Structural Stability of Steel: Concepts and Applications for Structural Engineers

381 Pages·2008·10.17 MB·English

by  Theodore V. Galambos

STRUCTURAL STABILITY OF STEEL:
CONCEPTS AND APPLICATIONS
FOR STRUCTURAL ENGINEERS
Structural Stability of Steel: Concepts and Applications for Structural Engineers
Theodore V. Galambos Andrea E. Surovek Copyright © 2008 John Wiley & Sons, Inc.
STRUCTURAL STABILITY OF
STEEL: CONCEPTS AND
APPLICATIONS FOR
STRUCTURAL ENGINEERS
THEODOREV.GALAMBOS
ANDREAE.SUROVEK
JOHNWILEY& SONS,INC.
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LibraryofCongressCataloging-in-PublicationData:
Galambos,T.V.(TheodoreV.)
Structuralstabilityofsteel:conceptsandapplicationsforstructuralengineers/Theodore
Galambos,AndreaSurovek.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-03778-2 (cloth)
1. Building,Ironandsteel–Congresses.2. Structuralstability–Congresses. I. Surovek,Andrea.
II. Title.
TA684.G262005
624.10821–dc22
2007035514
ISBN:978-0-470-03778-2
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
CONTENTS
PREFACE ix
CHAPTER1 FUNDAMENTALSOFSTABILITYTHEORY 1
1.1 Introduction 1
1.2 BasicsofStabilityBehavior:TheSpring-BarSystem 3
1.3 FundamentalsofPost-BucklingBehavior 7
1.4 Snap-ThroughBuckling 18
1.5 Multi-Degree-of-FreedomSystems 20
1.6 Summary 23
Problems 24
CHAPTER2 ELASTICBUCKLINGOFPLANARCOLUMNS 28
2.1 Introduction 28
2.2 Large-DeflectionSolutionofanElasticColumn 29
2.3 DifferentialEquationofPlanarFlexure 32
2.4 TheBasicCase:Pin-EndedColumn 36
2.5 FiveFundamentalCases 39
2.6 TheEffectofImperfections 43
2.7 StabilityofaRigidFrame 52
2.8 End-RestrainedColumns 55
2.9 RestrainedColumnExamples 62
2.10 ContinuouslyRestrainedColumns 74
2.11 Summary 80
Problems 80
Appendix 85
CHAPTER3 INELASTICCOLUMNBUCKLING 87
3.1 TangentandReducedModulusConcepts 87
3.2 Shanley’sContribution 93
3.3 ExampleIllustratingtheTangentModulusandtheReduced
ModulusConcepts 98
3.4 BucklingStrengthofSteelColumns 101
3.5 IllustrationoftheEffectofResidualStressesontheBuckling
StrengthofSteelColumns 103
v
vi CONTENTS
3.6 EffectofInitialOut-of-StraightnessandLoadEccentricity 108
3.7 DesignFormulasForMetalColumns 123
3.8 Summary 130
Problems 131
CHAPTER4 BEAM-COLUMNS 134
4.1 Introduction 134
4.2 GeneralDiscussionoftheBehaviorofBeam-Columns 135
4.3 ElasticIn-PlaneBehaviorofBeam-Columns 138
4.4 ElasticLimitInteractionRelationships 147
4.5 ExampleProblemsofBeam-ColumnStrength 149
4.6 SystematicMethodsofAnalysis:FlexibilityMethod 159
4.7 SystematicMethodsofAnalysis:TheStiffnessMethod 170
4.8 InelasticStrengthofBeam-Columns 186
4.9 DesignofBeam-Columns 197
Problems 199
CHAPTER5 FRAMESTABILITY 203
5.1 Introduction 203
5.2 Two-BayFrameExamples 206
5.3 Summary 230
5.4 SelectedReferencesonFrameswithPartiallyRestrainedJoints 231
Problems 232
CHAPTER6 LATERAL-TORSIONALBUCKLING 236
6.1 Introduction 236
6.2 BasicCase:BeamsSubjectedtoUniformMoment 237
6.3 TheEffectofBoundaryConditions 246
6.4 TheEffectofLoadingConditions 249
6.5 Lateral-TorsionalBucklingofSingly-SymmetricCross-Sections 259
6.6 Beam-ColumnsandColumns 270
6.7 InelasticLateral-TorsionalBuckling 278
6.8 Summary 288
Problems 289
CONTENTS vii
CHAPTER7 BRACING 290
7.1 Introduction 290
7.2 DiscreteBracing 292
7.3 RelativeBracing 297
7.4 Lean-onBracing 299
7.5 EffectsofImperfections 300
7.6 ColumnBracingProvisions 302
7.7 BeamBracing 306
7.8 AISCDesignProvisionsforBeamBracing 308
7.9 Summary 314
SuggestedReading 315
Problems 315
CHAPTER8 SPECIFICATION-BASEDAPPLICATIONS
OFSTABILITYINSTEELDESIGN 318
8.1 Introduction 318
8.2 DevelopmentoftheBeam-ColumnInteractionEquations 319
8.3 AssessmentofColumnStrength 323
8.4 AssessmentofBeamStrength 324
8.5 Specification-BasedApproachesforStabilityAssessment 330
8.6 EffectiveLengthFactors,K-factors 344
8.7 DesignAssessmentbyTwoApproaches 354
8.8 FrameDesignRequirementsinCanadaandEurope 359
8.9 Summary 361
Problems 361
REFERENCES 364
INDEX 369
PREFACE
In order to truly understand the behavior and design of metal structures, an
engineer needs to have a fundamental understanding of structural stability.
More so than structures designed using other construction materials, steel
structures are governed to a great extent on stability limit states. All major
international design specifications include provisions based on stability
theory. The purpose of this book is to provide students and practicing engi-
neerswith boththetheory governing stabilityof steel structures anda prac-
tical look at how that theory translates into design methodologies currently
implementedinsteeldesignspecifications.
Thetopicspresentedinthetextpertaintovariousaspectsofelasticbuck-
lingandinelasticinstability.Anunderstandingofstabilitylimitsisveryim-
portant in the design of structures: Catastrophic failures can, and tragically
have, resulted from violating fundamental principles of stability in design.
Maintaining stability is particularly important during the erection phase of
construction,whenthestructuralskeletonisexposedpriortotheinstallation
ofthefinalstabilizingfeatures,suchasslabs,wallsand/orcladding.
Thebookcontainsadetailedtreatmentoftheelasticandinelasticstabil-
ity analysis of columns, beams, beam-columns, and frames. In addition, it
provides numerous worked examples. Practice problems are included at
the end of each chapter. The first six chapters of this book are based on
lecture notes of the first author, used in his teaching of structural engineer-
ing graduate courses since 1960, first at Lehigh University in Bethlehem,
Pennsylvania, (1960–1965), then at Washington University in St. Louis,
Missouri, (1966–1981), and finally at the University of Minnesota in Min-
neapolis, Minnesota.
The genesis of the course material was in lectures at Lehigh University
given by Professors Bruce Johnston, Russell Johnson, and Bruno Thurli-
mann in the 1950s. The material in the last two chapters is concerned with
the application of stability theory in the practical design of steel structures,
with special emphasis on examples based on the 2005 Specification for
Structural Steel Buildings of the American Institute of Steel Construction
(AISC). Chapter 7 is based heavily on the work performed by Professors
JoeYuraandToddHelwig ofthe University of Texasin developingAppen-
dix6ofthe2005AISCSpecification.AportionofthematerialinChapter8
isbasedontheworkofthesecondauthorandProfessorDonWhiteofGeor-
gia Tech, as well as verification studies and design examples developed by
membersofAISCTC10,chairedbyDr.ShankarNair.
The material in the book is suitable for structural engineering students
at the graduate level. It is also useful for design engineers who wish to
ix
x PREFACE
understandthebackgroundofthestabilitydesigncriteriainstructuralspeci-
fications, or for those who may have a need to investigate special stability
problems. Since the fundamental mechanics governing the behavior of
beams, columns, beam-columns, and frames is discussed in the book, it is
also useful for an international structural engineering constituency. A back-
ground in both structural analysis approaches and differential equations is
essentialinunderstandingthederivationsincludedinthefirstsixchapters.
Chapter1is anintroductionto theprinciplesof stabilitytheory.Thevar-
ious aspects of behavior at the limits of instability are defined on hand of
simple spring-bar examples. Chapter 2 deals with the stability of axially
loaded planar elastic systems. Individual columns, simple frames, and sub-
assemblies of members are analyzed. The background for the effective
length concept of designing metal structures is also presented. Chapter 3
expands the analysis to the nonlinear material behavior. Tangent modulus,
reduced modulus, and maximum strength theories are introduced. Deriva-
tions are presented that lead to an understanding of modern column design
formulas in structural codes. The subject of Chapter 4 is the elastic and in-
elastic stability limit of planar beam-columns. Various aspects of the inter-
action between axial force and bending moment are presented, and the
interaction formulas in design specifications are evaluated. Chapter 5 illus-
trates many features of elastic and inelastic instability of planar frames us-
ingasexampleaone-storytwo-baystructure.
In Chapter 6 the out-of-plane lateral-torsional buckling of beams, col-
umns, and beam-columns is presented. Since stability of the structure is vi-
tally dependent on the strength and stiffness of the bracing systems that are
provided during erection and in the final stage of construction, Chapter 7 is
devotedentirelytothissubject.Moderndesignstandardsforstructuralsteel
design require an analysis procedure that provides stability through the di-
rectinclusionofthedestabilizingeffectsofstructuralimperfections,suchas
residual stresses and unavoidable out-of-plumb geometry. The topic of
Chapter 8 is the analysis and design of steel frames according to the 2005
SpecificationoftheAISC.
CHAPTER ONE
FUNDAMENTALS OF STABILITY THEORY
1.1 INTRODUCTION
It is not necessary to be a structural engineer to have a sense of what it
means for a structure to be stable. Most of us have an inherent understand-
ing of the definition of instability—that a small change in load will cause a
large change in displacement. If this change in displacement is large
enough,orisinacriticalmemberofastructure,alocalormemberinstabil-
ity may cause collapse of the entire structure. An understanding of stability
theory, or the mechanics of why structures or structural members become
unstable, is a particular subset of engineering mechanics of importance to
engineerswhosejobistodesignsafestructures.
The focus of this text is not to provide in-depth coverage of all stability
theory, but rather to demonstrate how knowledge of structural stability
theory assists the engineer in the design of safe steel structures. Structural
engineers are tasked by society to design and construct buildings, bridges,
and a multitude of other structures. These structures provide a load-bearing
skeletonthatwillsustaintheabilityoftheconstructedartifacttoperformits
intended functions, such as providing shelter or allowing vehicles to travel
over obstacles. The structure of the facility is needed to maintain its shape
andtokeepthefacilityfromfallingdownundertheforcesofnatureorthose
madebyhumans.Theseimportantcharacteristicsofthestructureareknown
asstiffnessandstrength.
Structural Stability of Steel: Concepts and Applications for Structural Engineers 1
Theodore V. Galambos Andrea E. Surovek Copyright © 2008 John Wiley & Sons, Inc.
2 FUNDAMENTALSOFSTABILITYTHEORY
This book is concerned with one aspect of the strength of structures,
namely their stability. More precisely, it will examine how and under what
loading condition the structure will pass from a stable state to an unstable
one. The reason for this interest is that the structural engineer, knowing the
circumstances of the limit of stability, can then proportion a structural
scheme that will stay well clear of the zone of danger and will have an ad-
equate margin of safety against collapse due to instability. In a well-
designedstructure,theuseroroccupantwillneverhavetoeventhinkofthe
structure’sexistence.Safetyshouldalwaysbeagiventothepublic.
Absolute safety, of course, is not an achievable goal, as is well known to
structural engineers. The recent tragedy of the World Trade Center collapse
provides understanding of how a design may be safe under any expected
circumstances, but may become unstable under extreme and unforeseeable
circumstances.Thereisalwaysasmallchanceoffailureofthestructure.
The term failure has many shades of meaning. Failure can be as obvious
andcatastrophicasatotalcollapse,ormoresubtle,suchasabeamthatsuf-
fers excessive deflection, causing floors to crack and doors to not open or
close. In the context of this book, failure is defined as the behavior of the
structure when it crosses a limit state—that is, when it is at the limit of its
structural usefulness. There are many such limit states the structural design
engineer has to consider, such as excessive deflection, large rotations at
joints,crackingofmetalorconcrete,corrosion,orexcessivevibrationunder
dynamicloads,tonameafew.Theonelimitstatethatwewillconsiderhere
is the limit state where the structure passes from a stable to an unstable
condition.
Instabilityfailuresareoftencatastrophicandoccurmostoftenduringerec-
tion. For example, duringthe late1960s and early 1970s,a numberof major
steel box-girderbridges collapsed,causing many deathsamong erectionper-
sonnel.ThetwophotographsinFigure1.1weretakenbyauthorGalambosin
August 1970 on the site two months before the collapse of a portion of the
Yarra River Crossing in Melbourne, Australia. The left picture in Figure 1.1
shows two halves of the multi-cell box girder before they were jacked into
place on top of the piers (see right photo), where they were connected with
high-strength bolts. One of the 367.5 ft. spans collapsed while the iron-
workers attempted to smooth the local buckles that had formed on the top
surfaceofthebox.Thirty-fiveworkersandengineersperishedinthedisaster.
There were a number of causes for the collapse, including inexperience
andcarelessness,buttheRoyalCommission(1971),initsreportpinpointed
the main problem: ‘‘We find that [the design organization] made assump-
tionsaboutthebehaviorof boxgirderswhich extendedbeyondtherangeof
engineering knowledge.’’ The Royal Commission concluded ‘‘ . . . that the
design firm ‘‘failed altogether to give proper and careful regard to the