كتاب Roark’s Formulas for Stress and Strain 8th Edition

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Roark’s Formulas for Stress and Strain 8th Edition
Warren C. Young
Richard G. Budynas
Ali M. Sadegh

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Contents
Preface to the Eighth Edition ix
Preface to the First Edition xiii
List of Tables xv
1 Introduction 1
1.1 Terminology 1
1.2 State Properties, Units, and Conversions 1
1.3 Contents . 13
1.4 References 14
2 Stress and Strain: Important Relationships 15
2.1 Stress 15
2.2 Strain and the Stress–Strain Relations 19
2.3 Stress Transformations . 22
2.4 Strain Transformations . 35
2.5 Mohr’s Circle . 35
2.6 Tables 39
2.7 References 43
3 The Behavior of Bodies under Stress 45
3.1 Methods of Loading . 45
3.2 Elasticity; Proportionality of Stress and Strain . 46
3.3 Factors Affecting Elastic Properties 47
3.4 Load Deformation Relation for a Body . 48
3.5 Plasticity . 48
3.6 Creep and Rupture under Long-Time Loading 48
3.7 Criteria of Elastic Failure and of Rupture . 50
3.8 Fatigue . 54
3.9 Brittle Fracture 58
3.10 Stress Concentration . 59
3.11 Effect of Form and Scale on Strength; Rupture Factor . 60
3.12 Prestressing . 62
3.13 Elastic Stability 63
3.14 Tables: Mechanical Properties of Materials 64
3.15 References 79
4 Principles and Analytical Methods 83
4.1 Equations of Motion and of Equilibrium 83
4.2 Principle of Superposition 83
4.3 Principle of Reciprocal De?ections . 84
4.4 Method of Consistent Deformations (Strain Compatibility) . 84
4.5 Energy Methods . 84
iiiiv C o n t e n t s
4.6 Castigliano’s Theorem . 85
4.7 Dimensional Analysis 90
4.8 Remarks on the Use of Formulas 91
4.9 References 93
5 Numerical Methods 95
5.1 The Finite Difference Method . 95
5.2 The Finite Element Method . 96
5.3 The Boundary Element Method . 101
5.4 Zeroes of Polynomials . 107
5.5 Solution of Differential Equations . 108
5.6 Numerical Integration . 108
5.7 References 110
5.8 Additional Uncited References in Finite Elements 110
6 Experimental Methods 113
6.1 Measurement Techniques . 113
6.2 Electrical Resistance Strain Gages 118
6.3 Detection of Plastic Yielding 128
6.4 Analogies 129
6.5 Wheatstone Bridge 129
6.6 Tables 131
6.7 References 138
7 Tension, Compression, Shear, and Combined Stress 141
7.1 Bar under Axial Tension (or Compression); Common Case 141
7.2 Bar under Tension (or Compression); Special Cases 143
7.3 Composite Members . 145
7.4 Trusses . 146
7.5 Body under Pure Shear Stress . 149
7.6 Cases of Direct Shear Loading . 150
7.7 Combined Stress 151
8 Beams; Flexure of Straight Bars 155
8.1 Straight Beams (Common Case) Elastically Stressed . 155
8.2 Composite Beams and Bimetallic Strips 165
8.3 Three-Moment Equation . 168
8.4 Rigid Frames . 169
8.5 Beams on Elastic Foundations . 174
8.6 Deformation Due to the Elasticity of Fixed Supports . 178
8.7 Beams under Simultaneous Axial and Transverse Loading . 179
8.8 Beams of Variable Section . 183
8.9 Slotted Beams . 189
8.10 Beams of Relatively Great Depth 189
8.11 Beams of Relatively Great Width 193
8.12 Beams with Wide Flanges; Shear Lag . 196
8.13 Beams with Very Thin Webs 198
8.14 Beams Not Loaded in Plane of Symmetry; Flexural Center . 199C o n t e n t s v
8.15 Straight Uniform Beams (Common Case);
Ultimate Strength 200
8.16 Plastic, or Ultimate Strength, Design . 204
8.17 Tables 208
8.18 References 292
9 Curved Beams 295
9.1 Bending in the Plane of the Curve . 295
9.2 De?ection of Curved Beams 302
9.3 Circular Rings and Arches 310
9.4 Elliptical Rings 319
9.5 Curved Beams Loaded Normal to
Plane of Curvature 320
9.6 Tables 326
9.7 References 399
10 Torsion 401
10.1 Straight Bars of Uniform Circular Section under
Pure Torsion 401
10.2 Bars of Noncircular Uniform Section under
Pure Torsion 402
10.3 Effect of End Constraint 407
10.4 Effect of Longitudinal Stresses 413
10.5 Ultimate Strength of Bars in Torsion . 415
10.6 Torsion of Curved Bars; Helical Springs 415
10.7 Tables 418
10.8 References 443
11 Flat Plates 445
11.1 Common Case 445
11.2 Bending of Uniform-Thickness Plates with
Circular Boundaries 446
11.3 Circular-Plate De?ection Due to Shear 450
11.4 Bimetallic Plates . 451
11.5 Nonuniform Loading of Circular Plates . 455
11.6 Circular Plates on Elastic Foundations 455
11.7 Circular Plates of Variable Thickness . 457
11.8 Disk Springs 458
11.9 Narrow Ring under Distributed Torque
about Its Axis . 459
11.10 Bending of Uniform-Thickness Plates with
Straight Boundaries 461
11.11 Effect of Large De?ection; Diaphragm Stresses 462
11.12 Plastic Analysis of Plates . 466
11.13 Ultimate Strength 466
11.14 Tables 469
11.15 References 544vi C o n t e n t s
12 Columns and Other Compression Members 549
12.1 Columns; Common Case . 549
12.2 Local Buckling 552
12.3 Strength of Latticed Columns . 558
12.4 Eccentric Loading; Initial Curvature . 559
12.5 Columns under Combined Compression and Bending . 561
12.6 Thin Plates with Stiffeners 563
12.7 Short Prisms under Eccentric Loading 565
12.8 Table . 569
12.9 References 574
13 Shells of Revolution; Pressure Vessels; Pipes 575
13.1 Circumstances and General State of Stress 575
13.2 Thin Shells of Revolution under Distributed Loadings
Producing Membrane Stresses Only 575
13.3 Thin Shells of Revolution under Concentrated or
Discontinuous Loadings Producing Bending and
Membrane Stresses 578
13.4 Thin Multielement Shells of Revolution 591
13.5 Thin Shells of Revolution under External Pressure . 602
13.6 Thick Shells of Revolution 604
13.7 Pipe on Supports at Intervals 606
13.8 Tables 608
13.9 References 699
14 Bodies under Direct Bearing and Shear Stress 703
14.1 Stress Due to Pressure between Elastic Bodies . 703
14.2 Rivets and Riveted Joints . 708
14.3 Miscellaneous Cases . 710
14.4 Table . 714
14.5 References 719
15 Elastic Stability 723
15.1 General Considerations 723
15.2 Buckling of Bars . 724
15.3 Buckling of Flat and Curved Plates 726
15.4 Buckling of Shells . 727
15.5 Tables 730
15.6 References 754
16 Dynamic and Temperature Stresses 759
16.1 Dynamic Loadings; General Conditions 759
16.2 Body in a Known State of Motion 759
16.3 Impact and Sudden Loading 767
16.4 Impact and Sudden Loading; Approximate Formulas 769
16.5 Remarks on Stress Due to Impact 771
16.6 Vibration . 771
16.7 Temperature Stresses . 777C o n t e n t s vii
16.8 Tables 782
16.9 References 798
17 Stress Concentration 801
17.1 Static Stress and Strain Concentration Factors . 801
17.2 Stress Concentration Reduction Methods . 806
17.3 Tables 809
17.4 References 829
18 Fatigue and Fracture 833
18.1 Fatigue in Materials 833
18.2 Fatigue Testing 834
18.3 Fatigue and Crack Growth 835
18.4 Fracture Mechanics 835
18.5 The Stress Intensity Factor 836
18.6 Fracture Toughness 839
18.7 Crack Tip Plasticity 841
18.8 The Energy Balance Approach of Fracture 842
18.9 The J Integral . 843
18.10 Tables 845
18.11 References 855
19 Stresses in Fasteners and Joints 857
19.1 Welding 857
19.2 Analysis of Welded Joints . 859
19.3 Strength of Welded Joints . 862
19.4 Riveted and Bolted Joints . 867
19.5 Shearing and Failure Modes in Riveted Joints . 868
19.6 Eccentric Loading of Riveted Joints 869
19.7 References 872
20 Composite Materials 873
20.1 Composite Materials Classifcations
and Components 873
20.2 Mechanics of Composite Materials . 876
20.3 Macromechanics of a Layer (Lamina) 876
20.4 Micromechanics of a Layer (Lamina) . 880
20.5 Failure Criterion for a Layer (Lamina) 883
20.6 Macromechanics of a Laminate 886
20.7 Classical Lamination Theory 887
20.8 Macromechanics of a Laminate: Stress and Strain
in a Laminate . 889
20.9 Inversion of Stiffness Equation in a Laminate 895
20.10 Example of Stresses and Strains in a Laminate . 897
20.11 Strength and Failure Analyses of Laminate 900
20.12 Tables 905
20.13 References 916viii C o n t e n t s
21 Solid Biomechanics 919
21.1 Introduction 919
21.2 Biomechanics of Bone 920
21.3 Biomechanics of Articular Cartilage 925
21.4 Biomechanics of Tendons and Ligaments . 926
21.5 Biomechanics of Muscles . 927
21.6 Biomechanics of Joints . 929
21.7 Biomechanics of the Knee . 929
21.8 Biomechanics of the Hip 932
21.9 Biomechanics of the Spine 936
21.10 Biomechanics of the Lumbar Spine 936
21.11 Biomechanics of the Cervical Spine 942
21.12 Biomechanics of the Shoulder . 943
21.13 Biomechanics of the Elbow . 945
21.14 Human Factors in Design . 946
21.15 Implants and Prostheses 946
21.16 The Knee Implants 951
21.17 Other Implants 952
21.18 Biomaterials 952
21.19 Tables 956
21.20 References 960
21.21 Glossary . 963
A Properties of a Plane Area 965
B Mathematical Formulas and Matrices 995
C Glossary 1023
Index

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