1 Introduction 1
1.1 A Motivating Example：Remodeling an Underwater Structure 1
1.2 Newton’s Laws：The First Principles of Mechanics 3
1.3 Equilibrium 4
1.4 Definition of a Continuum 5
1.5 Some Mathematical Basics：Scalars and Vectors 8
1.6 Problem Solving 11
1.7 Examples 12
2 Strain and Stress in One Dimension 25
2.1 Kinematics：Strain 25
2.1.1 Normal Strain 26
2.1.2 Shear Strain 28
2.1.3 Measurement of Strain 29
2.2 The Method of Sections and Stress 30
2.2.1 Normal Stresses 31
2.2.2 Shear Stresses 32
2.3 Stress-Strain Relationships 33
2.4 Limiting Behavior 37
2.5 Equilibrium 40
2.6 Stress in Axially Loaded Bars 42
2.7 Deformation of Axially Loaded Bars 44
2.8 Equilibrium of an Axially Loaded Bar 45
2.9 Statically Indeterminate Bars 46
2.9.1 Force （Flexibility） Method 47
2.9.2 Displacement （Stiffness） Method 49
2.10 Thermal Effects 51
2.11 Saint-Venant’s Principle and Stress Concentrations 52
2.12 Strain Energy in One Dimension 53
2.13 Properties of Engineering Materials 55
2.13.1 Metals 56
2.13.2 Ceramics 57
2.13.3 Polymers 57
2.13.4 Other Materials 58
2.14 A Road Map for Strength of Materials 58
2.15 Examples 60
3 Case Study 1：Collapse of the Kansas City Hyatt Regency Walkways 81
4 Strain and Stress in Higher Dimensions 89
4.1 Poisson’s Ratio 89
4.2 The Strain Tensor 90
4.3 The Stress Tensor 94
4.4 Generalized Hooke’s Law 97
4.5 Equilibrium 99
4.5.1 Equilibrium Equations 99
4.5.2 The Two-Dimensional State of Plane Stress 100
4.5.3 The Two-Dimensional State of Plane Strain 102
4.6 Formulating Two-Dimensional Elasticity Problems 102
4.6.1 Equilibrium Expressed in Terms of Displacements 103
4.6.2 Compatibility Expressed in Terms of Stress Functions 104
4.6.3 Some Remaining Pieces of the Puzzle of General Formulations 105
4.7 Examples 106
5 Applying Strain and Stress in Multiple Dimensions 115
5.1 Torsion 115
5.1.1 Method of Sections 115
5.1.2 Torsional Shear Strain and Stress：Angle of Twist and the Torsion Formula 116
5.1.3 Stress Concentrations 121
5.1.4 Transmission of Power by a Shaft 121
5.1.5 Statically Indeterminate Problems 122
5.1.6 Torsion of Solid Noncircular Rods 123
5.2 Pressure Vessels 126
5.3 Transformation of Stress and Strain 129
5.3.1 Transformation of Plane Stress 130
5.3.2 Principal and Maximum Shear Stresses 132
5.3.3 Mohr’s Circle for Plane Stress 134
5.3.4 Transformation of Plane Strain 136
5.3.5 Three-Dimensional State of Stress 138
5.4 Failure Prediction Criteria 139
5.4.1 Failure Criteria for Brittle Materials 139
5.4.1.1 Maximum Normal Stress Criterion 140
5.4.2 Yield Criteria for Ductile Materials 141
5.4.2.1 Maximum Shearing Stress （Tresca） Criterion 141
5.4.2.2 Von Mises Criterion 142
5.5 Examples 143
6 Case Study 2：Pressure Vessels 169
6.1 Why Pressure Vessels Are Spheres and Cylinders 169
6.2 Why Do Pressure Vessels Fail？ 174
7 Beams 181
7.1 Calculation of Reactions 181
7.2 Method of Sections：Axial Force，Shear，Bending Moment 183
7.2.1 Axial Force in Beams 183
7.2.2 Shear in Beams 183
7.2.3 Bending Moment in Beams 184
7.3 Shear and Bending Moment Diagrams 185
7.3.1 Rules and Regulations for Shear Diagrams 185
7.3.2 Rules and Regulations for Moment Diagrams 186
7.4 Integration Methods for Shear and Bending Moment 187
7.5 Normal Stresses in Beams and Geometric Properties of Sections 189
7.6 Shear Stresses in Beams 194
7.7 Examples 199
8 Case Study 3：Physiological Levers and Repairs 223
8.1 The Forearm Is Connected to the Elbow Joint 223
8.2 Fixing an Intertrochanteric Fracture 226
9 Beam Deflections 231
9.1 Governing Equation 231
9.2 Boundary Conditions 233
9.3 Beam Deflections by Integration and by Superposition 235
9.4 Discontinuity Functions 238
9.5 Beams with Non-Constant Cross Section 240
9.6 Statically Indeterminate Beams 241
9.7 Beams with Elastic Supports 244
9.8 Strain Energy for Bent Beams 246
9.9 Deflections by Castigliano’s Second Theorem 248
9.10 Examples 249
10 Case Study 4：Truss-Braced Airplane Wings 269
10.1 Modeling and Analysis 271
10.2 What Does Our Model Tell Us？ 275
10.3 Conclusions 276
11 Instability：Column Buckling 279
11.1 Euler’s Formula 279
11.2 Effect of Eccentricity 284
11.3 Examples 287
12 Case Study 5：Hartford Civic Arena 295
13 Connecting Solid and Fluid Mechanics 299
13.1 Pressure 300
13.2 Viscosity 301
13.3 Surface Tension 304
13.4 Governing Laws 304
13.5 Motion and Deformation of Fluids 305
13.5.1 Linear Motion and Deformation 305
13.5.2 Angular Motion and Deformation 306
13.5.3 Vorticity 308
13.5.4 Constitutive Equation for Newtonian Fluids 308
13.6 Examples 310
14 Case Study 6：Mechanics of Biomaterials 319
14.1 Nonlinearity 321
14.2 Composite Materials 322
14.3 Viscoelasticity 324
15 Case Study 7：Engineered Composite Materials 329
15.1 Concrete 329
15.2 Plastics 330
15.2.1 3D Printing 331
15.3 Ceramics 331
16 Fluid Statics 335
16.1 Local Pressure 335
16.2 Force due to Pressure 336
16.3 Fluids at Rest 338
16.4 Forces on Submerged Surfaces 342
16.5 Buoyancy 347
16.6 Examples 348
17 Case Study 8：St.Francis Dam 363
18 Fluid Dynamics：Governing Equations 367
18.1 Description of Fluid Motion 367
18.2 Equations of Fluid Motion 369
18.3 Integral Equations of Motion 369
18.3.1 Mass Conservation 369
18.3.2 Newton’s Second Law，or Momentum Conservation 371
18.3.3 Reynolds Transport Theorem 374
18.4 Differential Equations of Motion 375
18.4.1 Continuity，or Mass Conservation 375
18.4.2 Newton’s Second Law，or Momentum Conservation 376
18.5 Bernoulli Equation 379
18.6 Examples 380
19 Case Study 9：China’s Three Gorges Dam，三峡大坝 395
20 Fluid Dynamics：Applications 399
20.1 How Do We Classify Fluid Flows？ 399
20.2 What Is Going on Inside Pipes？ 401
20.3 Why Can an Airplane Fly？ 404
20.4 Why Does a Curveball Curve？ 406
21 Case Study 10：Living with Water，and the Role of Technological Culture 413
22 Solid Dynamics：Governing Equations 417
22.1 Continuity，or Mass Conservation 417
22.2 Newton’s Second Law，or Momentum Conservation 419
22.3 Constitutive Laws：Elasticity 420
References 423
Appendix A：Second Moments of Area 425
Appendix B：A Quick Look at the del Operator 429
Appendix C：Property Tables 433
Appendix D：All the Equations 437
Index 439