
as to the
the model
test
the conditions
for
[n both the Thornton
and the Livingston as wel I as other
was measured
waves
waves,
moment
occur
with
~
>
Platform
roll and bending
from the Livingston
test,
1,8
where
responses in a wide
it was found that heave
when shear,
Phase data
test results that
width.
heave
of regular
iti.
how-
steepness pos-
in beam seas are as follows:
maximum
ii.
whereas
tentative
maximum
cata-
moment,
one another.
in which
response
which
should
bending
maximum
and the hul Is due to side forces
force on the hulls cancel
sense genlarge
the hulls are at the nodes (with
experience
and hydrodynamic,
wave and ship locations
maximum
induce
inducing
to be of highest
When
they
of the cross-structure,
In the foregoing
would
is considered
two moments have opposite
suggestion;
the vertical
of opposite
when the crest is on the centerline
of the cross-structure
moment due to the weight
acceleration
force
condi-
is orI the crest and the
and at the same time
centerline),
both hydrostatic
the cross-structure.
vertical
If the wave
it is believed
for generating
When one hull
(damping)
ever,
si~e side forces,
have the potential
on the cross-structure
The velocity
crest or trough
1O-II,
on the hulls.
they experience
high shear force
maran roll .
Figure
approached
moment
Platform
range
zero
in
were maximum.
test in beam seas is as
follows: Maximum
shear 90°
out of phase with
Maximum
side force
in phase with
Maximum
yaw moment
90°
bending
bending
moment
moment
out of phase with
bending
moment Maximum
torsion
moment
180°
out of phase with
bending
moments are caused
bend-
ing moment This implies by vertical ing moment,
forces since
that maximum heave
and shear is 90°
is minimum
or zero
out of phase with
in waves
maximum
.-
which bending
by side forces and not cause maximum moment.
bend-
30 It on the ksis
can be stated that there is good agreement between the conclusions reached of the model test results and the visual inspection. This agreement pro-
vided
the encouragement
ment,
axial
to set up simple
force and shear force,
that the test data available
5.2
Development 5.2.1
to reach
of Design
equations
for maximum
whose presentation
follow.
the conclusions
is limited.
vertical Indeed,
bending
mo-
it is admitted
Load Equations
Equation
for Estimating
Moments
and Axial
Maximum
Force
Transverse
(See Figure
Vertical
11)
Assumptions: e Wave
is sinusoidal
s Wave
length
Wave
height
●
= twice >/1
=
hull o
centerline
space,
>
= 2b
(3.
Fig.
11
-
Loading
Condition
for
Maximum
Vertical
Bending
Moment
in
Beam Seas
31
●
Trough at centerline
●
Vertical
equals ●
of catamaran
acceleration
Magnitude
half
is lg (displacement
weight
and distribution
foot of length tion with causing
constant
magnitude
of the horizontal 1/4
draft
Cross-structure
weight
is evenly
●
Cross-structure
extends
between
t Velocity
per
sec-
acceleration
equals
the intact
wave
beam off the centerline
above
●
and the
as at transverse
side force
at a point
each hull and 0.65
force
beam
the dynamic
acceleration
of side hydrostatic
remain
maximum
c The aggregate
of one hull
of catamaran)
of
keel
distributed inboard
shel I of hul Is
ends are built in.
dependent
forces and impact
of wuter
particles
on the hulls are negligible.
Maximum
M.
M.
=
=
Vertical
Wave-induced
=
Moment:
bending
moment
for a weightless
over the breadth
of cross-structure
Side hydrostatic
force
center
‘MO
Bending
‘L
VL
=
=
- couple due to the horizontal + side inertia force moment
of buoyancy
(HLVL-HR
moment
VR)-+h+(A2:A
~gL
(DO+
2
d]-$
cross-structure,
YL)2
(D.
+ YL)
‘)ahd
=
=
. . . .. .. .
Side hydrostatic
Centroid
force
of HL below
constant
shift
(El)
on outkard
neutral
in
shell
axis of
cross-structure
Y~
=
}
cos(lT*)
= Wave surface above
still
waterline
at out-
board shel I
HR
VR=
=
qgL
dl-~(t)o
(D. -
. Y~)2 =
‘YR)
=
Side hydrostatic
Centroid structure
—
.-
force on inboard
of HR below
neutral
shel I
axis of cross-
32 YR
;C05(TT+)
=
=
Wave
c.
BE ---
=
h
2 (Do + YL) + (D.
23
(DO
-
+ YL) + (D.
YR)
- YR)
[
B
~
;3
Al
below still
waterline
at in-
1
flDo+yL ‘ -.—[1
=
h
surface
board shell
= Horizontal
.
Added
=
Aggregate
horizontal
acceleration
=
d] -0,65
Do = lever
cwm for inertia
=
Moment
mass of one hul 1 in horizontal
shift
in center
of buoyancy
direction
27 ah d Mc
at ends due to weight
Wc s
Ml
‘-
-n-
=
Maximum
=
Maximum
vertical
A&+MG
Side
=
P
bending
moment at iuncture
(E 2)
of
and hul I
*..
*’a. **n****
*
(E 3)
. . . . . . . . . ..
(E 4)
@*,.**.*,*.**
*..
Force
Maximum axial
=
P
of cross=structure
**,..,,.,.. ...................
cross-structure Ml
force
comp~e~ion
A+A1 — 2g
HL-HR+
ah
Due to the symmetry
of the assumed wave
t~ set down the equations
of moment and axial
and vessel ~ it is possiblel force
for the condition
by intuition
of wave
crest at
centerline. Ml
=
Ml
=
Ml
=
P
=
Maximum
vertical
bending
(HLvL
- HRVR)-
moment at the iuncture
of cross-structure
and hull
Wc s
I
Muximum
It is important for trough
axial
$
h + (~
tension=
“hd
I ‘T
A+A1
I
HL-HR_k~’
to note that absolute
at center! lne.
+ ~)
values
()
are signified
ah
since symbols refer
to figure
II
33
It should be recognized will
result
in the higher
Mc
and P.
However,
stress due to axial
that whether
direct
crest at centerline
stress wil I depend
by rough checks,
force
was greater
or trough at cepterl
on th~ relative
it was found that
ine
size of stress due to
for existing
catamarans
than stress due to cross-structure
weight
(or local
loads),
5.2.2
Equation
for EsFirnating
According shear occurs, this position
probably,
to the analysis
when one hull
the hulls experience
one another.
Again,
time as maximum
accordin~
force,
for maximum
shear coefficient
cal wave-induced
of vertical
=
0.41
=
Wave
equation
of this section,
acceleration
maximum
maximum
in the trough.
in opposite
]n
direction
shear.
his
Cw
w
induced
in the case
by picking
cross-structure only.
an im-
of vertical
bend-
the highest
sense,
6.
to obtain
Since the verti-
hen, (E 5)
weightless
Wc
*.*,,,,.*,
=
-T
FSc
=
Shear at ends due to cross-structure
F~l
=
Maximum
shear at iuncture
(E6)
........ ..
Fsd
weight
of cross-structure
and hull Fw
=
5,2.3
+ Fsc
●
Equation
for Estimating
Dinsenbacher’s in Appendix Tc
torsion
(E 7)
● ✎✎☛✎☛✎✎☛
Maximum moment
Torsion Moment
equation
which
is also reproduced
3 is =
=
Torque about Torque about shear acting
Tc
✎☛✎✎✎✌✎✌✎✎
=
I
$Cbg
center
of twist
center
of gravity
through
BO.6
~L2
of cross-structure of ship + torque
the ship’s center \2~
+
due to
of gravity 0.14
Mqt/S
an
nondimension-
the cross-structure
, . . . . . ..s. . ..**...,.
shear at ends,
not permit
test data
from Figure
on the hulls are of opposite
lg acceleration ~
and rol I will
to resort to the model
is done simply
for a weightless
+
acceleration
cross structure
Fsl
to
roll should occur at the same
as it WS possible
It is proposed
acceleration
can be assumed fo have Fso
vertical
to the analysis,
of a shear force
ing moment and axial al ized
at the beginning
shear,
writing
expression
Shear Force
is on the crest and the other
maximum
Combination mediate
Maximum
34
Torsion values with
the model
test results,
for the ASR model . term of secondary
as provided
by the first item,
as was done in Figure
Even for the ASR model,
in an irregular
T1 would
sea with
of Miami
nificant
wave
provide
50-foot
model
height
design purposes.
torsion
significant
It is pertinent
to point
of maximum that
is half
of maximum
would
be
If
t
=
shar
shear.
except
the second
to replace
$c~ I
the second
Even though
the use of
in light
shear in oblique
to a weightless
L2/~n
JXL2/2~
distance
maximum
seas is approximately cross-structure.)
to assume that shear in phase with
I- (t)
[1 +
(0.53
(t)
from ship LCG
the torsion
x0.5xmax
0.11
$
Cw
twist
center
= O
then =
T
To
=
5.2.4
Comments
s The equations neglect ticles ●
0.7~
$Cbg
are quasi-dynamic
velocity
dependent
and semi-empirical
forces as well
any other assumption
it passes the catamaran seen that wave
with
wave
would
hydrostatic
The new equations ciated
would
than
in nature.
as the impact
them.
presented
that wave
be difficult
form does deform
the deformed
forces or larger ●
Equations
of water
They par-
on the hulls.
Although
that
L2/2~1
on the Proposed
between
form remains
intac~ as
to handlel
in reality,
the hut Is.
it is conjectured
not cause higher
loadings
than a wave
acceleration which
do not have any lmck-up
torsion
equation
shear in beam seas)
+
to cross-structure
test
of the obiection
test results,
~
II
of the limited
the equation.
model
(This applies
be conservative
for
selected
term in light
to the
sig-
severe
Dinsenbacher
using the symbols of this report,
0.7
Longitudinal
that
due to the
A 50-foot
sufficiently
moments.
According
in T1 was re-
if the data scatter
is iustified
and maximum
O.6
as any test value
test is neglected.
Then,
$Cbg 0.7 =
height
of torsion
in beam seas.
it would
if the constant
out at this time
3 of this report.
shear and torsion are out of phase,
Tc
was zero
making
at least as large
that had to be made to derive
It is proposed to it in Section
It is conjectured
wave
torsion , conservativeness
data and the many simplifications
Tc
small
sea state 8 and it is considered
O.6 to suit the ASR long term prediction
53 percent
7 that
values
test and the undisclosed
represents
O.7 may overestimate
raised
can be compared
importance.
by O.7 then
University
T1,
t for model
t was relatively
It can be seen from Figure placed
7, since
it is
dependent
remains derivation
intact. asso-
35
The procedure
for calculating
used by Schade The use of ~ with
test results which
refinement
The method
the added were
there
to consider
independent
one another’s
hul Is is quite
opposite sense. Unfortunately, have sway results to evaluate
Figure
9,
of Loads Calcu Iated
posed equation
wave
7, 8 and 9 provide shear,
and torsion
and other
As a matter
5.4
by , Pro~osed !
for the catamarans moment
using Series 60 data,
method
The reason with
~x
could
being
that
2W and
Eauations
respectively,
listed
in Table
2,
as calculated
the vertical
by the pro-
Other methods include model tests, Scott’s method an d Lankford’s method for torsion moment due to
shear and bending
were also calculated
height
Method
remains
constant.
weightless
moment
for a wave The values
with
cross-structure
for the Thornton, ~
since
$SR,
= 2b and H = ~\~10
of maximum
load/wave
height
for Design Loads Estimate 10 presents
developed
and the oblique
and for
from the test reports.
Table equations
frequencies)
methods.
of interest,
Platform
load/wave
were obtained
do not on added
Method
grounding. Al I calculations are for catamarans with model tests results are for weightless cross-structure.
assuming
in waves
to be slim.
moment and torsion,
and Livingston
can constrain true
of the two hulls have
the proposed
moment.
of the critical
Com~arison and by Other
for bending
the bending
of occurrence is likely
Tables
since they
encounter
that for sma I I catamarans
H =2W/10
moment,
hul I as if they
be particularly
estimates
on
Whether
model test results gathered this. Until new information
hulls is forthcoming,
much overestimate
frequency
bending
information
wil I have to suffice.
It is suspected very
hulls and form of hulls.
acceleration
(wave
The
and simplicity.
for catamarans.
questionable
mass in sway at low frequencies unsymmetrical
symmetry
mass of each
This should
2b where the horizontal
with AS
to 2 .OW.
is no published
direction
the added
sway motion.
in accordance
1 .8W
for unsymmetrical
mass in the horizontal
it is satisfactory
~=
to sustain
As far as it can be determined,
is the same as
is not quite
suggest
is sacrificed
does not account
force
(12) and (13).
= 2b in beam sea condition
the model
possible
side hydrostatic
and Dinsenlmcher
a recommended
in Section
seas as given
5.2
design
load schedule
and the ratios of the maximum
in Table
which
is kased on the
load
in the beam seas
6.
.-
36 Table 7 - Wave-Induced Transverse Vertical Bending Moment in Beam Seas Nntm[ Al I ~uluw
E.W,
m nlnulo ampl Itudm In foot tom andfor walght Imncronl-ntructu; A5R
E,W, Thnrntm $hlb A
Thornton
ASR
M
(2)**Calc.1/1000Hl@h-it In SW S!at* 8
33.24o
1,045,244
32,547
3,091 ,9a2
(3) SR 192 M,thod
50.4sa
1,426,323
40,518
4,195,741
(4)
SA,4
I ,020,000
729,000
Lavlnnmtun PlatfOrm 199,206
4,325,545
51,925
Note: All values are single amplitudes in foot tons and for
220,764
756,000
1,947,,Brn
244,400
weightless 54,040
1/2
55,051 0,443
(6) (1)/(3) 0, (2)/(3)
0,459
(7I (~)/(4) or W(4)
0,440
1.255
(q (3)/(5)
0,933
0.734
TermPradlotlon of Maximum
0.421
0.737
cross-
structure
200,407
0.803
(9)*** lonu
** ***
Mohole Platform ——
(Scbttli Mmthod)
(5) ~(%o)
k
U, of Mldml Ship A
0.903 0,944
0,936
O,aob I ,100
63,300
Max. or I/1000 hlghc~t, wh Iahavm Ii grater RAO from model ban?nEnd ma ntate dadhd ~ Plwio~-Moikowltz From R*fOrOnce @)
5peatrum
Table 8 - Wave-Induced Shear in Beam Seas Nata: All valumI are tln~le ~mplltuda 1~ foot iom and for wrnlgk
E .W.
Thornton sh!p A
E.W. Thornton
ASR ASR —
w
(1)
Note: All values are single amplitude in foot tons and for weightless cross-structure
Im crom-~tructure
U ,oF Mlaml Ship A
Maholo Platform
Lovlng!ton Platform
6,450
2,4ao
1,190
(2)
**culc# 1/1000 Hl#hmt In Sea slate 8
551
6,9M
2.02
9,134
.
.
.
(3)
0.41 (A /2)&’W) (Cw) SR192 M*thOd
749
10,110
304
9,880
.
2,9&3
I ,40U
605
.
349
.
.
.
I ,0
0.923
.
0.837
(4)
~O(2b/10)1/2
(5)
(1)/(3)
0.726
or (2)/(3)
O.&b
—
*
MEX. or l/1000 hl~hmt. whlchovor It oraatar
Table 9 - Wave-Induced Torsion
Moment
in
Oblique
Seas
**** A5R
Therntcm Ew. (1) KModel Tait lvidx. [n S* State 8
Thornton
~
1,625,000
-
193,452
I,ao,ooo
1B,810
\ ,090,000
1,35,000
2,206,BB
23,495
2,433,077
2,526,971
2S,560
11,055,502
I ,043,no
1,044,577
(3) ***
41,400
4a,240
L@vln@ItOfi Platform 93,304
Note:
009,401
5a,545
(4)0.04LA
Moholo Platform .—
9,536
(2)** Cal,, l/1000 Hltih01! In s-a Stato 8 Sk 192 Mnth.d
J!!!&
M
U” OFMlqml Ship A
-
192,000
99,500
eo,mo
(Scott’i Molh.d) (5) 0.175 LA (Grbmdlna)
2~195B
9,455,092
102,790
10,444,711
350,350
(6) (1)/(3) or (2)/(3)
0.95
0.02
0.5!
0.74
I .2b
1.01
0.94
(n (1)/(4)0,(2)/(4)
0.86
0,47
0,44
0.33
0.64
0.81
1.16
* ** +** *w.
bx. or 1/1000 high.tt, whlahmvw II orutmr RAO from modal tmnraEnd UE Bmt. d#narlb*d b pl@rmn-Malk*wlt~ $Cb~Bx0,7~ L2/21Y A~,”~*d L = LBP. 5 H
sP=ttum
—
values are single amplitude in foot tons and for weightless cross-structure
All
090 0.850
37 Table 10 - Design Load Schedule
Loading for Direci Stressat Midspan of cross-Structurs Beam Waves
Load
Oblique Seus
Axial Force
P from (E4)
0.48 of P from (E4)
Moment, Weightless Cross-Structure
M.
O.&
LOCQILoad (CrossStructure Weight)
Wc
from (El)
of M. from (E 1)
Wc
Loading for Direct Stressat Juncture of Cross-Structure and Hul I Axial Force
P from (E4)
0,48 of P from (E4)
Moment, Weightless Cross-Structure
M. from (E 1)
0.48 of M. from (E 1)
Local Locsd(CrossStructuresweight)
WG
Wc
Torsion
0,49 of Tc from (Es)
Tc from (E8)
Loading for Shear at Juncture of Cross-Structure and Hul 1, Acting Concurrently with Moment Torsion
0,49 of TG from
Locol Load
Wc
Tc from (E8)
(E8)
Wc
Loading for Shear at Juncture of Cross-Structure and Hull, Acting Out of Phase with Moment Shear
0.53 of F~o from (E5)
Fso from (E 5)
Local Load
The method
schedule. to estimate obiects
and
is considered
It will
be noted
In the
opinion
that
depth.
~ested
that
individual
weight
and
real istic
AS
designer support
and
grounding
to vessel
speed,
docking
consider
oblique
appropriate
designs.
loads
are
not
torsion
loads
are
nearly
shape,
size
far as torsion loads due to docking
points
..
for conceptual
the grounding
of the authors,
as they are so subjective water
satisfactory
docking
with
to his vessel
.,.
included
and
strength
are
concerned
most likely
in the
impossible of striking it is sug-
docking
.
.. .
38 6.
HULL
FLEXIBILITY
It was apparent lishment
AND
at the beginning
of catamaran
preliminary critical
size limits
structural
loads were
Lankford’s available.
analysis
method,
a method
which
structural
calculations
discussed
in Section
at their
junction.
using Lankford’s
at once that only the hull were
simulated
method
bending
fluence
partially
of hull
rotation
it was deemed
weak-
between
the
desirable
to find
for which
Research
attraction Catamaran
were available
and it was decided for which
in-house.
and shear deformation model .
struc-
It must be menin the longi-
The space frame analysis
by its flexibility
is inherent
indicative
and the relative
numerical rotation
on the cross-structure, on the individual
hull
to values
between
and the in-
structure
in the
area .
The method proiect
is computerized
if structural
changes
It can include
which
analysis
[t can assume several
different
maximum
could
be a great
was necessary
in the structural
and secondary
mathematical ●
was readily
were available.
at least,
flexibility
of the cross-structure
transition
mary
2,
two maior
and to try it out on a vessel
flexibility
the hul 1s and the cross-structure
●
for the
once the
in Appendix
is no relative
in the mathematical
It should provide,
on the influence
quick
catamaran,
to have
had an immediate method
of structure
the method .
●
the estab-
method
advantages:
s Representation
●
of a large
Hence,
16 Oceanographic
based on Lankford’s
had the fol lowing
a suitable
it appeared
and there
of space frame analysis
direction
in order to attempt
3 and detailed
previously,
did not have these weaknesses
calculations
tudinal
that
to select
of the cross-structure
to try it out on the T-AGOR tioned
of the project
It assumes the hulls to be rigid
The method
STRESSES
it was necessary
as mentioned
hul Is and the cross-structure
tural
TRUCTURE
estimated.
However,
nesses.
CROSS-5
amount
asset later
for several
types of loading
in the
ships.
at once and permits
configuration. of structure
loads by employing
effective
progressively
in taking
pri-
more detailed
model .
[t can conveniently
handle
structure
with
more than one material,
say
steel and aluminum. Figure
12 shows the bare
ates its mathematical the IBM- 1130
“Stress”
model
outline
of the T-AGOR
incorporated
structure
and Figure
in the space frame analysis
which
13 delineemployed
program.
The analysis used the original T-AGOR 16 design loads. The loadings which control led the primary members of the cross-structure were the grounding loads and the transverse
vertical
suggested
by Lankford
necessary
modification
bending
moments in beam seas.
and the latter to reflect
were obtained
different
—
principal
The former were obtained
from the ASR load estimates characteristics).
as (with
39 /
/ (
L KT,
/
L
04
%
LENGTH
/
PE12!7 —
22:
/ Y“l A I 11 ~1 ~; 7Z
/
/
1 < S’z
t! 23
< 37
?7~o” 34’-O’d zl~d’ 19’-6”
— HULL CLEAR5PACING — DEPTHTOMNW, AT51DE WiTH OFCR055STF?(KT, AT~ — —
o“
,$. o~~
BEAMoVEEALL — BEAMEA HULL — HULLh 5PACING—
/
24’- o“
51’-d
Fig. 12 - T-AGOR16 Structural Configuration
5---
-NEUWU
2
NOTE HULL AT
LOA!25 JOINTS
AXIS
OF
Fig.
The resulting condition Table
THE
THE
Other
13 -
Structural “Stress”
Model Program
less critical
conditions
and grounding
are provided
in
Design are also tabulated
than the cross-structure
for comparison.
are not tabulated,
Imsed on American
since
the
Bureau Rule and their
stresses
readily. the following
and cross-structure The flexural
conclusions
with
those taken
using Lankford’s
Those for beam condition stresses are less critical
.—
with
respect
Imsed on the structural from the T-AGOR
model
are in
16 structural
method.
. The shear stresses for grounding
the discrepancy
can be drawn
stresses:
stresses calculated
good agreement
.—. —
output
are omitted.
16 Structural
other
From the tabulation,
analysis
For IBM- 1130
The flexural stresses and shear members based on the stress program output and those
in the T-AGOR
can not be calculated
●
T-AGOR16
from the “Stress” program
design for those members were
flexibility
of
moments and shear forces in the beam sea condition
Stresses in the structures structural
AEEmtiTNUMBEFC3.
HULL%
stresses in the six cross-structure as calculated
HULL
NWTKAL
for the cross-structure
11.
OF THE
LWCIECLM?%UEE5
INTRODUCED ALONG
MI>
: Cli?CLED FIGuEEE.AE’E ME14Mt2 NUMM%5,
conditian
show less a g rep than flexural
are in fair agreement. m e n t.
Since
the shear
stresses in beam sea condition,
in shear stresses is not considered
important.
to hull
40
a It appears, duction
admittedly
bed
on this limited
of the longitudinal
flexibility
on the stress in cross-structure, the hulls @ Since
to be rigid
simplified,
structure have
method,
cross-structure
such as Lank ford’s
transverse
modulus,
requirement
addition
~nd torsional
and component
method,
to hull
about
frame
longitudinal
(decks,
assumes
model
can be theyall etc.
the preliminary
with
Detail
analysis
a conventional
the same accuracy
analysis.
cross-
i e,,
shear area,
that
handled
in results,
design
such structure
cross-structure
bulkheads,
which
similar,
of inertia~
flexibility
the introinfluence
al I the transverse
it may be stated
with
deformation,
structure
study,
can be conveniently
as the space
that
selection.
the mathematical
moment
of the last two conclusions,
the same time ccmsider,in
rigid
can be assumed structurally
the same section
of a cat~maran
the scantlings
For a prel iminury
bulkheads
onlyr
has small
i .e. ~ the simplification
not affect
the hul Is can be assumed
greatly
In light
would
check
of the hulls
deformation
and about
analysis
response in various
should
as the hull directions
etc. ) deformation,
Table 11 - T-AGOR16 Catamaran Stress Summary Section Modulus
Bhd —
Shear Area
ln2
[n2 ~~
Mmmber
Bend. Mom.
—.
KiJ&
m Beam
6&7 15&16 24 &25 32 &33 41 &42 50 &51
96 84 72 52 z
105.0 102,0 82.5 94.9 102,0 120.0
650.0 833.3 632,9 784.6 633,0 B53.0
Secl Condlfion
16,900 19,244 19,749 24,951 21,901 20,471
74 67 M 55 74 70
Grounding
7.
DESIGN 7.1
105.0 102,0 82.5 94.9 102,0 120.0
650.0 833.3 632.9 784.6 833”0 853.0
647 15 & 16 24 &25 32 & 33 41 &42 50 &51
94 84 72 52 37 23
that
U .S.
[oined
crfloat,
together upper
limit
were
loads predictio~
was to make a preliminary that
structural
that
Whether
was dependent
the cross-structure
that
shipbuilding
on the premise
able
23.6 23.9 24,1 26.5 23.9 26,5
3.3 3.1 2,8 2.8 3.1 3.2
21.0 11.0 6.6
9.1 5,0 1,4 0.3 5.4 9,3
21,4 11,5 8.1 4.2 10,B 8.9
10.5 7.7 4.6 3.6 7,6 10.8
limits,
Section2,
Condlflon
952 506 116 24 554 1,114
13(619 9,216 4,187 2,535 10,999 15,780
of the features
existing
foot catamarans
believed
0.7 0.7 0.0 0,5 0.7 0,7
1$; 18,5
SHIP
The analysis
structure
24.6 23.1 31.2 31,8 26.3 24.0
Purpose
indicated
able
Strew, Klps/ln2 $Wesn Program Design Calca Shear Flexur91 Shear Flexural —— ——
Shear
individual
1000-foot .
Hence,
and structural design
design
information
hul Is would should
the necessary once
analysis
were
would
become
scantling
1000-
in a drydock
be proposed
and
as a present
prob-
size and the weight
methods
1000-foot
apparent.
approximately
be built
evaluated,
the inadequacies,
size
handle
the available
of an approximately
in the course of the design,
catamaran
could
length
on whether
practical
may impose facilities
the logical catamaran.
if there
of
for cross-
be any,
next step Also,
it is
of the avail-
41
Table 12 - Design Ship Particulars
Hull
Symmetry
Length
Bet.
Perp.,
Beam Overall, Beam Each
Symmetrical 9421- oil
L
W
Hull,
B b (corresponding
Hull
~Space,
Clear
Hull
Depth
to Upper
Depth
of Cross-Structure
Length
Spacing,
to ~ b – -0.21)
S
Deck
at Side
of Cross-Structure
Draft Cross-Structure
Clearance
from Waterline
Block
Coefficient,
Cb
Coefficient,
Prismatic
Speed
0.572 0.701
Cw
(corresponding
Horsepower
to —v FL
-– 0.24)
52, L87 Tons
Weight 28,439
Cross-Structure
5,598
Electric
1,150
Plant
2r&o 280 5,950 3,800 4,790
Propulsion Communication Outfit
& Controls
Systems & Furnishings
Margin,
25 Knots 150,000
Hu I I Structure
Auxiliary
Tons
0.952
Cp
Coefficient,
Instal I Shaft Lightship
-011
0.54 CR
Coefficient,
Waterplane Service
301
90,800
Displacement
Midship
300’- o“ 100’- o“ 200’- o“ 100’- o“ 106’- O“ 45 ‘ -0,, 8oo1- oli 31’ - o“
10%
38,113
Deadweight
Tons
Container
Capacity
@ 11 Tons/Container
3, 10 I Containers
Container
Capacity
@ 15 Tons/Container
2,247
Containers
Container
Capacity
on Upper
3,136
Containers
Deck,
8’ x 8’ x 20’
I
LBP
WIDTH F 30~
= 942’-0’
D!5AFT =
31’-0”
I?EPTH
~T
DISPLACEMENT
= 90,800
= 10~-
I
0“
ToN5
Fig. 14 - Design Ship Profile and Plan
‘o“
200 100’-
o“
I
100’-0’
100 - a“
I
I
I
1
I AVEt?AGE
HULL
I BHD
sHIP
F&6 s .62%”
4
SYMBOL (HIT,)=
FOE
3TEEL1
MINIMuM 100 000FSl 5TRE NGTH E%EEL
ylELD
(B, H,) = AM GRADE B.H. SKEL = MILD STEEL
(M.5.)
Fig.
15
-
Design
Ship
-
Typical
Bulkhead
Structure
43 7.2
Design
Description
The preliminary The readers suitability
can expect to provide
bulkhead
design presented
improvement.
that
if large
the limited
It is assumed that payload
catamarans
carriers
.
ous plating
the vessel would
12 lists the design
terline
spacing
etc.,
particulars
can all absorb consider-
ship since
to monohulls
it is well
it would
and Figure
made to obtain
that the design’s
to ship length
To design
for Froude
a 36-knot
speed would
which
by far.
accepted
be as high-speed,
14 shows the profile
hydrostatic
properties
and vari-
areas.
and O.3 respectively,
spacing
system,
be a container
found superior
A rough set of lines were
It wil I be observed 0.4
assumed framing
are at all
Table
and plan views.
(or recycled)
from the authors for the design other than for its The selected shape coefficient, information desired.
and deck arrangements,
able
here is not optimized
no more defense
ratio
of 0.21
suggested
was considered
render ratio
would
the design
of 0.3
impractical
require
require
and the hull
to the values
characteristics .
hull
To design
centerline
cen-
of 0.3
to
(see Appendix
1).
It was felt
that
a speed of 36 knots.
uneconomical
would
number of 0.24
do not correspond
for good resistance
number of 0.35
to ship length
Froude
for hul I centerline
spacing
of 314 feet
.
The 100’ x 800’ cross-structure
is composed
of four structural
decks,
includ-
ing the upper deck
and the bottoml and seventeen identical full structural transverse bulk The cross-structure is assumed to be fixed at the inboard shel I heads spoced at 50 feet. of the hulls. full
In order to validate
transverse
structure.
bulkheads
Figure
15 depicts
Figure
16 provides
the catamaran
American
section
moduli
7.3
bending.
above
tional
following vertical
of the assumed effective
section
modulus
for the hulls
structures, bsed
on
the
It will be noted that the minimum permissible modulus considerably in excess of that required. This is
depth as compared
to a monohul 1 to have sufficient
for Effective
Structure
Explanation
is warranted
for the structure
On the face of it an immediate the deck plating strength
The structural Lankford’s
method,
Appendix
axial
by the bulkheads
together
with
The effective
, rather
(as distinct
moment,
assumed effective
question
be considered
calculation
analysis
bending
the two hulls.
modul i of the individual
cross-structure
the waterline.
longitudinal
head.
sketches
of the
of the cross-
at a bulkhead.
on the section
Explanation
why should all
decks and bulkheads
rules.
in a section
due to the increased
It includes
and the required
Bureau of Shipping
scant lings result clearance
.
four of the decks and seventeen with
structure
the information
hulls and the cross-structure calculated
this assumption,
in the hulls are aligned
effective than
iust 24-foot
In Lankford’s
force , shear as well effective
deck
in bending
from the design 2.
plating
deck
plating
breadth
in cross-structure
may come to the mind of the reader; iust as in the conven-
breadth
load estimate) method,
as the torsion acting
all
with
each
bulk-
was performed
the principle
moment,
as fixed-end
of 24 feet was calculated
loads,
are absorbed beams between by reference
44
I
--AK+=%= Y-J--+’* Main
;
Section
Modulus
=198,500
ln2
,,,:,
Section
Hul I
Required
by ABS
Ft per Hull
Modulus,
Including
10% for
Longitudinal:
~“;
I
0.50” ——— —,.
–k””-” ‘-- ““——
Main
T7----~
Dk
0.75”
Deck:
269,000
ln2 Ft
Bottom:
266,090
In2 Ft
Hulls
F::ETe ‘“k“‘H”’”)
P
~12’’x6-l/2’’x27#
al
/ Q_-
-1 -“”f~y
0.625”
l/T
(H.’.
Cross. Structure Effective
)
Bhd PI (H. T.)
5/8 “ X 24’
(BH)
~*v-
ln2
Axial Load Area [n2
j! . _,~ -, 0.50” Bhd PI ..! (MS)
1-1/4” x 10’
148,800
Modulus
Shear Area, ~--,...
Piating
Four Decks
Section ,n3
I
““
130,056
300
300
923
803
●
L
s.
0
J---AL
‘BH)
1
0.625”
Bhd PI (H.’.j
Symbol
for S*eel:
(H. T.)
= Minimum Strength
(H. T.)
(B. H.)
= ABS Grade
(M. S.)
=Mild
Cross-Structure
Fig.
16 -
Design
Ship
100,000
Section
Modul i
psi yield
Steel
Steel
B.H . Meel
45 to the wel l-known considered 50 feet
paper
as multiple
between
(24) on }he subject
webs for each deck
webs.
Among
ered by Professor Schade, j
by Professor $chade. with
the various
load and fixed
[mding
at
the smal I er effective discussion
moment
breadth.
and with
side shell
as double
The 20-inch 16,
was reached
this is provided
that
web plating
Appendix
the same section
10 feet should
plating
is 97°10.
of the center webs.
(see
bulkhead
web,
Figure
The reasoning
for
2.
inch plate
a 10-foot
thickness
modulus as available
be quite
of the deck
of the outer
16 also shows that if arbitrarily 1-1/4
maior
was used as it gave
no centerline
at top and Imttom
of the length
- equal
Professor Adams proved
breadth
of
consid-
viz:
the structure’s
combination
for a monohul I with
the effective
one-sixth
effective,
proximately plate;
webs,
by Lankford,
Figure be considered
Even though
bothends, the latter
paper)
effective
by taking
ends.
in question,
were
width
of load and end fixity
to the structure
Using the same reference,
to Professor Schade’s
The bulkheads
of 100 feet and plating
combinations
two were appl icable
moment at both ends or uniform is due to equal
length
deck
would with
plating
be necessary
5\8-inch
width
were
to provide
x 24-foot
to ap-
effective
conservative.
interpretation
Although 24-foot effective breadth was arrived at with prolmbly adequate that the structure in question is real I y of the structural i t is acknowledged
integrated
box structures.
to derive
effective
7.4
Further,
structure
Cross-structure
in Section
Thornton
and ASR Series,
is insufficient
in i ieu of the method
test data on box girders employed.
Loads and Stresses
The wave-induced proposed
that there
directly
design
5 of this report, Section
14 were
4,
summarized
in Table
equations.
The stresses are within
loads as deduced
from the method
by Dinsenbacher’s are summarized
calculated
(13) method in Table
by using maximum
the allowable
13.
(labeled
SR-192)
and from the The stresses which
loadings
predicted
stresses for 100,000
are
by SR-192
psi yield
strength
steel .
calculated
Although grounding is not considered a design criteria, for the grounding condition and are included in Table
to be considered
as a design
as the shear stress is 47,280 7.5
Design a.
criteria
the selected
inadequate
Conclusions
Direct
stresses are higher
Required
largest
The required
largest
related
100,000
psi,
seas than
thickness
to value
scantling
on a hopeful Iy conservative true only
in beam seas than
in oblique
deck plating
on the assumptions
.. .
be quite
lb/in2.
Shear stress is higher
b.
scantl ing would
stresses were also 14. If grounding was
is very
of effective
of approximately assumption
structural
seas.
much dependent plating. 1-1/4
and steel yield
are common to shipbuilding
for the particular
in oblique
in beam seas.
today.
configuration
inch,
based
strength
Of course, employed.
of
this
is
46
c.
If grounding structure
d.
wws to be considered
would
be quite
The imperative (17 bulkheads
a design
criteria
need to sustain and four decks)
the continuity
of structural
of the cross-structure
hulls causes the main hul Is structural
configuration
cal,
monohull
e .g. , unlikely
foot main
that a 1000-foot
bulkhead
the assumed
inadequate. members
into the main to be uneconomi-
would
require
50-
spacing.
Table 13 - Design Ship, Wave-Induced Cross-Structure Loads BEAM SEAS: MAXIMUM
TRANSVERSE VERTICAL BENDING
Single
Amplitude
MOMENTS
in Foot Tons Method
Weightless
1,658,464
:,061,106
Cross-Structure,
71-- .... L-.. r— —!-. Inornron ~erlea
Dinsenbacher
SR-192
2,048,785
At?nHJR
. >eHes
2,869,346
Constant with
Cross-Structure
?,427,439
Weight,
3,966,364
At ends of Cross-Structure BEAM
SEAS:
MAXIMUM SHEAR AT ENDS
Single weightless With
Amplitude
Weight
BEAM SEAS:
5,636
30,646
36,411
MAXIMUM
Single
in Tons
8,M6
Cross-Structure
Cross-Structure
At Midspan
Amplitude
AXIAL
SEAS:
MAXIMUM
Sinale
Amplitude
8,032
FORCE
in Tons
* 52,367
OBLIQUE
5,9ia
33,074
TORSION
MOMENTS
in FOO~ Tons
*** >,948,449
* Used for Structural Analysis ** Assumed Cross-structure Weight ***
Assumed LCG
= Steel
+ Ship’s
with
Longitudinal
of Ship Coincides
Cross-Structure
Twist Center
2,403,794
2,527,242
Deadweight Location
of
2,188,600
47
8.
TOPICS FOR FUTURE Researchers
have generally and the topics conclusion
(4),
(8) and (13),
very similar
for the desirable model
conservative b
(2),
reached
of this proiect
bY conducting would
(1),
RESEARCH AND DEVELOPMENT
unduly
.
However,
heavy.
Table
using existing
Also,
catamaran
Section
would
Modulus
Loading
Ins
=
300
ln2
Axial
=
923
ln2
BEAM SEA CONDITION Total
method
Shear Area Load Area
can be designed
Stress
148,800
=
(Trough
A significant
and generally
now
adopting
the resulting
be unacceptable
Cross-Structure
technology
in the technology
program.
structure
information
of the design
such an approach
Design Ship,
14 -
and development
design
.by nature
catumaran
as to the deficiencies
research
is that a safe large
tests,
approach
who h~ve appraised
conclusions
future
PROGRAM
a
structure
if a large
num-
Summary
(See Figure
16)
at Centerline)
on Cross Structure:
Vertical
Bending
Torsion Moment
Moment = 0.53
Without
x Max.
Local
Load (Cross-Structure
Axial
L~d
Cross-Structure
in Oblique
Weight
Seas
3,061,106 1,562,000
Weight)
Ft Tons Tons
43,960
Tons
52,367
Tons
32,527 5,535
Lb/ln2 Lb/]n2
Stress on End Bulkheads: Primary
Bending
Bending
due to Shear due to Torsion
Bending
due to Local
Load
-
34,169
Subtotal Axial
Compression
7,473
Tota I Stress Shear Acting
41,642 Concurrently
with
Bending
and
Shear due to Torsion Shear due to Local Total
Load
Shear
Out of Phase with
Bending and
Lb/]n2 Lb/ln2
Lb/ln2
1,371
Kips
2,897
Kips
4,268
Kips Lb/ln2
Torsion
Shear Shear Stress
—.
Lb/ln2
Torsion:
14,230
Shear Stress Shear
3,893
-.
4,039
K ips
13,463
Lb/ln2
.—
48
Table
14 -
Design
Ship,
Cross-Structure
OBLIQUE
Total
Loading
Stress
Summary,
(Cent’d)
SEA CONDITION
on Cross-Structure:
Vertical 0.48
Bending
Moment
xMax.
in Beam Seas
Without
Cross-Structure
Weight
1,469,331 2,948,449
Torsion Moment Local
Load (Cross-Structure
Axial
Load,
0.48
x Max.
Weight) in Beam Seas
Ft Tons Ft Tons
43,960
Tons
25,136
Tons
Stress on End Bulkh~ds: Primary
Bending
Bending Bending
due to Shear due to Torsion due to Local
Loads Subtota I
Axial
Tension
Total
-
Lb/ln2 Lb/ln2
3,893
Lb/In*
29,936
Lb/ln~
2,587 26,349
Stress
Shear Acting
15,613 10,430
Concurrently
with
Lb/InZ Lb/#
Bending and Torsion:
Shear due to Torsion
2,587
Kips
Shear due to Local
2,897
Kips
5,484
Kips
18,280
Kips
Total
Load
Shear
Shear Stress
GROUNDING For Reference Tots I 1.oading
Only
- Not
Used as a Design
Criteria
on Cross Structure: 12,850,000
Torsion Moment Local
CONDITIONS
Load
Ft Tons
43,970
Tons
45,500
Lb/ln2
3,893
Lb/ln2
49,393
Lb/ln2
11,288
Kips
2,897
Kips
14,185
Kips
47,280
Lb/ln2
Stress on End Bulkheads: Bending due to Shear due to Torsion Bending due to Local Total
Load
Stress
Shear due to Torsion Shear due to Local Total
Shear
Shear Stress
Load
49 ber of vessels were
contemplated.
sive list of study topics ensure the availability which
would a.
[n view
is prepared systematic
tend towards
The nature,
design
information
location
magnitude,
centerbody;
a following
to develop
comprehentechnology,
catamaran
and
structure
the optimum.
on the hul Is; the distribution terbody
of this conclusion,
to close the major gaps in catamaran
magnitude
and frequency
and location
and the hul Is.
of hydrodynamic
of loads in ~he cross-structure of local
These wi 1I require
wave
impacts
theoretical
loads
or the on the cen -
and experimental
programs. Model m
Test Program:
Series tests which etrical
hull
vertical
location;
cating
Series suitable
●
Model
b.
c. d.
e.
9.
extent
measurement
gathered.
)
structure
is relatively
It would
technique
be prudent simple
program.
Hull
for minimum
to clean
in various
unsymmetrical,
Added
mass and mass moment of inertia and unsymmetrical
bodies at wave
vidually
and as catamarans)
.
Construction
Cofitribution
to minimize
by cross-structure
modes.
and ship motions for multi-screw
encounter
in a seainstallation
motion
of sym-
frequencies
(indi-
bodies.
and compartmentation
Drydocking
is
mass and mass moment of inertia
of unsymmetrical
techniques
the data
whose cross-
for the horizontal
metrical
Added
once
to develop
analysis.
vibratory
resistance
Hull
stability
at
(Necessary
a catamaran
and amenable
particularly
feet.
and data analysis
way.
motion
lo-
the centerbody,
to select
response
form and spacing
in
distribution.
Dynarni cs of structural
Damaged
and unsymmvariations
and longitudinal
can simulate
load measurement
yard responsibilities). h.
which
and weight
FIJI I sca [e centerbody
the vertical f.
spacing;
.
test methods
form,
symmetrical
of hull
for ships from 100 feet to 1000
its weight
acceptable
include
longitudinal
of centerbody
~
least
would
forms; range
requirements.
need for new facilities
(ship-
facilities.
to the longitudinal
strength
of the
vessel . i.
Behavior
of Imx girders
under combined
bending,
torsion
and shear
loads.
i.
Stress concentrate ion at the hul I and cross-structure and extent
of necessary
reinforcement
and structural
juncture. detai Is.
Nature
for
.
50 9.
CONCLUSIONS
1.
The maior
constraints
individual
shipyard
to catamaran construction
size wit I be imposed
capabilities,
ckydock
by economics, facilities
and pier
facilities. Existing
United
proxinmtely be joined bors.
with
New
2,
facilities
hulls afloat;
drydocking
be essential problem
States yard
.
35-foot
facilities
Discharge
can handle
loads on large
draft
of cargo
information to provide
hull
spacing
model
great
in the streams could
tests to date
Additional
test data
optimum
have
research catamaran
an appreciable
ability
of unpublished
special
acknowledgement
their Friede
permission
plied
with
is feasible.
100-foot
beam
This does not
the model
through
test data
for specific
work
the accomplishment belonging
model
designs only and have
including
systematic
of reliable
design
of the proiect
to private
model
test
methods
for
THORNTON,
a copy of his senior thesis which
drilling
platform
was appreciated.
Friede
test data on their
Thanks are due to the Livingston for their
In this respectl
Dril I ing Company
test data orI the E .W.
to use the model
is due to the avail-
companies.
& Bates Offshore
whom the tests were contracted.
for permission .
developed
the centerbody.
for the establishment
is due to the Reading
of Miami
loads are not
structure.
degree,
lnc.
cross-structure
methods are not adequately
been performed
and development
to use the complete
and Goldman
providing
the pier
in either.
model test data
are also to be thanked for the University
harwill
of loads on the cross-structure prel iminary prediction of
draft
for predicting
analytical
of not simulating
programs are necessary
To
facilities
remove
long catamaran
and 31 -foot
confidence
had the drawback 5.
or new pier
for the estimation guidance to make
and the existing
to provide Model
have to
thafthe structural configuration willnecessarily be attractive.
sufficient
4.
would
in most maior
catamarans.
100-foot
The ava i Iable
3.
is acceptable
and modified
With respectto scantl ings, a 1000-foot imply
hul Is of ap-
.
Existing design is iust adequate
hulls,
individual
The hulls and the centerbody
1050 ft x 140 ft.
design.
Mr.
and Goldman
catamaran
Shipbuilding
for
and to lnc.
design
Company
John L. Glaeser
for sup-
51
The authors Ship
Design
wish
to thank
Division,
M.
Kaiii
Kyokai,
Messrs.
Rosenblatt
Sam T.
& Son,
Tsui and
N . K . K .
w ho assisted
Inc .,
with
Raman
of the
several
Basic
tasks of the
proiect.
Nippon ten descriptions
of their
Germanischer
general
approach
Lloyd
and
Det
to catamaran
Norske
design
Veritas
review
provided
which
were
writappre-
ciated.
Mr. cussions
Walter
Structure” Journal,
by Beniamin
Group
from
477-489,
for which
Jr.,
contributed
the authors Design
published
of The
grateful
1967,
Society
1970
Society
informal
.
Naval
of Naval
Loads
in October
by permission
with
of the ASR Catamaran
for Estimating
published
are
in August
of the American
“A Method
L . Dinsenbacher
pages
Eda willingly
“ The Structural
Lankford,
from
Haruzo
CrossEngineers
Engineers.
on Catamaran Marine
of Naval
Cross
Technology, Architects
and
Engineers.
Last, and
4,
Dr.
by permission
3 is quoted
by Alfred No.
W.
625-635,
Appendix Structure”
and
of the proiect
2 is quoted
pages
Vol . 7,
Michel
of some aspects
Appendix
Marine
H.
but not least,
11, Ship
practical
Structural
guidance
acknowledgements Design,
to the
Ship
proiect.
are
Research
due
to al I the
Committee
who
members provided
of the Advisory enthusiastic
dis-
52
REFERENCES
1.
General
Dynamics
Department 30 April
Bond,
John R.,
Eckhart,
M.
Jr.,
Leopold,
70
“A New
9.
15,
1970
Fisher,
Peter
A.;
Praught,
Lankford,
Beniamin ” American Naresh
in Irregular
10.
Scott,
11.
Robert,
of Naval
Michael
W.;
” Society 18,
- Dream
or Real ity, ”
“Structural
Center,
n167,
Analysis July
of
1970
Volume-Limited and Marine
Engineers,
Jr.,
“The Structural of Naval
“Motions ” Davidson
Catamaran Evaluation
Laboratory
Structure:
“Feasibility
Launch
and Marine
Design
ContainerEngineers,
of i-he ASR Catamaran
Journal,
Loading
August
January
and Hu I I Weight,
John
Report 2378,
Transactions, N.;
May
Pincus,
1965.
Appendix 70,
S.;
1962
“Model
” Naval
4 to
Society
Test
Ship Research
1967
Study for Ocean-Going Company,
Daniel
Catamaran
Mandel,
Volume
Cross Structure,
Cross-
1967
of a 106-Foot
Ship Types, ” by Philip
Engineers
Andrews,
and Tugboat
News,
“A Catamaran
Architects
Report LR-8231
Strength
of Novel
Alfred
Center
and Engineering
James E.;
Engineers
and Structural
and Marine L.;
Reporter
1969
of Sea Loads on Catamaran
H .A.,
of Naval
1970
Architects
$oden,
Dinsenlmcher,
Schade,
MA-4318,
Number
Society
Entitled
of Naval
Determination
the Crowley
August
Hul I Form for High-Speed
Society
Architects
and Development 120
Catamarans
Development
Maritime
April
W.,
M.,
Waves,
“A Comparative of Naval
No.
Publications
“ American
for Lecture
and
Ship,
Trade,
Meeting,
Structure, Maniar,
fm- U.S.
Contract
1969
lndus tries Twin-Hu[l
Section
Paper, Journal,
Notes
Ships, ” Society
ship for Trans-Atlantic
8.
on ASNE
Ship Research
Reuven A.,
January
Gulf
Service
or Reality,
Engineers
Outline
O.,
” Naval
Spring Meeting, Litton
- Dream
“Comment
Displacement-Type
6.
Information
under
1970
of Naval
Geoffrey
Catamarans, 5.
June
Society
Thomas,
Technical
“Catamarans
Journal,
American 4.
Study ’’prepared
Administration
to PB 183793.
Engineers 30
“Catamaran
Division), Maritime
National
1969.
PB 183787 2.
(Quincy
of Commerce,
California,
Catamaran, June
” Prepared
1965
for
53
i3.
14.
Dinsenkcher,
Alfred
” Marine
Technology,
Glaeser,
John L.,
“A Theoretical
and the Shear and Webb 15.
Institute
Livingston, E -W.
16.
Section
Meeting,
Michel,
Walter
18.
and Michel,
Naresh
oratory
Letter
Meier,
Herbert
19.
Chey,
Young
Loading
M.,
20.
Numata Davidson
21.
E.,
Walter
“Model
“Model
H.,
Alan
Senior
Thesisr
“The Catamaran
Architects
Drill
and Marine
Ship -
Engineers,
Gulf
Ship,
Its Features
and Marine
and
Engineers,
Its
Gulf
Sec-
Dril]ing
Ship, ” Davidson
Lab-
1965
Design
Volume
5,
of a Catamaran
Submarine
No.
1968
Tests to Evaluate
1, January Seakeeping
ic Vessel,
Rescue Ship
Qua] ities and Structural
” Davidson
La boratow
Letter
1962
Laboratory
of Naval
H .,
Test of a Catamaran
ocemograph
“1/100-Scale
Society
of a Catamaran
1968
Architects
January
Technology,
McClure,
Cross-
1970
Into the Motions
Catamaran
of Naval
“Preliminary
A.,
April
on Catamaran
October
1966
1052,
of a Catamaran
Report 891,
Lwds
4,
1961
Report
(ASR), ” Marine
May
“ The Sea-Going
April
No.
on its Cross- Structure,”
of Naval
February H.,
7,
Investigation
Moments
” The Society
tion Meeting,
for Estimating
Volume
Architecture,
” The Society
Thornton,
Maniar,
Bending
of Naval
C.W.
Feasibility,
17.
“A Method
L.,
Structure,
C.,
Model
Letter
Report
“Development
Architects
Tests of Mohole 1084,
January
of the Proiect
and Marine
Drilling
Platform
in Waves,
”
1967 Mohole
Engineers,
Drilling
” Transactions
Platform, Volume
” 73,
1965. 22.
Numata Davidson
23.
24.
Edaf
E.,
“Model
Laboratory
Haruzo
Water,
sactions
Volume
Schade,
H .A.,
73r
Semi-Submersible
Drilling
Vessel,
”
Report 1234
Jr.;
” The Society
C.
Lincoln,
of Naval
“Steering
Architects
Characteristics and Marine
of Ships
Engineers,
Tran-
1965
“The Effective
Loads, ” The Society 59,
Letter
and Crane,
in Calm
Volume
Test of a 6-Column
of Naval
Breadth of Stiffened Architects
and Marine
Plating
Under
Engineers,
Bending Transactions,
1951
—
-.
54
APPENDIX CATAMARAN
Of al 1 the tion.
aspects of catamaran
Considerable
and model
of this appendix
design,
represent
as well
valuable
certain
conditions,
tal resistance
published
to general
Contributions making
to resistance
Frictional tance
by other
and,
Catamaran (V/~L),
hull
theoretical reduce
calm water
wave
is general can occur
irrespective
as a ratio
not be compatible
where
given
between the level
From a practical constrain
the influence
surface,
of wave-
in this discussion. degree
agreement
speed.
is a function
of surface
rough-
resis-
number
the hulls can interfere
favorably
to
to the two hulls running
components
of the combined
wave
180°.
between Beneficial of
of the Froude
1 and 2) has demonstrated
appropriate
frequency
theory
in the Froude number
with with
effects
can be sepa-
or viscous and wave-making.
to the sum of the frictional
resistance
effects
drag to below
and model test data that
range of approximately hull
appears course,
separation
0.3<
in terms of the center
to be in the order of 0.3.
what
the beneficial V/~<
may be beneficial
0.4, to center
Further,
opti-
for resistance
may
the rest of the design.
The purpose of the foregoing interference
15%
it is equal
Eggers (references
of the ship~s length
varies
frictional
of the wetted
wave-making
of hull separation.
mum spacing
than the to-
hulls.
This is possible
There
at the end
it has been shown that
can be made smaller
small and are omitted
are out of phase by approximately
interference spacing
is a function
IY that the wave-making
in isolation. pattern
is because
, including
phenomena
form and hull spacing.
the catamatun
on the subiect.
prediction listed
singly.
for the catamarans,
of the individual
information
of catamarans
are relatively
resistance
ness and speed,
References
components , namely,
on viscous resistance,
the most atten-
, it is assumed here that resistance
practice
into two independent
has received
correlation.
in resistance
net resistance
of the two hul Is considered
According rated
resistance
both in the areas of theoretical
as their
The main reason for the interest under
RESISTANCE
work has been done,
test measurements
1
are obtained
design
viewpoint
the design within
discussion
in a narrow
is to show that range
the net resistance
the above
narrow
of Froude benefit
range of Froude
beneficial
wave-pattern
number and hull separation. has to be appreciable
to
number and hul I separation.
The conclusion reached on the hsis of data available to date is that no more than net reductionin total resistance of large catamarans should be expected in ideal
conditions
when com~red
the same time,
the increase
to the total
resistance
is not expected
of two hulls running
to be more than
15°A.
independently.
At
55
REFERENCES 1.
2.
General
Dynamics
for U .S.
Department
Contract
No.
Eggers,
K .,
Translation
Eggers, Bd. 9,
4.
Everett,
K.,
Society
1969 of Two-Body
(1 955)).
die Ermittlung
durch Analyse
Ships, ” BSRA von Zweikorperschiffen,
des Wel Ienwiderstandes
Seines Wellensystems,
eines
“Schiffstechnik
1962 J . T.,
of Engineers Turner,
Conditions
“Ca~amaran Study” prepared Maritime Administration under
Widerstandsverhaltnisse
Gesellschaft
“Uber
and Multi-Hul
5.
30 April
“Resistance 1860 (Uber
Schiffsmodells
Division),
of Commerce,
MA-4318,
J . Schiffkutech 3.
(Quincy
“Some Research led Vessels
and Shipbuilders,
H. and
Taplin,
of Naval
A.,
Architects
on the Hydrodynamics
in Calm Water,
” North
Transactions “The
Resistance
and Marine
of Catamarans
East Coast
Institution
1967-1968 of Large
Engineers
Powered
Transactionsr
Catamarans, Volume
” 76,
1968
.-
56 APPENDIX
This is a reproduction maran Cross-Structure” is devoted
of reference
by Ben]amin
to the description
this ship’s hull
2
Lankford,
of the statistical
to sea condition
“ The Structural
(8),
W.
beyond
Jr.,
Design
” excluding
methods used to predict
the capabilities
Cata-
of the ASR
the first part which the response of
of model tests.
SHEAR FORCES The foregoing
discussion
beam sea condition. The shear force
There
is of a higher
ment results in a negligible tons.
Shear becomes
be described
has only value
design
sponse amplitude
All
bending
cluding
foot tons.
bulkhead
will
is 72,000
As a separate
as a ratio be given
the fol lowing
a.
foot tons represents moment
been determined. direction
the design
conditions
were
The ship could starboard of plane.
hull
mo-
caused
water
maximum
1000 foot tons) .
since
moment
Since dead
load is less, or about
maior
of each
of assumed web areas.
cross-structure member.
member
The shear
A summary of the sea loads for
paragraph.
LOADS
CONSIDERED
the cross-structure
torsional
re-
to this moment.
this ship in still The total
foot tons (nearest
the total
of any bending
must be added
assuming
of this moment to each
in a later
condition,
possible
600 will
in the same way as the mo-
is independent
of the assumed moments of inertia
OTHER
the maximum
used is appro:{imately
mo-
SEA LOADS
load bending
in the upward
The distribution
loads were distributed each
a dead
load effect
was ba$ed on a ratio
but the associated
needs to do is to use the proper
of 63,300
this moment
of any sea waves has already
the dead
from a
test.
for the ASR was calculated
load opposes the sea forces 55,000
the designer
predicted
Since
of the structure,
load moment
the effect
resulting
from loads of other sources which
OF THE DESIGN
moment
ment on one side of the ship. The dead
sea heading,
The shear force
problem
from the model
DISTRIBUTION
by the weight
in the quarter
response can be determined
discussion.
operators
The final
moment
in the beam sea condition,
paragraph.
Shear or any other design men~ in the foregoing
the bending
a SI ight shear force
value.
more of a design
in another
described
is, however,
was designed
load on the cross-structure.
for what was considered
To determine
considered:
be drydccked
with
blocks out of plane
the port hull or the keel
blocks and could
be out
these loads,
in-
57
b.
The ship may possibly
For these conditions
the ship was assumed to be supported
tion 4) and on the other torsional
moment to each
of the linear loaded
run aground.
distance
hull aft (Station bulkhead
from the center
hulls) and full
cross~ection bulkheads
catamaran
load displacement
of one of the transverse between
upper and lower
deflection
in each
significance
other than that
through
with
tons.
similar
it provides
8.
use of
a satisfactory
scantl ings of norms I dimension. deckhouses
breadth
supporting
to Figure The
Figure
(26
The transverse
of plating
as the
cross-structural
mem-
9 carrying
the loads.
six bulkheads arrangement
and distributes The three
breadth
9 shows a typical
for the A5R.
an effective
and access requirements
aft form two separate
an 86 foot maximum
of 3600
the primary
are shown on Figure
compartment
bulkheads
with
is considered
There are six of these bulkheads
surate with
OF THE ASR
support bulkhmds
the two hul Is along
flanges
of these bulkheads
three
of the applied
is assumed to be a function
of torsion and the vertical
CONFIGURATION
The ASR is a 251 foot LOA foot wide
girders
The load distribution
in the cross-structure
(Sta-
bulkhead.
STRUCTURAL
ber.
18).
on one hul I forward
Locations
has no special for structure
the imds
bulkheads
commen-
into the hull
forward
with an open wel I between
and the for rescue
operations.
~la
,
I-—Y+T,..4
8 -
Forces Caused by the Settlement of Supports
SKETC.H FOR CAWJLATIOf~ OF 5tlEAR LOADS (DOWIFJG.G.ROL)ND ING)
P
Fig.
8
58
=“”=- .....1 Fig. 9 - Typical Transverse Bulkhead for ASR
THE DESIGN The calculation dock condition
PROCEDURE
of the load distribution
is as follows
(See Figure
to each
bulkhead
from the grounding-
8):
Assumptions 1.
The algebraic torsion
sum of moments akut
is assumed to be the centroidal
the center
Ad Torque
of torsion
= O, where
axis of the assumed bulkhead (EQUATION
= ~
center
of
a-.
1)
Where: A= d
Total =
(both hulls) 4 to Station 18
ship displacement
Distance
Station
P“
=
Shear Load on Bulkhead
Xn
=
Distance
to Bulkhead
n.
n.
Deflectionin each bulkhead isdirectlyproportionalto the linear
2*
from center
of torsion.
bn C=y n Where: c$n
=
Deflection
C
=
Tangent
of Bulkhead of the Angle
n. (for smal I angles)
distance
(Xn)
59 In order to evaluate stants,
forces
in the bulkheads
it is convenient
to compute
spring con-
Kn , due to support settlement.
spring
Bending and shear strains were included in the It was assumed that the torsional strength of the hul i is large compared constants.
constant.
the spring
&n . &
hen.e:
Kn ‘1
or—=
‘2 —. K2X2
KIX1
3.
+
The cross-structure settlement
c
.
r ..-
& KnXn
Pn — KnXn
bu Ikheads
of the support.
(EQUATION
are assumed to be fixed
(See Figure
ended
2)
beams undergoing
a
8)
Calculations Equating (Equation
1)
the external Torque
=
Iy applied ~
forces and internal
resisting
forces
-
= ‘~
Where: Y=+d
[1 A T
From Equation
y
=
Plxl
+
P2X2
+
. . . . . Pnxn
2: P1X2K2
‘2
=
K,x,
f
p3=—
KnXnPl
P1X3K3
..... Pn = KIX1
‘
K]X1
[+IY=‘1 [xl+-2+ .-K-I The equation Equation
3.
Moment
is solved far P] . All other Pn values From the shear loads (Pn), bending moments
=
=
can now be obtained from in the bulkheads are attained
PnLn ~
Span of cross-structure
between
3)
‘EQ”AT’0N4)
Where: Ln
(EQUATION
the hulls (Figure
8).
to
60
The final lated
moments and shear values
by the foregoing
condition
represent
the actual
values
an initial
scantling
selection
for the new inertias
for each
bulkhead
and the predicted
used for the ASR design. has been made the design
and web areas obtained
As can be seen from the resulting gives the highest
combination
bulkhead
especial
Iy the web plating
Bulkhead
21 resulted
the other
bulkheads.
as opposed
to resist buckling. that there
and
to those assumed originally.
the docking-grounding
loads above,
calcu-
below
It must be noted however that after loads were re-cycled and checked
of shear and moment which
from the fact
in the cross-structure
sea forces are recorded
governs
the forward
The large
was a deck
height
condition
variance
and aft of loads orI
difference
in depth
from
Calculated Predicted
Docking-Grounding
Sea Loads
Loads
Moment
Shear
Moment
Shear
Ft.
Tons
Ft.
Tons
Tons
Tons
Frame 21
4,600
80
5,180
305
Frame 37
11,600
104
6,650
342
Frame 49
13,200
104
3,900
230
Frame 84
13,200
104
4,150
244
Frame 86
14,700
104
6,900
406
Frame
14,700
104
10,200
596
72,000
600
36,980
110
Total The resisting designed outer
similar
flange
plus about
ing moment. tire
web.
cross-structure
to transverse 1/6
The total
of the depth
shearing
For stability,
bulkheads
force
the outer
the necessary
shear or compressing
the remaining
2/3
strength
equal
portion
is based on actual
trated
in the flanges
line distribution moment.
The 1/6
above,
whichever
to develop .
that the moment
web depth
the
resist the bend-
distributed
to the en-
was worse,
the
while
a shear buckling
The above in a plate
this method
width
somewhat
Although
is effective,
to consider
used is an approximate
the upper and lower The ac~ual
breadth.
plating.
much more plating decided
strength,
been
girder,
of the web was sized to develop
stress of the material
four feet of normal
heads as an effective
fore,
buckling
(8) describes
is probably
Approximately stiffened
plate
plate girder
girder is concen-
but drops off rapidly toward the neutral axis, unlike the straight . As a result, the center portion of the web cannot be
bulkheads.
ered in the design
with
86 and 110) have
of the web assumed to entirely
portion
tests indicating
Reference
As mentioned cross-structure
84,
Of the total
was assumed to be equally
1/6
yield
49,
used generally
assumed to contribute. actual
37,
carriers.
of the web was designed
to the shearing
theory
(21,
bents on aircraft
2,173
covering
the
and test results.
levels
form a flange
of plating,
or “effective
for the maior breadth” “consid-
conservative. deck
plating
The cross-structure,
is considered however,
under torsional
and bending
test data of large
box girders
The plating
value
between
bulkheads
to act with
the bulk -
is more of a box girder loads it is assumed that is limited.
to provide
It was,
an additional
therefactor
61
of safety model
rather
than
tests can be conducted
precise
effective
fective,
breadth .
the design
heads resisting considered
between
the cross-structure
web plating
could
flange
and vice
longitudinal
and bottom
E .W.
Thornton, damaged
To solve
presented
most of the problems,
strength
calculations.
of the cross structure
in the Gulf
the ship was moored.
.
of Mexico,
effect
These farces somewhat
However,
a visit
no effect
that shell
could
AS a result of the local damage found on the drilling board on the ASR was designed for 1500 pounds per square foot. members
the length
intermittently
of the ship.
welded
For the ASR,
.
These welds suffered
continuous
welding
hydroplating
drilling
stiffening
rig,
was
the two hul 1s while found by the model
be predicted
test.
framing
for local
for the shell
the effect
stiffening
of the
The hulls are designed
of structure
of seas between
resembled
on local
the incontinu-
failure.
to the catamaran
it was discovered
of the pocketing
through
was carried
and is the basis for this
ships except
During
the insert plate
an interlacing
loads.
Design
bulkheads
was also a prob-
not lead to a maior
the main hull and local
the neces-
to the hul 1, the
plating
This provides
would
four feet
a most critical
continuously
bulkhead
deck .
delamination
There
this problem,
was carried
to that found on conventional
as a result
test for the ASR.
versa .
shell and second so plate
has been said about
badly
model
only
and main hull
was made intercostal
of the cross-structure
the cross-structure
loads is similar
inboard
With
was considered
from stress concentrations.
second deck and the transverse
the inboard
using standard
and main hull
in the cross-structure
If the cross-structure
delaminate,
into the
little
static
was added
stress resulting
delamination.
Since
and shear .
is inef-
to one of bulk-
9.
stressed structure
paper.,
pure bending
problem
shown on Figure
ously through highly
box girder
a more
bulkheads
modulus for the structure
as the lower
board shell
from a torsional
to determine
between
to use inserts to provide
the nominal
plate
that plating
it was necessary
lem of plate acting
in the near future
the assumption
is then reduced
It is hoped that structural
breadthf
Additional
to reduce
on box structures
the loads imposed through
The joint area .
it in the design at this time .
With
for the effective
sary section
shell
including
by the
rig, the shell inThe drilling rig had
cracking
throughout
is specified.
CONCLUSION The primary
purpose of tlis paper
some basic knowledge simple
approach
tests on various
of the problems
to the solution hull
has been to provide encountered
of these problems.
forms and spacings
before
developed. ltwillthen become important and attempt
to correlate
the commercial maran
now being
ariulytical
ship E .W. designed,
with
Thornton,
to instrument
along
wil I provide
structure
with
full
solution
with
and a
to conduct
analytical
more
can be
these hul Is once they are built scale
ship tests.
with a new oceanographic
valuable
hull
It wil I be necessary
a completely
predictions
the ship design engineer
catamaran
information
The ASR and
research
for future
designs.
cata-
62
REFERENCES
(1)
A.L.
Dinsenbacher,
J . Andrews
Sea Loads on Catamaran
and
D.
“Model
Pincus,
Cross Structure
(Prel iminaty),
Test Determination
” DTMB
of
Report of Sept.
1966.
(2)
J . Williamson,
(3)
Moskowitz,
“Long Term Distribution
Cross Structure,
” Webb
“Estimates
Institute
Report dated
of the Power
Speeds of 20 to 40 Knots, ” New Sept.
(4)
Nils
Spectra
York
Moment
14 Ott.
1966.
for Fully
University
on ASR Catamaran
Developed
Technical
Seas for Wind
Report to ONR,
1963. “ The Prediction
R .H . Compton, ing Moment
(5)
of Bending
from Model
Nordenstrom,
Midship
Bending
of Long-Term
Tests, ” Webb
“An
Estimation
Moments
Distributions
Reportl
dated
of Long-Term
on Ships, ” Chalmers
July
of Wave-Induced
Bend-
1966.
Distribution Tekniska
of Wave-Induced
Hogskola,
dated
Aug.
1963. (6)
Warnsinck
et al,
“Report
ceedi rigs, Vol . 1, dated (n
(8)
H .U . Rol 1, “Height,
of Committee July
Length
and Steepness
Dimensions
of Seawaves
as Functions
No.
1-19,
dated
1958.
L.$.
Beedle
354.3,
Lehigh
(9)
Samuel
(lo)
W.J
Dec.
and others,
B. Richmond,
. Pierson,
“Structural
University, Jr.,
dated
L. Moskowitz, Record’s Obtained York I I
University ,’
W .J.
Pierson,
by OWS Technical
Steel
Conditions,
” ISSC Pro-
Design,
Analysis” Spectra
in the North
” SNAME
” Fritz
2nd Ediold Method
T.
Atlantic
and
& R. Bul Ietin,
Engineering
Report
No.
“ Wa~e
Explorer
Report to ONR,
Press Co.,
New
for Observing
York
1964.
and Forecasting
:
and Statistics,
and E. Mehr,
Weather
Force,
1962.
“Practical
and the ‘3 VOIS.,
” Hydrographic Office PubI I I I Spect~a Estimated fr~m Wtws 0W5 Nov~
Weather 1962,
Repo,rter, ” New
Mar.
1943,
June 1965.
I
!,
I
I
I 1
II I
of Seawaves
of Wind
Spring
“Statistical and Others,
Ocean Waves by lyleans of Wave Iication No. 603-1958.
(11)
1 on Environmental
1964.
1’
I
I I
I
‘1
,,
I I
I
63 APPENDIX
This is a reproduction ciated
nomenclature
Cross-Structure”
of the “$ummary
for reference
(1 3),
3
and Discussion”
“A Method
section
for Estimating
with
the asso-
Loads on Catamaran
by A . L. Dinsenbacher.
NOMENCLATURE (For Appendix
3 Only)
A
wave
amplitude
Ab
wave
amplitude
for computing
bending
At
wave
amplitude
for computing
torque
B
beam of one hull
b
half
c
center
beam of entire
load load
ship
of twist of cross-structure
D
instantaneous
Do
st i I Iwater
d
distance
mean draft
draft from top of cross-structure
G
center
9 HI
gravitational
HL
horizontal
hydrostatic
force
hydrostatic
force on inboard
depth
of gravity
down to neutral
HR L
ship length
Lw
wave
m(y)
‘
to top of cross-structure)
P=
transverse
bending
at iunction
Tc t
= =
coordinate
of cross-structwre
and hull,
y
not including
and mass of ~ross-stru cture
effects
of
I
hydrostatic
~ressure
shear force
clea~ span between torque
moment at transverse
axia I load on cross-structure
horiz~ntal vertical
=
bending
moment at midspan of cross-structure
weight
Q= s
side of a hul I side of a hull
(LBp)
cross structure moment
=
on outboard
length
M (0) = MQ =
P
of ship
acceleration
(keel
horizontal
axis of cross-structure
hulls
on cross-structure
horizontal
distance
about
(positive
its twist
forward)
center
from cross-structure
twist
center
to
ship’s CG VL
=
dista~ce
from keel
dutbourd “R
=
distance
from keel
inboard
w= Wc x,y,
to center
of pressure of horizontal
hydrostatic
force
on
to clenter of pressure of horizontal
hydrostatic
force
on
side of a hull side of a hull
ship weight
,= ~ =
weight
of cro,ss-structure
coordinate
system fix~d
on ship representation
with
origin
at center
elevation
to wuve
of
gravity!
B
,=
1’ half
A ?= 5=
‘=
instantaneous
the clear
density distance,
span between displacement
hulls or buoyancy
of water positive
downward,
from mean surface
surface
64
SUMMARY The equations trated
in Figs.
1 and 2.
(1 ~ O .4) appears; sign corresponds and (S/2)
obtained
the positive to downward
of positive
sign indicates developed
axial
, vertical
bending
and some are illusupward,
now substituted
the term
the negative S/2
for~
in the text. from the beam and are as-
and shear loads.
The directions
3.
and amplitude,
A (wave
height
= 2
A I ),
for this loading
case
to be Lw —
=
(70)
2(S + B)
A=Ab=-~ The axial
we have
previously
loads wil 1 now be
in the following,
1, the waves are approaching
the greatest
length
given
the ship accelerating Also,
acceleration.
loads are shown in Fig.
The wave
cross-structure
in the Nomenclature,
of the equations
+ B for b in the equations
sumed to produce
for estimating
been defined
In several
For Ioadi ng condition
are taken
thus br
The symbols have
summarized.
DISCUSSION
AND
(71)
—
load on the cross-structure
is
P = -2ggLA (1 t 0.4) Do sin —
llB
(72)
2(S+B)
The moment at the transverse M(0)=
-qg
- D02
iTB LAsin — 2(S + B) ~2 - ~
(1 ~ 0.4)2
w
sin
mid-span 2D0
(1 ~0.4)
sin2
2(su+BB)
where A
is given
in
(71) .
M
in (72),
-d)
TTB
W(S+B)A 211Do
1
WC(S + 2B) 8
The sign of A is positive
(73)
for a wave
trough
between
the
hulls,
for a crest.
The moment at the junction
where
1
is
+
Cos _
+(1 ~o.4) and negative
(HI
[
‘B 2(S+B)
[
of the cross-structure
() ~
+
=
M (0) is obtained
of cross-structure
M(o) -(1 ‘0.4)
from (73).
WcSfi
Whichever
the same sign must be employed
and hull
is
(74)
sign is chosen in the term of (1 ~ O .4)
in that same term in (73) and (74).
65
View Iooki ng rorward rrom s~ern
NOTES:
Coordintite
on ship with origin
S)’sLC’M fixed
\Yave leng[h,
&
. ?(fi+~)
A is wa!,e amplitude
(if A negntive,
crest
I
-B
-b
acc.?nter or gravily
(G) o~ship
= 2(S+B) be[.wecn
hulls)
b
P
L-+A---LB-J--J
MEAN 5URFACE
I
I
ELEVATION
i Dis tance
i
heighL or wave surrace from keel
~(~)is}ertical coordinateij
above keel atcenter
to mean
surrace
location
orwavesurrace
(~ positive
Forwwesurracr:
plane ofl?uil
(als.odis.
elevation) from mearielevntion,
attrans,erse
in trough)
leL<(~).
Acos~ (b+t3
Immcrsionorhul!
at~.D-~(~)=D-Aco5u-
(b+~)
Fig. 1 - Loading Condition 1
The estimate and hull,
for maximum
shear,
in beam waves,
at the junction
of crws-structure
is
(75)
Q=(l
in which
MQ
= M(0) -(1~0.4)Wc
M (0) in (76) is obtained consistent
throughout
It is important that the various
from (73).
(76)
(S+2B)/8 Again,
the choice
of sign in (1 ~ 0.4)
must be kept
(73-76). , in estimating
combinations
the shear and moment acting
resulting
This is to insure that the maximum
froim the choices
loads are found.
-—
on the cross-structural
of +- A and (1 ~ O .4) be comp uted.
66
6 =
~
tan-’g
. 2( S+B)sind
L S+R
.
@#7h~ M point p (on port hull centerplane), surface
disknce
kom mean surface
elevation
to wave
is
‘,=-
“0s(”+%9=’ —
co’% —
But, up = : – Xp Cose () so
%7x $ .,4 sin— P L girt
. D - fp . D- .-l sin+
and immersion
Fig. 2 - Loading
For loading as shown in Fig.
~
condition 2.
=
is reminded
The estimate
torsion),
and amplitude
2
the wave
advances
=
(77) A+=0.6~
(78)
—
that the wave
for maximum @bg
obliquely
are
L(S+B)/j~ A
The reader
2 (for maximum
The wwve length
Condition
heighf
torsional
BAL2 /217
+
is twice
load
the magnitude
in waves
O. 14Mqt/S
of the amplitude.
is
(79)
as
67
Table 1 - Loading Schedule A - For Direct Stress at Mid-Span of Cross-Structure
Load
Beam Waves
Quartering
Waves
P from (72)
O.4 of P from (72)
Moment
M (0) from (73)
O.4 of M (0) from (73)
Shear
Not Applicable
Axial
Force
Torsion
(N. A.)
N.A.
N.A.
N.A.
Table 2 - Loading Schedule B - For Direct Stress at Junction of Cross-Structure and Hull
Load Axial
Force
Beam Waves
O.4 of P from (72)
P from (72)
M ( &~)
Moment
Quartering Waves
from (74)
0.40fT=from
Torsion
from (74)
N.A.
N.A.
Shear
+ ~) s
0.40fM(-
(79)
TC from (79)
Table 3 - Loading Schedule C - For Shear Stress at Junction of Cross-Structure and Hull Load Axial
Force
Moment
Beam Waves
Quartering
Waves
N, *A .
N.A.
N.A.
N.A.
Shear
Q from (75)
O.4 of Q from (75)
Torsion
O.4 -of T= from (79)
Tc from (79)
—..—
68
F
-lM P
INTERNALLOADS
~
II) Q G
—y
●
HL ‘R 111111
WEW LOOKING FORWARD FROM STERN
-=r r
Fig. 3 - Positive Internal Loads
in which torque
A is defined
about
To estimate multaneous
by (78),
*he center
y,
MQ
is computed
from (76),
and T= is the magnitude
of the
of twist of the cross-structure.
the maximum
in certain
stresses on the cross-structure
proportions,
the loads found
it is necessary
in the foregoing.
to apply
si-
As has been
stated in the text, the model test results showed moments and shears in quartering seas to be about O.4 of their magnitude in beam waves. Also the torque in beam seas was found to be about
O.4 of its value
of maximum
stresses,
the loading
schedules
in Tables
stress, and for the ship operating stresses of interest, Iated
which
and summed.
row in which
that
The equation
1, 2 and 3.
Each loading
Schedule
B, Table
load can produce
the hul Is (2,
by relating, design
case the are cal cuin the
linking
bending
and hul Is.
The reason
moments on the ends of the trans-
REMARKS
to develop
simple
the hul Is of a catamamn.
empirically
loads are used in
that torsion
expressions Although
have been made , some compensation
albeit
practices
2,
9).
has been made herein
on the structure
tions and approximations current
For each column,
load is indicated
of the cross-structure
CONCLUDING
duced
with
is for a specific
waves.
a particular
estimates
in accordance
by the loads in the “Load”
to use to obtain
in Loading
spanning
An attempt
to obtain
schedule
in both beam and oblique
stresses at the I unction
for this is that the torsional
Iwds
Therefore,
waves.
the loads should be applied
load is designated.
the direct
verse bulkheads
that
are produced
It may be observed computing
in quartering
it is suggested
and/or
for longitudinal
heuristically,
for estimating
several
gross
gross assump-
for these has been introto model
test results and
strength.
REFERENCES
1.
H .A.
Schade,
the Crowley 2.
A .L.
“Feasibility Launch
Dinsenbucher,
and Tugboat J. N.
of Sea Loads on Catamatan ment Center
.
(NSRDC)
Study for an Ocean-Going Company,
Andrews,
California,
June
and D. S. Pincus,
Cross Structure,
Report 2378,
Catamaran,
May
” Naval 1967.
“Model
” prepared
for
1965. Test Determination
Ship Research
and Develop-
69
3.
J .T.
Birmingham
and A.L
in Random Seasr” 4.
M.
St. Denis,
C-555, 5.
J . N.
6.
7.
Thomas, SNAME, Andrews
and A .L.
N.H.
B .W. Naval
of a Liberty
Ship
(DTMB) Report2081, November 1965.
Design of the Midship
Section,
” DTMB
Report
VOI.
76,
and A.L.
“ Structural
” NSRDC Static
Report 2177, Balance
Response of a Carrier April
Approach
Model
to Longitudinal
Strength,
1968. Dinsenbacher,
Operators
“Agreement
and Whipping
Jasperl
et al .
“Statistical
of Essex-Class
Lankford, Engineers
“The
Aircraft Structural
Journal,
August
Presentation Carriers,
of Model
and Prototype
Response, ” NSRDC
Design 1967.
of Motions
” DTMB
in
1966.
Report 2351,
1967.
Moments
9.
“Stresses and Motions
Basin
Dinsenbacher,
“An Extended
Response Amplitude
8.
Model
the Structural
and Random Waves,
Trans.
April
. Dinsenbacher, Taylor
1954.
Andrews
G. O.
J . N.
“On
October
Regular
David
and Hul I Bending
Report 1251,
of the ASR Catamaran
June
1960.
Cross- Structure,”
”
UNCLASSIFIED Security
Classification
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ACTIVITY
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titfc,
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and
iflu’e,vlnp
,JnnofaricJn
mu.1
be entered
when
rhe
2a. REPORT
authorJ
Oversll
5ECu
rcporf
R1TY
is
Classified)
CLASSIFICATION
Unclassified
Inc.
M. Rosenblatt & Son, REPORT
>h.
GROUP
TITLE
Catamarans - Technological Limits to Size and Appraisal and Procedures of Structural Design information DE SC R[PT!VE
NOTE5
(TyP,
Of
,e)mrt
a“d
;nctllvi”e
dsfes)
Final Report (Fi@t
AU THOR(SI
rwme,
middle
rnit!al,
last
name)
Naresh M. Maniar, Wei P. Chiang REPORT
DATE
ra.
TOTAL
NO.
Sept. 1971 a,
CONTRACT
OR
OF
7b.
PAGEs
NO.
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NAVSHIPS No. 0911-001-1010
SSC-222
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Distribution of this document is unlimited. !.
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NOTES
SPONSORING
MILITARY
ACTIVITY
Naval Ship Systems Command s,AB5
TRACT
Existing United States shipbuilding facilities can handle 1000-foot catamarans with up to 140-foot individual hull beams on the premise that the hulls would be joined afloat. Major harbors and channels of the world suggest an overall beam limit of 400feet and 35-foot draft. Drydocking for catamarans over 140-foot in breadth will require new facilities or extensive modification to existing facilities. Scantlings of a 1000-foot catamaran cargo liner can be expected to be within current shipbuilding capabilities. The uniqueness of the catamaran design lies in the cross-structure and the important facets of the cross-structure design are the prediction of the wave-induced loads and the method of structural analysis. The primary loads are the transverse vertical bending moments, axial force, shear, and torsion moments. Designers have relied heavily on model tests to obtain design loads and have used general structures principles and individual ingenuity to perform the structural analysis in the absence of established guidelines. Simple semi-empirical equations are proposed for predicting maximum primary loads. A structural analysis method such as the one proposed by Lankford may be employed for conceptual design purposes. The Lankford method assumes the hulls to be rigid and the cross-structure loads to be absorbed by a group of transverse bulkheads and associated effective deck plating. This procedure in general should provide an overall conservative design and not necessarily an economic or optimized design. Additional research and development work including systematic model test programs are necessary for accumulating additional knowledge in areas of uncertainty and for the establishment of reliable design methods for catamaran structure.
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Catamaran Size Limits Design Procedures
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SHIP RESEARCH COMMITTEE Maritime Transportation Research Board National Academy of Sciences-National Research Council
The Ship Research Committee has technical cognizance of the inter-agency Ship Structure Committee’s research program:
PROF. R. A. YAGLE, Chairman, Prof. of Naval Axvhiteeture, Univ. of Miehigan DR. H. N. ABRAMSON, Di~eetioz+ Dept. of Meelz.Seieneez, Southuest Research Institute MR. W. H. BUCKLEY, Chief, S-LmeLu.raZCrike~ia and Loads, Be21 .&rosystems Co. MR. E. L. CRISCUOLO, Sen. l!Ton-Desti~uetive Test. Spa., DR. W. D. DOTY, Swio~
l!laval Ordnance Lab.
Research Consultant, U.S. Steel Co~po~atiion
PROF. J. E, GOLDBERG, School of Engineering, ~rdue
Univemitg
PROF. W. J. HALL, Prof. of CiUi2 Enginee~{ng, Univ. of Illinois MR. J. E. HERZ, Chief StruetiuraZDes. Engineer, Sun Shipbuilding & Dry Dock CO. MR. G. E. KAMPSCHAEFER, JR., Manage~, Appzieation Enginee~ingJ ARMCO Stce~ CoYp. MR. R. C. STRASSER, Di~eetio~of Resecweh, Newport lVewsShipbuilding & Dry Dock Co. CDR R. M. WHITE, USCG, Chief, AppZied Engineering Sec., U.S. Coast ~uard Academy MR. R. W. RUMKE, Exeeutive Seeratary, Ship Research Committee
Advisory Group II, “Ship Structural Design” prepared the prcject prospectus and evaluated the proposals for this project:
MR. J. E. HERZ, Chairman, Chiaf Strue. Des. Eng~., Sun Shipbuilding z Dq MR. C. M. COX, Asst. iVavaZArch., Hu~l Des. Div.,
Dock Co.
lVewpo~tNews Shipbuilding & Dry Dock Co.
MR. C. R. CUSHING, ~esident, Cushing & flordst~om,Inc. PROF. J. E. GOLDBERG, SehooZ of Engineering, Purdue Un
ofiVav.
AYch., U. of Ca2ifomia
MR. D. P. ROSEMAN, NavaZ Arehiteek, Ilydronau.ties, Inc.
.;
CDR R. M. WHITE, USCG, Chief, AppZiedEngineeringi5ee., U.S. Coast GuardAcademy
SHIP
STRUCTURE
COMMITTEE
PUBLICATIONS
These documents are distributed by the National Technical Information Sexwiee, Springfield, Va. 22151. These documents have been announced in the Clearinghouse journal U.S. Govwnment Research & Development Reports (USGRDR) under the indicated AD numbexw. SSC-209, Results from FulZ-Scale Measwements of Midship Bending Stresses on Y7wee Dry Cargo Skips by 1. J. Walters and F. C. Bailey. 1970 All 712183. SSC-21O, Analysis of Skmming Data f~om the “S. S. Wolverine State’rby ~. W. Wheaton, C. H. Kane, P. T. Diamant, and F. C. Bailey. 1970. AD 713196. SSC-211, Design and Installation of a Ship Response In.stwmentation System Aboard the Containe~ Vessel “S. S. Boston“ by R. A. Fain, J. Q. Cragin and B. H. Schofield. (To be published). SSC-212, Ship Response Instw.mentation Aboard the Containe? Vessel “S. S.
Boston”: Results from the 1st Operational Season in North Atlantic Semiee by R. A. Fain, J. Q. Cragin, and B. H. Schofield. 1970. AD 712186. SSC-213, A Guide for Ultrasonic Tasting and Evaluation of Weld Flaw Youshaw. 1970. AD 713202.
by R. A.
SSC-214, Ship Response Instrumentation Aboa~d the Container Vessel “S. S.
Boston”: Results f?om Two OpeYationaZ Seasons in North Atlantic AD 712187. Service by J. Q. Cragin. 1970. SSC-215, A Guide fop the Synthesis of Ship Structures Pa?t One - The Midship
Hold of 1970. SSC-216, (To
be
a
Transve~sely-Fmmed Dry Caz=goShip by Manley St.
IleniS.
AD 717357. published).
\
SSC-217, Comp~essive Strength of Ship Hull Girde~s - Part I - Unstiffened plates by H. Becker, R. Goldman, and J. Pozerycki. 1971. AD 717590. SSC-218, Design Considerations fop Aluminum Hull Structures: Study of Aluminum Bulk Carriers by C. J. Altenburg and R. d. Scott. 1971. SSC-219, c~ack propagation and Arrest in Ship and Other SteeZ.sby G. T. Hahn, R. G. Hoagland, P. N. Mincer, A. l?.Rosenfield, and N. Sarrate. 1971. SSC-220, A Limited Survey of Ship Structu~al Dmage Levine, and R. Taggart. 1971. SSC-221, Response of 1971.
—.———
by S. Hawkins, G. H.
the Delta Test toSpecimen Variables by L. J. McGeady.
—.
.—-
