Loading...Introduction to Solid Mechanics – An Integrated Approach
Jacob Lubliner, Panayiotis Papadopoulos
Contents
Preface v
1 Forces and Moments 1
1.1 Introduction 1
1.2 Review of Vectors . 14
1.3 Forces . 24
1.4 Moments 30
1.5 Statically Equivalent Force Systems . 39
2 Equilibrium 49
2.1 Equilibrium of Particle Systems 49
2.2 Equilibrium of Rigid Bodies in Two Dimensions 62
2.3 Equilibrium of Rigid Bodies in Three
Dimensions 83
2.4 Method of Sections 93
3 Articulated Assemblages of Rigid Members 103
3.1 Method of Joints . 103
3.2 Two-Dimensional Trusses . 111
3.3 Three-Dimensional Trusses 122
3.4 Frames and Machines 129
3.5 Chains and Cables 137
4 Stress 149
4.1 Normal Stress, Saint-Venant’s Principle . 149
4.2 Shear Stress 157
4.3 Simple Stress States, Stress-Based Design . 164
4.4 General State of Stress . 175
4.5 Local Equilibrium Equations 183
viiviii Contents
4.6 Stress Transformation, Principal Stresses,
Mohr’s Circle . 190
5 Deformation and Strain 209
5.1 Longitudinal Strain . 209
5.2 Shear Strain 218
5.3 Displacement, General State of Strain 224
5.4 Strain Transformation, Principal Strains 233
6 Elasticity 241
6.1 Springs and Hooke’s Law (Axial and Shear) . 241
6.2 Generalized Hooke’s Law 251
6.3 Elongation of Axially Loaded Elastic Bars 266
6.4 Static Indeterminacy in Linearly Elastic Bodies 279
6.5 Elastic Energy 290
6.6 Thermoelastic Properties of Solids 305
7 Torsion 313
7.1 Torsion of Elastic Circular Bars 313
7.2 Torsion of Non-circular Thin-Walled Tubes . 325
7.3 Compound Shafts 332
7.4 Open Thin-Walled Sections . 338
8 Elastic Bending of Beams 345
8.1 Shear and Bending-Moment Diagrams 345
8.2 Pure Bending of Beams . 358
8.3 Bernoulli–Euler Beam Theory . 371
8.4 Calculation of Elastic Beam Deflections . 383
9 Additional Topics in Bending 397
9.1 Composite Cross-Sections 397
9.2 Asymmetric Bending of Beams 405
9.3 Shear Stresses in Beams 413
9.4 Stresses in Beams Under Combined Loading 426
10 Elastic Stability and Buckling 433
10.1 Buckling Fundamentals and Simple Models 433
10.2 Stability and Energy . 442
10.3 Buckling of Elastic Columns 448Contents ix
11 Inelasticity and Material Failure 463
11.1 Stress–Strain Diagrams . 463
11.2 Material Failure . 475
11.3 Structural Failure 485
Appendix A: Singularity Functions 499
Appendix B: Tables B-1–B-6 503
Photo Credits 507
Index
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