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The Principles of
Naval Architecture Series
Strength ofShipsandOcean Structures
Alaa Mansour
University of California, Berkeley
Donald Liu
American Bureau of Shipping
J. Randolph Paulling, Editor
2008
Published by
The Society of Naval Architects and Marine Engineers
601 Pavonia Avenue
Jersey City, NJ
Copyright
C
2008 by The Society of Naval Architects and Marine Engineers.
It is understood and agreed that nothing expressed herein is intended or shall be construed to
give any person, firm, or corporation any right, remedy, or claim against SNAME or any of its
officers or members.
Library of Congress Cataloging-in-Publication Data
A catalog record from the Library of Congress has been applied for
ISBN No. 0-939773-66-X
Printed in the United States of America
First Printing, 2008
A Word from the President
The Society of Naval Architects and Marine Engineers is experiencing remarkable changes in the Maritime Industry
as we enter our 115
th
year of service. Our mission, however, has not changed over the years . . . “an internationally
recognized . . . technical society . . . serving the maritime industry, dedicated to advancing the art, science and practice
of naval architecture, shipbuilding, ocean engineering, and marine engineering . . .encouraging the exchange and
recording of information, sponsoring applied research . supporting education and enhancing the professional status
and integrity of its membership.”
In the spirit of being faithful to our mission, we have written and published significant treatises on the subject of
naval architecture, marine engineering and shipbuilding. Our most well known publication is the “Principles of Naval
Architecture”. First published in 1939, it has been revised and updated three times – in 1967, 1988 and now in 2008.
During this time, remarkable changes in the industry have taken place, especially in technology, and these changes
have accelerated. The result has had a dramatic impact on size, speed, capacity, safety, quality and environmental
protection.
The professions of naval architecture and marine engineering have realized great technical advances. They include
structural design, hydrodynamics, resistance and propulsion, vibrations, materials, strength analysis using finite el-
ement analysis, dynamic loading and fatigue analysis, computer-aided ship design, controllability, stability and the
use of simulation, risk analysis and virtual reality.
However, with this in view, nothing remains more important than a comprehensive knowledge of “first principles”.
Using this knowledge, the Naval Architect is able to intelligently utilize the exceptional technology available to its
fullest extent in today’s global maritime industry. It is with this in mind that this entirely new 2008 treatise was
developed – “The Principles of Naval Architecture : The Series”. Recognizing the challenge of remaining relevant and
current as technology changes, each major topical area will be published as a separate volume. This will facilitate
timely revisions as technology continues to change and provide for more practical use by those who teach, learn or
utilize the tools of our profession.
It is noteworthy that it took a decade to prepare this monumental work of nine volumes by sixteen authors and by
a distinguished steering committee that was brought together from several countries, universities, companies and
laboratories. We are all especially indebted to the editor, Professor J. Randolph (Randy) Paulling for providing the
leadership, knowledge, and organizational ability to manage this seminal work. His dedication to this arduous task
embodies the very essence of our mission . . . “to serve the maritime industry”.
It is with this introduction that we recognize and honor all of our colleagues who contributed to this work.
Authors:
Dr. John S. Letcher Hull Geometry
Dr. Colin S. Moore Intact Stability
Robert D. Tagg Subdivision and Damaged Stability
Professor Alaa Mansour and Dr. Donald Liu StrengthofShipsandOcean Structures
Dr. Lars Larson and Dr. Hoyte Raven Resistance
Professors Justin E. Kerwin and Jacques B. Hadler Propulsion
Professor William S. Vorus Vibration and Noise
Prof. Robert S. Beck, Dr. John Dalzell (Deceased), Prof. Odd Faltinsen and
Dr. Arthur M. Reed
Motions in Waves
Professor W. C. Webster and Dr. Rod Barr Controllability
Control Committee Members are:
Professor Bruce Johnson, Robert G. Keane, Jr., Justin H. McCarthy, David M. Maurer, Dr. William B. Morgan, Profes-
sor J. Nicholas Newman and Dr. Owen H. Oakley, Jr.
I would also like to recognize the support staff and members who helped bring this project to fruition, especially
Susan Evans Grove, Publications Director, Phil Kimball, Executive Director and Dr. Roger Compton, Past President.
In the new world’s global maritime industry, we must maintain leadership in our profession if we are to continue
to be true to our mission. The “Principles of Naval Architecture: The Series”, is another example of the many ways
our Society is meeting that challenge.
ADMIRAL ROBERT E. KRAMEK,
President
Foreword
Since it was first published 70 years ago, Principles of Naval Architecture (PNA) has served as a seminal text on
naval architecture for both practicing professionals and students of naval architecture. This is a challenging task –
to explain the fundamentals in terms understandable to the undergraduate student while providing sufficient rigor
to satisfy the needs of the experienced engineer – but the initial publication and the ensuing revisions have stood
the test of time. We believe that this third revision of PNA will carry on the tradition, and continue to serve as an
invaluable reference to the marine community.
In the Foreword to the second revision of PNA, the Chairman of its Control Committee, John Nachtsheim,
lamented the state of the maritime industry, noting that there were “. too many ships chasing too little cargo,”
and with the decline in shipping came a “. corresponding decrease in technological growth.” John ended on a
somewhat optimistic note: “Let’s hope the current valley of worldwide maritime inactivity won’t last for too long.
Let’s hope for better times, further technological growth, and the need once more, not too far away, for the next
revision of Principles of Naval Architecture.”
Fortunately, better times began soon after the second revision of PNA was released in 1988. Spurred by the expand-
ing global economy and a trend toward specialization of production amongst nations around the world, seaborne
trade has tripled in the last twenty years. Perhaps more than ever before, the economic and societal well being of
nations worldwide is dependent upon efficient, safe, and environmentally friendly deep sea shipping. Continuous
improvement in the efficiency of transportation has been achieved over the last several decades, facilitating this
growth in the global economy by enabling lower cost movement of goods. These improvements extend over the en-
tire supply train, with waterborne transportation providing the critical link between distant nations. The ship design
and shipbuilding communities have played key roles, as some of the most important advancements have been in the
design and construction of ships.
With the explosive growth in trade has come an unprecedented demand for tonnage extending over the full
spectrum of ship types, including containerships, tankers, bulk carriers, and passenger vessels. Seeking increased
throughput and efficiency, ship sizes and capacities have increased dramatically. Ships currently on order include
16,000 TEU containerships, 260,000 m
3
LNG carriers, and 5,400 passenger cruise liners, dwarfing the prior generation
of designs.
The drive toward more efficient ship designs has led to increased sophistication in both the designs themselves
and in the techniques and tools required to develop the designs. Concepts introduced in Revision 2 of PNA such as
finite element analysis, computational fluid dynamics, and probabilistic techniques for evaluating a ship’s stability
and structural reliability are now integral to the overall design process. The classification societies have released
the common structural rules for tankers and bulk carriers, which rely heavily on first principles engineering, use of
finite element analysis for strengthand fatigue assessments, and more sophisticated approaches to analysis such
as are used for ultimate strength assessment for the hull girder. The International Maritime Organization now relies
on probabilistic approaches for evaluating intact and damage stability and oil outflow. Regulations are increasingly
performance-based, allowing application of creative solutions and state-of-the-art tools. Risk assessment techniques
have become essential tools of the practicing naval architect.
The cyclical nature of shipbuilding is well established and all of us who have weathered the ups and downs of the
marine industry recognize the current boom will not last forever. However, there are reasons to believe that the need
for technological advancement in the maritime industries will remain strong in the coming years. For example, naval
architects and marine engineers will continue to focus on improving the efficiency of marine transportation systems,
spurred by rising fuel oil prices and public expectations for reducing greenhouse gas emissions. As a consequence
of climate change, the melting Arctic ice cap will create new opportunities for exploration and production of oil and
other natural resources, and may lead to new global trading patterns.
SNAME has been challenged to provide technical updates to its texts on a timely basis, in part due to our reliance
on volunteerism and in part due to the rapidly changing environment of the maritime industry. This revision of
PNA emphasizes engineering fundamentals and first principles, recognizing that the methods and approaches for
applying these fundamentals are subject to constant change. Under the leadership of President Bob Kramek, SNAME
is reviewing all its publications and related processes. As the next SNAME President, one of my goals is to begin
strategizing on the next revision of PNA just as this third revision comes off the presses. Comments and ideas you
may have on how SNAME can improve its publications are encouraged and very much appreciated.
FOREWORD
PNA would not be possible without the contributions of SNAME members and other marine professionals world-
wide, who have advanced the science and the art of naval architecture and then shared their experiences through
technical papers and presentations. For these many contributions we are indebted to all of you. We are especially
indebted to its editor, Dr. J. Randolph Paulling, the Control Committee, the authors, and the reviewers who have
given so generously of their time and expertise.
R. KEITH MICHEL
President-elect
vi
Acknowledgments
The authors wish to acknowledge their indebtedness to the author of Chapter 4, “Strength of Ships”, in the pre-
ceding edition of Principles of Naval Architecture from which they have freely extracted text and figures. They
also acknowledge the advice and assistance of the Control Committee, members of which provided reviews of early
versions of the manuscript.
The present volume, StrengthofShipsandOcean Structures, could not have been completed without the as-
sistance of a number of associates, colleagues and former students who read and critiqued portions or all of the
manuscript, helped with illustrations, tracked down references and provided other vital services. The authors wish
especially to acknowledge the contributions of the following individuals:
Dr. Jianwei Bai, University of California, Berkeley
Dr. Hsao H. Chen (Ret), American Bureau of Shipping
Mr. Robert Curry (Ret), American Bureau of Shipping
Professor Jorgen J. Jensen, Technical University of Denmark
Mr. Gregory Pappianou, University of California, Berkeley
Professor Preben T. Pedersen, Technical University of Denmark
Mr. Martin Petricic, University of California, Berkeley
Dr. Yung S. Shin, American Bureau of Shipping
Dr. Ge Wang, American Bureau of Shipping
Mr. Omar El Zayat, University of California, Berkeley
Finally, the Editor extends his thanks to the authors for their time and monumental efforts in writing the vol-
ume, to the Control Committee, and to the individuals listed above as well as others whose advice and assistance
was essential to the successful completion of the task. He is especially grateful to Susan Evans Grove, SNAME’s
Publications Director, for her patience, ready advice and close attention to detail without all of which this work
could not have been accomplished.
Biography of Alaa Mansour
CoAuthor “Strength ofShipsandOcean Structures”
Dr. Alaa Mansour is a Professor of Engineering in the Department of Mechanical Engineering of the University of
California at Berkeley. He was the Chairman of the Naval Architecture and Offshore Engineering Department at the
University of California, from 1985 to 1989, and Chaired the Executive Committee of the Ocean Engineering Graduate
Program at Berkeley from 2002 to 2005. He received his Bachelor of Science degree in Mechanical Engineering
from the University of Cairo and has M.S. and Ph.D. degrees in Naval Architecture and Offshore Engineering from
the University of California, Berkeley. Between 1968 and 1975 he was Assistant then Associate Professor in the
Department ofOcean Engineering at the Massachusetts Institute of Technology. He is a registered Professional
Engineer in the Commonwealth of Massachusetts.
Dr. Mansour has been the North and South American Chief Editor of the Journal of Marine Structures since its
inception and an editor of the Journal of Marine Science and Technology. In 2000–2003 he served as Chairman of the
International Ship and Offshore Structures Congress and has authored or co-authored over 100 publications.
In 2001, the Technical University of Denmark conferred upon Dr. Mansour its highest honor, the Honorary Doc-
torate Degree, “Doctor Technices Honoris Causa”, in recognition of his “significant contributions to development of
design criteria for shipsand offshore structures.” He is the recipient of the Davidson Medal presented by the Soci-
ety of Naval Architects and Marine Engineers for “Outstanding Scientific Accomplishment in Ship Research”, and is
currently a Fellow of the Society.
Biography of Donald Liu
CoAuthor “Strength ofShipsandOcean Structures”
Dr. Donald Liu retired in 2004 from the American Bureau of Shipping as Executive Vice President and Chief Technol-
ogy Officer after a 37-year career at ABS. He is a graduate of the U.S. Merchant Marine Academy, the Massachusetts
Institute of Technology where he obtained both BS and MS degrees in Naval Architecture and Marine Engineering,
and the University of Arizona where he received his Ph.D. in Mechanical Engineering. He has authored or coau-
thored more than forty papers, reports and book chapters dealing with Finite Element analysis, structural dynamics,
ultimate strength, hull loading, structural stability, structural optimization and probabilistic aspects of ship loading
and strength.
Dr. Liu has been an active participant in key national and international organizations that are concerned with ship
structures research, development and design. He served as the ABS representative on the interagency Ship Struc-
tures Committee, and as a member of the Standing Committees of the International Ship and Offshore Structures
congress (ISSC) and the conference on Practical Design ofShipsand Mobile Units (PRADS)
In 1994 Dr. Liu received the Sea Trade “Safety at Sea” award in recognition of his role in developing the ABS
SafeHull system. He is the recipient of the Rear Admiral Halert C. Shepheard Award in 1998 from the Chamber
of Shipping of America in recognition of his achievements in promoting merchant marine safety, and in 2002 was
awarded the United States Coast Guard (USCG) Meritorious Public Service Award in recognition of his contributions
to marine safety. In 2004 he was awarded the Society of Naval Architects and Marine Engineers David W. Taylor
Medal for notable achievement in naval architecture and in 2006 he received the Gibbs Brothers Medal, awarded
by the National Academy of Sciences for outstanding contributions in the field of naval architecture and marine
engineering. Dr. Liu is a Fellow of the Society of Naval Architects and Marine Engineers.
Nomenclature
A area, generally
AC acceptance criteria
A
f
total flange cross-sectional area
A
s
shear area
A
w
web cross-sectional area
B beam
b buoyancy
c crack length
C
b
block coefficient
CL centerline; a vertical plane through the
centerline
C
w
water plane coefficient of ship
D depth
T Draft
D diameter, generally
d distance, generally
DLA dynamic load approach
DLP dominant load parameter
DWT deadweight
E mean value
E Young’s modulus of elasticity
F force generally
FE finite element
FEA finite element analysis
FEM finite element method
F
H
horizontal shear forces
f
p
permissible bending stress
FRP fiber reinforced plastics
F
w
vertical wave shear force
g acceleration due to gravity
G shear modulus of elasticity, E/2(1 + υ)
H transfer function
H wave height
h head, generally
HAZ heat affected zone
HSC high-speed crafts
HSLA high strength low alloy
J torsional constant of a section
K load combination factor
k spring constant per unit length
L length, generally
L length of ship
L life in years
LBP, L
pp
length between perpendiculars
LCF load combination factor
LCG longitudinal position center of gravity
M moment, generally
m mass, generally
M margin
M
H
wave-induced horizontal bending
moment
m
n
spectral moment of order n
MPEL most probable extreme load
MPEV most probable extreme value
M
sw
stillwater bending moment
M
T
twisting moment
M
u
ultimate bending moment
M
w
vertical wave induced bending moment
N shear flow
NA neutral axis
NE non-encounter probability
p probability, in general
p pressure
p.d.f, PDF probability density function
p
f
probability of failure
q load per unit length
R auto-correlation function
R return period
r radius
RAO Response Amplitude Operator
s contour coordinate
SM section modulus
S
x
(ω) wave spectrum
S
xy
(ω) cross spectrum
S
y
(ω) response spectrum
T period, generally
t thickness, generally
t time, generally
T torsion moment
T
M
torsion moment amidships
T
M
modal period
T
m
twist moment
TMCP Thermo-Mechanical Controlled Process
V Total vertical shearing force across a
section
V velocity in general, speed of ship
w deflection
w weight
x distance from origin along X-axis
y distance from origin along Y-axis
z distance from origin along Z-axis
ε strains generally
∇ volume of displacement
α Skewness
α ship heading angle
β safety index
β width parameter
β wave heading angle
β kurtosis
δ non-linearity parameter
ε bandwidth parameter
standard normal cumulative
distribution function
St. Venant torsional constant
γ shear strain, generally
γ safety factor
η torsion coefficient
xii NOMENCLATURE
λ wave length
µ covariance
µ wave spreading angle
µ heading
ν Poisson’s ratio
twist angle
ρ mass density; mass per unit volume
ρ effectiveness
ρ correlation coefficient
ρ virtual aspect ratio
Abbreviations for References
AA Aluminum Association
ABS American Bureau of Shipping
ANSI American National Standards Institute
ASCE American Society of Civil Engineers
ASNE American Society of Naval Engineers
ASTM American Society for Testing and
Materials
BMT British Maritime Technology
BS British Standard
BV Bureau Veritas
CCS China Classification Society
CFA Composite Fabricators Association
CSA Canadian Standards Association
DNV Det Norske Veritas
DTNSRDC David Taylor Naval Ship Research and
Development Center
GL Germanisher Lloyd
IACS International Association of
Classification Societies
IMO International Maritime Organization
ISO International Organization for
Standardization
σ standard deviation
σ Stress, generally
ω angular velocity
ω circular frequency
ω warping function
ζ wave amplitude
σ
T
ultimate tensile strength
σ
Y
yield strength
χ curvature
ISSC International Ship and Offshore
Structures Congress
ITTC International Towing Tank Conference
JIS Japanese Industrial Standard
KR Korean Register
LR Lloyd’s Register
NF Normes Francaises
NK Nippon Kaiji Kyokai
NSMB CRS Netherlands Ship Model Basin
Cooperative Research Ships
NSWCCD Carderock Division of the Naval
Surface Warfare Center
RINA Registro Italiano Navale
RS Russian Register of Shipping
SAMPE Society for Advancement of Materials
Processing and Engineering
SNAME Society of Naval Architects and Marine
Engineers
SOLAS Safety of Life at Sea
SSC Ship Structure Committee
UNI Unificazione Nazionale Italiana
Preface
During the twenty years that have elapsed since publication of the previous edition of this book, there have been
remarkable advances in the art, science and practice of the design and construction ofshipsand other floating
structures. In that edition, the increasing use of high speed computers was recognized and computational methods
were incorporated or acknowledged in the individual chapters rather than being presented in a separate chapter.
Today, the electronic computer is one of the most important tools in any engineering environment and the laptop
computer has taken the place of the ubiquitous slide rule of an earlier generation of engineers.
Advanced concepts and methods that were only being developed or introduced then are a part of common engi-
neering practice today. These include finite element analysis, computational fluid dynamics, random process meth-
ods, numerical modeling of the hull form and components, with some or all of these merged into integrated design
and manufacturing systems. Collectively, these give the naval architect unprecedented power and flexibility to ex-
plore innovation in concept and design of marine systems. In order to fully utilize these tools, the modern naval
architect must possess a sound knowledge of mathematics and the other fundamental sciences that form a basic
part of a modern engineering education.
In 1997, planning for the new edition of Principles of Naval Architecture was initiated by the SNAME publications
manager who convened a meeting of a number of interested individuals including the editors of PNA and the new
edition of Ship Design and Construction. At this meeting it was agreed that PNA would present the basis for the
modern practice of naval architecture and the focus would be principles in preference to applications. The book
should contain appropriate reference material but it was not a handbook with extensive numerical tables and graphs.
Neither was it to be an elementary or advanced textbook although it was expected to be used as regular reading ma-
terial in advanced undergraduate and elementary graduate courses. It would contain the background and principles
necessary to understand and to use intelligently the modern analytical, numerical, experimental and computational
tools available to the naval architect and also the fundamentals needed for the development of new tools. In essence,
it would contain the material necessary to develop the understanding, insight, intuition, experience and judgment
needed for the successful practice of the profession. Following this initial meeting, a PNA Control Committee, con-
sisting of individuals having the expertise deemed necessary to oversee and guide the writing of the new edition
of PNA, was appointed. This committee, after participating in the selection of authors for the various chapters, has
continued to contribute by critically reviewing the various component parts as they are written.
In an effort of this magnitude, involving contributions from numerous widely separated authors, progress has
not been uniform and it became obvious before the halfway mark that some chapters would be completed before
others. In order to make the material available to the profession in a timely manner it was decided to publish each
major subdivision as a separate volume in the “Principles of Naval Architecture Series” rather than treating each as
a separate chapter of a single book.
Although the United States committed in 1975 to adopt SI units as the primary system of measurement the transi-
tion is not yet complete. In shipbuilding as well as other fields, we still find usage of three systems of units: English
or foot-pound-seconds, SI or meter-newton-seconds, and the meter-kilogram(force)-second system common in en-
gineering work on the European continent and most of the non-English speaking world prior to the adoption of the
SI system. In the present work, we have tried to adhere to SI units as the primary system but other units may be
found particularly in illustrations taken from other, older publications. The symbols and notation follow, in general,
the standards developed by the International Towing Tank Conference.
This new revised volume on StrengthofShipsandOceanStructures addresses several topics of ship strength in
greater depth than in the previous edition of PNA, bringing much of the material up to date and introducing some
new subjects. There is extensive coverage of the latest developments in dynamic sea load predictions, including
nonlinear load effects, slamming and impact plus new sections on the mechanics of collisions and grounding. The
incorporation of the various loadings in structural design and analysis is covered including long term extreme and
cumulative fatigue effects. There is a more extensive treatment ofstrength analysis using finite element methods
than was included in the previous edition. Ultimate strength evaluation of the hull girder and components is covered
and there is a section on structural safety assessment applying reliability concepts including fatigue effects.
Particular attention is given to problems encountered in shipsof special type and size that have been developed
in recent years, many of which, by reason of size, configuration or lack of a history of design experience, require
[...]... types of failure that can occur in ship structures are generally those that are characteristic ofstructures made of stiffened plate panels assembled through the use of welding to form monolithic STRENGTH OF SHIPS ANDOCEANSTRUCTURESstructures with great redundancy (i.e., having many alternative paths for lines of stress) It should be noted that structural failure might occur in different degrees of. .. structuresand a discussion of the practical aspects of the structural design ofships as they are influenced by the combined experience and analysis embodied in classification society rules is given in Chapters 17 and 18 of Lamb (2003) This work should be treated as a complement to this chapter To aid in understanding the nature of the behavior of ship structures, further details of some of their most... (referred to as JPDF in later STRENGTHOFSHIPSANDOCEANSTRUCTURES sections) of the wave elevation at two instants of time t1 and t2 Ensemble averages ofocean waves are defined as follows The expected value of a given function g(x) is defined as +∞ E[g(x)] = expected value of g(x) = g(x) f (x)dx −∞ If g(x) = x, then +∞ E[x] = xf (x)dx = mean or ensemble average (11) −∞ For ocean waves, the mean is usually... records ofocean waves Ocean waves are usually represented as a narrow band random process A random process is said to be a narrow band process if S(ω) has significant values only in a band or range of frequencies whose width is small compared with the magnitude of the center frequency of the band ωo This is to be distinguished from a wide band process, where S(ω) has significant values over a wide range of. .. studying a much broader range of sea and load conditions than would be possible in a model test program, and of STRENGTHOF SHIPS ANDOCEANSTRUCTURES doing so at considerably less cost Hence, the principal use for model testing is to provide verification for such computer techniques On the other hand, a number of early experiments were intended to shed light on the fundamental nature of the dynamic wave-induced... length and with the frequency of wave encounters In the foregoing discussion of force applied on a ship section, a procedure is described in which the total force is subdivided into several components, each of which STRENGTHOFSHIPSANDOCEANSTRUCTURES can be computed independently of the others Consequently, because of the assumed linearity underlying strip theory, it is possible to calculate shear and. .. ships of various types and sizes have been conducted by several ship classification societies and research organizations, and descriptions of such work may be found in ¨ Little and Lewis (1971), Boentgen (1976), Nordenstrom (1973), and Stambaugh and Wood (1981) These longterm, full-scale measurements are used to verify theoretical predictions, and some of measured data—for example, those by Little and. .. in classification society strength standards and modern rule developments are covered including Common Structural Rules for tankers and bulk carriers The concluding sections discuss materials other than steel, including composites and aluminum, and vessels of unusual geometry and performance such as multihulls, hydrofoils, and SWATH craft J RANDOLPH PAULLING Editor viii Table of Contents Page A Word... in Fig 7 As a result of symmetry about the longitudinal vertical plane of ship and waves, the motions and loads will have components only in this plane At any instant of time, the motions of the ship will consist of the timevarying motions of pitch, heave, and surge superimposed on a mean ward velocity, Uo One of the important assumptions of linear theory is that both the wave and ship motion amplitudes... treatment, and consequently the design of the structure continues to involve a judicious and imaginative blend of theory and experience This section will deal in detail with the loads acting on a ship’s hull, techniques for analyzing the response of its structure to these loads, and both current and evolving new methods of establishing criteria of acceptable structural design A detailed description of ship structures . Tagg Subdivision and Damaged Stability
Professor Alaa Mansour and Dr. Donald Liu Strength of Ships and Ocean Structures
Dr. Lars Larson and Dr. Hoyte Raven. buoyancy and weight distribu-
tions, the net load curve (3) is the difference between the
STRENGTH OF SHIPS AND OCEAN STRUCTURES 7
STRENGTH OF SHIPS
STILL