Fundamentals of Structural Stability
2006 Elsevier Inc.
Author(s): George J. Simitses, Professor Emeritus, and Dewey H. Hodges, Professor
ISBN: 978-0-7506-7875-9
Table of Contents
Preface, Pages xi-xii
1 - Introduction and fundamentals, Pages 3-18
2 - Mechanical stability models, Pages 19-46
3 - Elastic buckling of columns, Pages 47-101
4 - Buckling of frames, Pages 103-144
5 - The energy criterion and energy-based methods, Pages 145-171
6 - Columns on elastic foundations, Pages 173-183
7 - Buckling of rings and arches, Pages 185-234
8 - Buckling of shafts, Pages 235-249
9 - Lateral-torsional buckling of deep beams, Pages 251-277
10 - Instabilities associated with rotating beams, Pages 279-295
11 - Nonconservative systems, Pages 297-328
12 - Dynamic stability, Pages 329-363
Appendix
Work- and Energy Related principles and theorems, Pages 367-381
Author index, Pages 383-385
Subject index, Pages 387-389
PREFACE
Knowledge
of
structural stability theory
is
of
paramount
importance
to
the prac-
ticing structural engineer.
In
тапу
instances, buckling
is
the primary consideration
in the design
of
various structural configurations. Because
of
this, formal courses in
this important branch
of
mechanics are available to students in Aerospace Engin-
eering, Civil Engineering, Engineering Science
and
Mechanics,
and
Mechanical
Engineering
at
тапу
institutions
of
higher learning. This
book
is
intended to serve
as
а
text in such courses. The emphasis
of
the
book
is
оп
the fundamental concepts
and
оп
the methodology developed through the years to solve structural stability
problems.
The material contained in this text is ideally suited for
а
two-semester Master's level
course, although with judicious deletion
of
topics, the text
тау
Ье
adopted for
а
one-
semester course.
The first chapter introduces the basic concepts
of
elastic stability
and
the approaches
used in solving stability problems.
It
also discusses the different buckling phenom-
ena that have been observed in nature.
In
Chapter
2,
the basic concepts
and
methodology are applied
to
some simple mechanical models with finite degrees
of
freedom. This is done
to
help the student understand the fundamentals without
getting involved with lengthy and complicated mathematical operations, which is
usually the case when dealing with the continuum (infinitely
тапу
degrees
of
freedom). In Chapter
3,
а
complete treatment
of
the elastic stability
of
columns
is
presented, including effects
of
elastic restraints. New to this edition are treatments
of
the elastica theory
of
beams
and
of
the buckling
of
thin-walled beam-columns. This
new material facilitates the solutions
of
several problems in later chapters. Some
simple frame problems are discussed in Chapter
4.
Moreover,
а
nonlinear analysis
of
frames
is
presented, which clearly shows
that
in some cases, buckling occurs through
limit-point instability. This chapter
is
of
special importance
to
the Civil Engineering
student. Since energy-based methods have been successfully used in structural
mechanics,
Chapter
5 presents
а
comprehensive treatment
of
the energy criterion
for stability
and
contains
тапу
energy-related methods. The study
of
this chapter
requires some knowledge
of
work-
and
energy-related principles
and
theorems.
ХI
Х"
PREFACE
These topics
аге
presented in the Appendix
[ог
the benefit
of
the student who never
had
а
[огтаl
course in this
агеа.
Columns
оп
elastic foundations
аге
discussed in
Chapter
б.
Chapter 7 presents
а
comprehensive treatment
of
the buck1ing
of
thin
rings and high and low arches. In this chapter,
а
complete analysis
is
given
[ог
а
shallow, pinned sinusoidal arch
оп
аn
elastic foundation subject to
а
sinusoidal
transverse loading. This
is
аn
interesting model
[ог
stabi1ity studies because,
depending
ироп
the values
of
the different parameters involved, it exhibits
аН
types
of
buckling
that
have
Ьееn
observed in different structural systems: top-of-
the-knee buckling, stable bifurcation (Euler-type), and unstable bifurcation. The use
of
elastica theory augments the
тоге
traditional treatment illustrating how
а
buck-
ling analysis
сап
Ье
сапiеd
out
with very
few
restrictive assumptions. Chapter 8
treats the buckling
of
shafts, making use
of
both the elastica theory and energy
methods. This chapter
is
important
[ог
Mechanical
and
Aerospace Engineering
students, showing
that
torques which differ
Ьу
infinitesimal amounts
сап
have
buckling loads that radically differ,
and
that compressive forces and spin
сап
affect
stability as well. Chapter 9
is
devoted to lateral-torsional buckling
of
deep beams,
emphasizing the
го!е
of
certain secondary effects such as the Vlasov
рЬеnотепоп,
initial curvature, the offset
of
the load, the way torque
is
applied, etc. In Chapter
10
we
examine various instabilities
of
rotating rods and beams. Chapter
11
is
devoted
to the stability
of
nonconservative systems undergoing follower forces.
Ап
extended
version
of
the elastica theory
is
shown to facilitate analysis
of
such systems, which
must
Ье
ana!yzed according to kinetic theory. Chapter
12
classifies the various
"dynamic instability"
рЬепотепа
Ьу
taking into consideration the nature
of
the
cause, the character
of
the response and the history
of
the problem. Moreover, the
various concepts and methodo!ogies, as developed and used
Ьу
different investiga-
tors,
аге
[иПу
described. Finally, the concepts and criteria
[ог
dynamic stability
аге
demonstrated through simp!e mechanica! models.
ТЬе
emphasis
Ьеге
is
оп
suddenly
applied loads
of
constant magnitude and infinite duration
ог
extremely small dur-
ation (idea! pu!se).
The authors
аге
indebted to the late Profs. J. N. Goodier and N. J.
Hoff
and to
Prof. George
Нептапп
[ог
introducing
тапу
topics and
[ог
va!uable suggestions.
Special thanks
аге
due to Professor
М.
Е.
Raville
[ог
providing tangible and
intangible support,
[ог
reading large sections
of
the manuscript
[ог
earlier editions,
and
[ог
making
тапу
сопесtiопs.
Numerous discussions with Profs.
W. W.
King,
О.
М.
Rentzepis,
С.
У.
Smith Jr., David
А.
Peters,
М.
Stallybrass,
А.
N.
Kounadis and
Izhak Sheinman
аге
gratefully acknowledged. Thanks
аге
also due to several
[огтег
students
ofthe
first author:
С.
М.
B!ackmon,
У.
Ungbhakom,
J.
Giri,
А.
S.
Vlahinos,
О.
Shaw and
J.
О.
Simitses; and
of
the second author:
А.
R. Ati!gan, R. R.
B!ess,
and
У.
У.
Volovoi.
George J. Simitses
Dewey
Н.
Hodges
Georgia Institute
of
Techno!ogy
1
INTRODUCTION
AND
FUNDAMENTALS
1.1
маТIVАТЮN
Мапу
problems
аге
associated with the design
of
modern structural systems.
Economic factors, availability
and
properties
of
materials, interaction between the
external loads (e.g. aerodynamic)
and
the response
of
the structure, dynamic
and
temperature effects, performance, cost, and ease
of
maintenance
of
the system
аге
аll
problems which
аге
closely associated with the synthesis
of
these large
and
compli-
cated structures. Synthesis
is
the branch
of
engineering which deals with the design
of
а
system
[ог
а
given mission. Synthesis requires the most efficient
таппег
of
design-
ing
а
system (i.e., most economical, most reliable, lightest, best,
and
most easily
maintained system), and this leads to
optimization.
Ап
important
part
of
system
optimization is structural optimization, which
is
based
оп
the assumption that
certain parameters affecting the system optimization
аге
given (i.e.,
оуегаll
size
and
shape, performance, nonstructural weight, etc.).
It
сап
only
Ье
achieved through
good theoretical analyses supported
Ьу
well-planned and well-executed experimental
investigations.
Structural analysis
is
that branch
of
structural mechanics which associates the
behavior
of
а
structure
ог
structural elements with the action
of
external causes. Two
important questions
аге
usually asked in analyzing
а
structure:
(l)
What
is the
response
of
the structure when subjected to external causes (loads and temperature
changes)?
In other words, if the external causes
аге
known,
сап
we
find the deform-
ation patterns
and
the internal load distribution?
(2)
What
is
the character
of
the
response?
Неге
we
аге
interested in knowing
if
the equilibrium
is
stable
ог
if the
motion
is
limited (in the case
of
dynamic causes).
For
example, if
а
load is period-
ically applied, will the structure oscillate within certain bounds
ог
will it tend to
тоуе
without bounds?
If
the dynamic effects
аге
negligibly small, in which case the loads
аге
said to
Ье
applied quasistatically, then the study falls in the domain
of
structural statics.
Оп
the
other hand,
if
the dynamic effects
аге
not
negligible,
we
аге
dealing with structural
dynamics.
3
