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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