Mechanics of Materials, 6th Edition

Chapter 1 Introduction and Review of Statics 1

1-1 Introduction 1

1-2 Classification of Forces 2

1-3 Equilibrium of a Rigid Body 4

1-4 Equilibrium of a Deformable Body 30

1-5 Internal Forces 34

Summary 44

Chapter 2 Analysis of Stress: Concepts and Definitions 48

2-1 Introduction 48

2-2 Normal Stress under Axial Loading 48

2-3 Shearing Stress in Connections 49

2-4 Bearing Stress 51

2-5 Units of Stress 51

2-6 Stresses on an Inclined Plane in an Axially Loaded Member 65

2-7 Stress at a general point in an Arbitrarily Loaded Member 72

2-8 Two-dimensional or Plane Stress 74

2-9 The Stress Transformation Equations for Plane Stress 75

2-10 Principal Stresses and Maximum Shearing Stress—Plane Stress 85

2-11 Mohr’s Circle for Plane Stress 98

2-12 General State of Stress at a Point 108

Summary 117

Chapter 3 Analysis of Strain: Concepts and Definitions 121

3-1 Introduction 121

3-2 Displacement, Deformation, and Strain 121

3-3 The State of Strain at a point 129

3-4 The Strain Transformation Equations for Plane Strain 130

3-5 Principal Strains and Maximum Shear Strain 135

3-6 Mohr’s Circle for Plane Strain 140

3-7 Strain Measurement and Rosette Analysis 142

Summary 148

Chapter 4 Material Properties and Stress-Strain Relationships 153

4-1 Introduction 153

4-2 Stress-Strain diagrams 153

4-3 Generalized Hooke’s law 164

4-4 Thermal Strain 176

4-5 Stress-Strain Equations for Orthotropic Materials 180

Summary 184

Chapter 5 Axial Loading Applications and Pressure Vessels 189

5-1 Introduction 189

5-2 Deformation of Axially Loaded Members 189

5-3 Deformations in a System of Axially Loaded Bars 201

5-4 Statically Indeterminate Axially Loaded Members 209

5-5 Thermal Effects 225

5-6 Stress Concentrations 234

5-7 Inelastic Behavior of Axially Loaded Members 239

5-8 Thin-Walled Pressure Vessels 246

5-9 Combined Effects—Axial and Pressure Loads 254

5-10 Thick-Walled Cylindrical Pressure Vessels 257

5-11 Design 264

Summary 270

Chapter 6 Torsional Loading of Shafts 276

6-1 Introduction 276

6-2 Torsional Shearing Strain 277

6-3 Torsional Shearing Stress—The Elastic Torsion formula 279

6-4 Torsional Displacements 281

6-5 Stresses on Oblique Planes 295

6-6 Power Transmission 300

6-7 Statically Indeterminate Members 303

6-8 Combined Loading—Axial, Torsional, and Pressure Vessel 315

6-9 Stress Concentrations in Circular Shafts under Torsional Loadings 322

6-10 Inelastic Behavior of Torsional Members 325

6-11 Torsion of Noncircular Sections 331

6-12 Torsion of Thin-Walled Tubes—Shear flow 333

6-13 Design Problems 339

Summary 344

Chapter 7 Flexural Loading: Stresses in Beams 349

7-1 Introduction 349

7-2 Flexural Strains 352

7-3 Flexural Stresses 354

7-4 The Elastic Flexure formula 356

7-5 Shear forces and Bending Moments in Beams 366

7-6 Load, Shear Force, and Bending Moment relationships 376

7-7 Shearing Stresses in Beams 391

7-8 Principal Stresses in Flexural Members 405

7-9 Flexural Stresses—Unsymmetrical Bending 410

7-10 Stress Concentrations under Flexural Loadings 418

7-11 Inelastic Behavior of Flexural Members 422

7-12 Shearing Stresses in Thin-Walled Open Sections—Shear center 431

7-13 Flexural Stresses in Beams of Two Materials 441

7-14 Flexural Stresses in Reinforced Concrete Beams 445

7-15 Flexural Stresses in Curved Beams 450

7-16 Combined Loading: Axial, Pressure, Flexural, and Torsional 457

7-17 Design Problems 475

Summary 480

Chapter 8 Flexural Loading: Beam Deflections 487

8-1 Introduction 487

8-2 The Differential Equation of the Elastic Curve 487

8-3 Deflection by Integration 489

8-4 Deflections by Integration of Shear Force or Load Equations 502

8-5 Singularity Functions 507

8-6 Deflections by Superposition 520

8-7 Deflections due to Shearing Stress 530

8-8 Deflections by Energy Methods—Castigliano’s Theorem 532

8-9 Statically Indeterminate Beams 542

8-10 Design problems 567

Summary 574

Chapter 9 Columns 578

9-1 Introduction 578

9-2 Buckling of Long, Straight Columns 579

9-3 Effects of Different Idealized End Conditions 587

9-4 Empirical Column Formulas—Centric Loading 592

9-5 Eccentrically Loaded Columns 600

9-6 Design problems 606

Summary 610

Chapter 10 Energy Methods and Theories of Failure 614

10-1 Introduction 614

Part A: Energy Methods 615

10-2 Strain Energy 615

10-3 Elastic Strain Energy for Various Loads 617

10-4 Impact Loading 624

Part B: Theories of Failure for Static Loading 637

10-5 Introduction 637

10-6 Failure Theories for Ductile Materials 637

10-7 Failure Theories for Brittle Materials 650

Summary 654

Appendices

A Second Moments of Area 659

B Tables of Properties 683

Index 705