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Eisley
ANALYSIS OF STRUCTURES
Waas
ANALYSIS
An Introduction Including Numerical Methods
Joe G. Eisley and Anthony M. Waas
A
OF STRUCTURES
University of Michigan, USA
N
Analysis of Structures: An Introduction Including Numerical Methods offers an original way of A
introducing engineering students to the subject of stress and deformation analysis of solid objects, and
helps them become more familiar with how numerical methods such as the finite element method are L An Introduction Including Numerical Methods
used in industry. Y
Eisley and Waas secure for the reader a thorough understanding of the basic numerical skills and insight S
into interpreting the results these methods can generate.
I Joe G. Eisley and Anthony M. Waas
Throughout the text, they include analytical development alongside the computational equivalent, S
providing the student with the understanding that is necessary to interpret and use the solutions that are
obtained using software based on the finite element method. They then extend these methods to the
O
analysis of solid and structural components that are used in modern aerospace, mechanical and civil
engineering applications.
F
Analysis of Structures: An Introduction Including Numerical Methodsis accompanied by a website
(www.wiley.com/go/waas) housing exercises and examples that use modern software which generates
S
color contour plots of deformation and internal stress. It offers invaluable guidance and understanding to
senior level and graduate students studying courses in stress and deformation analysis as part of aerospace, T
mechanical and civil engineering degrees as well as to practicing engineers who want to re-train or
R
re-engineer their set of analysis tools for contemporary stress and deformation analysis of solids and structures.
U
(cid:129)Provides a fresh, practical perspective to the teaching of structural analysis using
C
numerical methods for obtaining answers to real engineering applications
(cid:129)Proposes a new way of introducing students to the subject of stress and deformation T
analysis of solid objects that are used in a wide variety of contemporary engineering
U
applications
(cid:129)Casts axial, torsional and bending deformations of thin walled objects in a framework that
R
is closely amenable to the methods by which modern stress analysis software operates.
E
S
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ANALYSIS OF
STRUCTURES
P1:TIX/XYZ P2:ABC
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ANALYSIS OF
STRUCTURES
AN INTRODUCTION INCLUDING
NUMERICAL METHODS
JoeG. Eisley
AnthonyM.Waas
CollegeofEngineering
UniversityofMichigan,USA
A John Wiley & Sons, Ltd., Publication
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LibraryofCongressCataloging-in-PublicationData
Eisley,JoeG.
Analysisofstructures:anintroductionincludingnumericalmethods/JoeG.Eisley,AnthonyM.Waas.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-97762-0(cloth)
1.Structuralanalysis(Engineering)–Mathematics. 2.Numericalanalysis. I.Waas,AnthonyM. II.Title.
TA646.W332011
624.1(cid:3)71–dc22
2011009723
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:9780470977620
E-PDFISBN:9781119993285
O-bookISBN:9781119993278
E-PubISBN:9781119993544
MobiISBN:9781119993551
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ToMarilyn,PaulandSusan
—Joe
ToDayamal, Dayani, SheharaandMichael
—Tony
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Contents
AbouttheAuthors xiii
Preface xv
1 ForcesandMoments 1
1.1 Introduction 1
1.2 Units 1
1.3 ForcesinMechanicsofMaterials 3
1.4 ConcentratedForces 4
1.5 MomentofaConcentratedForce 9
1.6 DistributedForces—ForceandMomentResultants 19
1.7 InternalForcesandStresses—StressResultants 27
1.8 RestraintForcesandRestraintForceResultants 32
1.9 SummaryandConclusions 33
2 StaticEquilibrium 35
2.1 Introduction 35
2.2 FreeBodyDiagrams 35
2.3 Equilibrium—ConcentratedForces 38
2.3.1 TwoForceMembersandPinJointedTrusses 38
2.3.2 SlenderRigidBars 44
2.3.3 PulleysandCables 49
2.3.4 Springs 52
2.4 Equilibrium—DistributedForces 55
2.5 EquilibriuminThreeDimensions 59
2.6 Equilibrium—InternalForcesandStresses 62
2.6.1 EquilibriumofInternalForcesinThreeDimensions 65
2.6.2 EquilibriuminTwoDimensions—PlaneStress 69
2.6.3 EquilibriuminOneDimension—UniaxialStress 70
2.7 SummaryandConclusions 70
3 Displacement,Strain,andMaterialProperties 71
3.1 Introduction 71
3.2 DisplacementandStrain 71
3.2.1 Displacement 72
3.2.2 Strain 72
3.3 Compatibility 76
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viii Contents
3.4 LinearMaterialProperties 77
3.4.1 Hooke’sLawinOneDimension—Tension 77
3.4.2 Poisson’sRatio 81
3.4.3 Hooke’sLawinOneDimension—ShearinIsotropicMaterials 82
3.4.4 Hooke’sLawinTwoDimensionsforIsotropicMaterials 83
3.4.5 GeneralizedHooke’sLawforIsotropicMaterials 84
3.5 SomeSimpleSolutionsforStress,Strain,andDisplacement 85
3.6 ThermalStrain 89
3.7 EngineeringMaterials 90
3.8 FiberReinforcedCompositeLaminates 90
3.8.1 Hooke’sLawinTwoDimensionsforaFRPLamina 91
3.8.2 PropertiesofUnidirectionalLamina 94
3.9 PlanfortheFollowingChapters 96
3.10 SummaryandConclusions 98
4 ClassicalAnalysisoftheAxiallyLoadedSlenderBar 99
4.1 Introduction 99
4.2 SolutionsfromtheTheoryofElasticity 99
4.3 DerivationandSolutionoftheGoverningEquations 109
4.4 TheStaticallyDeterminateCase 116
4.5 TheStaticallyIndeterminateCase 129
4.6 VariableCrossSections 136
4.7 ThermalStressandStraininanAxiallyLoadedBar 142
4.8 ShearingStressinanAxiallyLoadedBar 143
4.9 DesignofAxiallyLoadedBars 145
4.10 AnalysisandDesignofPinJointedTrusses 149
4.11 WorkandEnergy—Castigliano’sSecondTheorem 153
4.12 SummaryandConclusions 162
5 AGeneralMethodfortheAxiallyLoadedSlenderBar 165
5.1 Introduction 165
5.2 Nodes,Elements,ShapeFunctions,andtheElementStiffnessMatrix 165
5.3 TheAssembledGlobalEquationsandTheirSolution 169
5.4 AGeneralMethod—DistributedAppliedLoads 182
5.5 VariableCrossSections 196
5.6 AnalysisandDesignofPin-jointedTrusses 202
5.7 SummaryandConclusions 211
6 Torsion 213
6.1 Introduction 213
6.2 TorsionalDisplacement,Strain,andStress 213
6.3 DerivationandSolutionoftheGoverningEquations 216
6.4 SolutionsfromtheTheoryofElasticity 225
6.5 TorsionalStressinThinWalledCrossSections 229
6.6 WorkandEnergy—TorsionalStiffnessinaThinWalledTube 231
6.7 TorsionalStressandStiffnessinMulticellSections 239
6.8 TorsionalStressandDisplacementinThinWalledOpenSections 242
