Structural and stress analysis : theories, tutorials and examples

232 Pages·2008·2.229 MB·English

by  Jianqiao Ye

Structural and Stress Analysis
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Structural and Stress Analysis
Theories, tutorials and examples
Jianqiao Ye
Firstpublished2008
byTaylor&Francis
2ParkSquare,MiltonPark,Abingdon,OxonOX144RN
SimultaneouslypublishedintheUSAandCanada
byTaylor&Francis
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©2008JianqiaoYe
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LibraryofCongressCataloginginPublicationData
Ye,Jianqiao,1957-
Structuralandstressanalysis:theories,tutorialsandexamples/JianqiaoYe.
p.cm.
Includesbibliographicalreference sandindex.
ISBN978-0-415-36865-0(hardback:alk.paper)--
ISBN978-0-415-36879-7(paperback:alk.
paper)--ISBN978-0-203-02900-8(ebook)1.Structural
analysis(Engineering)I.Title.
TA645.Y432008
624.1’71--dc22
2007030738
ISBN 0-203-02900-3 Master e-book ISBN
ISBN10:0–415–36865–0(hbk)
ISBN10:0–415–36879–0(pbk)
ISBN10:0–203–02900–3(ebk)
ISBN13:978–0–415–36865–0(hbk)
ISBN13:978–0–415–36879–7(pbk)
ISBN13:978–0–203–02900–8(ebk)
To my wife Qin and my daughter Helen
with love and gratitude

Contents
Preface xi
Acknowledgements xiii
1 Introduction 1
1.1 Forcesandmoments 1
1.2 Typesofforceanddeformation 3
1.2.1 Force 3
1.2.2 Deformation 3
1.3 Equilibriumsystem 3
1.3.1 The method of section 3
1.3.2 The method of joint 4
1.4 Stresses 5
1.4.1 Normal stress 5
1.4.2 Shear stress 6
1.5 Strains 7
1.6 Strain–stressrelation 7
1.7 GeneralizedHooke’slaw 8
1.8 Strength,stiffnessandfailure 10
1.9 Keypointsreview 11
1.10 Basicapproachforstructuralanalysis 12
1.11 Conceptualquestions 13
1.12 Minitest 14
2 Axial tension and compression 16
2.1 Signconvention 16
2.2 Normal(direct)stress 16
2.3 Stressesonanarbitrarilyinclinedplane 17
2.4 Deformationofaxiallyloadedmembers 18
2.4.1 Members of uniform sections 18
2.4.2 Members with step changes 18
viii Contents
2.5 Staticallyindeterminateaxialdeformation 19
2.6 Elasticstrainenergyofanaxially
loadedmember 20
2.6.1 Strain energy U in an axially loaded member 20
2.6.2 Strain energy density, U 20
0
2.7 Saint-Venant’sprincipleandstressconcentration 20
2.8 Stressescausedbytemperature 21
2.9 Keypointsreview 22
2.10 Recommendedprocedureofsolution 23
2.11 Examples 23
2.12 Conceptualquestions 31
2.13 Minitest 33
3 Torsion 36
3.1 Signconvention 36
3.2 Shearstress 37
3.3 Angleoftwist 38
3.4 Torsionofrotatingshafts 38
3.5 Keypointsreview 39
3.6 Recommendedprocedureofsolution 39
3.7 Examples 40
3.8 Conceptualquestions 49
3.9 Minitest 51
4 Shear and bending moment 53
4.1 Definitionofbeam 54
4.2 Shearforceandbendingmoment 54
4.3 Beamsupports 54
4.4 Signconvention 54
4.4.1 Definition of positive shear 54
4.4.2 Definition of positive bending moment 55
4.5 Relationshipsbetwe enbendingmoment,shearforceand
appliedload 56
4.6 Shearforceandbendingmomentdiagrams 57
4.7 Keypointsreview 57
4.8 Recommendedprocedureofsolution 58
4.9 Examples 58
4.10 Conceptualquestions 75
4.11 Minitest 77
5 Bending stresses in symmetric beams 80
5.1 Normalstressesinbeams 81
5.2 Calculationofsecondmomentofinertia 82
5.3 Shearstressesinbeams 84
5.4 Keypointsreview 85
5.5 Recommendedprocedureofsolution 86
5.6 Examples 87
Contents ix
5.7 Conceptualquestions 102
5.8 Minitest 105
6 Deflection of beams under bending 107
6.1 Signconvention 108
6.2 Equationofbeamdeflection 108
6.2.1 The integration method 108
6.2.2 The superposition method 109
6.2.3 Macaulay’s method (step function method) 110
6.3 Keypointsreview 112
6.4 Examples 113
6.4.1 Examples of the integration method 113
6.4.2 Examples of the superposition method 118
6.4.3 Examples of Macaulay’s method 123
6.5 Conceptualquestions 127
6.6 Minitest 128
7 Complex stresses 130
7.1 Two-dimensionalstateofstress 131
7.1.1 Sign convention of stresses 132
7.1.2 Analytical method 133
7.1.3 Graphic method 137
7.2 Keypointsreview 138
7.2.1 Complex stress system 138
7.2.2 Mohr’s circle 139
7.3 Examples 139
7.4 Conceptualquestions 148
7.5 Minitest 149
8 Complex strains and strain gauges 151
8.1 Strainanalysis 154
8.2 Strainmeasurementbystraingauges 155
8.3 Keypointsreview 156
8.3.1 Complex strain system 156
8.3.2 Strain measurement by strain gauges 157
8.4 Examples 157
8.5 Conceptualquestions 164
8.6 Minitest 164
9 Theories of elastic failure 166
9.1 Maximumprincipalstresscriterion 167
9.2 Maximumshearstresscriterion(Trescatheory) 169
9.3 Distortionalenergydensity(vonMisestheory)criterion 169
9.4 SpecialformsofTrescaandvonMisescriterions 170
9.5 Keypointsreview 171
9.6 Recommendedprocedureofsolution 171