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1STRESS 3

1.1 Introduction 3

1.2 Equilibrium of a Deformable Body 4

1.3 Stress 22

1.4 Average Normal Stress in an Axially Loaded Bar 24

1.5 Average Shear Stress 32

1.6 Allowable Stress 48

2STRAIN 67

2.1 Deformation 67

2.2 Strain 68

3MECHANICAL PROPERTIES OF MATERIALS 83

3.1 The Tension and Compression Test 83

3.2 The Stress-Strain Diagram 85

3.3 Stress-Strain Behavior of Ductile and Brittle Materials 89

3.4 Hooke’s Law 92

3.5 Strain Energy 94

3.6 Poisson’s Ratio 104

3.7 The Shear Stress-Strain Diagram 106

3.8 Failure of Materials Due to Creep and Fatigue 109

4AXIAL LOAD 117

4.1 Saint-Venant’s Principle 117

4.2 Elastic Deformation of an Axially Loaded Member 120

4.3 Principle of Superposition 133

4.4 Statically Indeterminate Axially Loaded Member 134

4.5 The Force Method of Analysis for Axially Loaded Members 140

4.6 Thermal Stress 148

4.7 Stress Concentrations 156

4.8 Inelastic Axial Deformation 162

4.9 Residual Stress 167

5TORSION 177

5.1 Torsional Deformation of a Circular Shaft 177

5.2 The Torsion Formula 178

5.3 Power Transmission 189

5.4 Angle of Twist 198

5.5 Statically Indeterminate Torque-Loaded Members 213

5.6 Solid Noncircular Shafts 220

5.7 Thin-Walled Tubes Having Closed Cross Sections 223

5.8 Stress Concentration 234

5.9 Inelastic Torsion 237

5.10 Residual Stress 244

6BENDING 255

6.1 Shear and Moment Diagrams 255

6.2 Graphical Method for Constructing Shear and Moment Diagrams 264

6.3 Bending Deformation of a Straight Member 282

6.4 The Flexure Formula 286

6.5 Unsymmetric Bending 304

6.6 Composite Beams 315

6.7 Reinforced Concrete Beams 322

6.8 Curved Beams 324

6.9 Stress Concentrations 334

6.10 Inelastic Bending 343

6.11 Residual Stress 352

7TRANSVERSE SHEAR 363

7.1 Shear in Straight Members 363

7.2 The Shear Formula 365

7.3 Shear Stresses in Beams 366

7.4 Shear Flow in Built-up Members 382

7.5 Shear Flow in Thin-Walled Members 391

7.6 Shear Center 396

8COMBINED LOADINGS 409

8.1 Thin-Walled Vessels 409

8.2 State of Stress Caused by Combined Loadings 416

9STRESS TRANSFORMATION 439

9.1 Plane-Stress Transformation 439

9.2 General Equations of Plane-Stress Transformation 444

9.3 Principal Stresses and Maximum In-Plane Shear Stress 448

9.4 Mohr’s Circle—Plane Stress 462

9.5 Stress in Shafts Due to Axial Load and Torsion 471

9.6 Stress Variations Throughout a Prismatic Beam 472

9.7 Absolute Maximum Shear Stress 478

10STRAIN TRANSFORMATION 489

10.1 Plane Strain 489

10.2 General Equations of Plane-Strain Transformation 491

10.3 Mohr’s Circle—Plane Strain 498

10.4 Absolute Maximum Shear Strain 505

10.5 Strain Rosettes 508

10.6 Material-Property Relationships 512

10.7 Theories of Failure 524

11DESIGN OF BEAMS AND SHAFTS 539

11.1 Basis for Beam Design 539

11.2 Prismatic Beam Design 541

11.3 Fully Stressed Beams 554

11.4 Shaft Design 558

12DEFLECTIONS OF BEAMS AND SHAFTS 569

12.1 The Elastic Curve 569

12.2 Slope and Displacement by Integration 573

12.3 Discontinuity Functions 590

12.4 Slope and Displacement by the Moment-Area Method 600

12.5 Method of Superposition 614

12.6 Statically Indeterminate Beams and Shafts 622

12.7 Statically Indeterminate Beams and Shafts—Method of Integration 622

12.8 Statically Indeterminate Beams and Shafts—Moment-Area Method 628

12.9 Statically Indeterminate Beams and Shafts—Method of Superposition 634

13BUCKLING OF COLUMNS 649

13.1 Critical Load 649

13.2 Ideal Column with Pin Supports 652

13.3 Columns Having Various Types of Supports 658

13.4 The Secant Formula 669

13.5 Inelastic Buckling 677

13.6 Design of Columns for Concentric Loading 683

13.7 Design of Columns for Eccentric Loading 694

14ENERGY METHODS 705

14.1 External Work and Strain Energy 705

14.2 Elastic Strain Energy for Various Types of Loading 710

14.3 Conservation of Energy 724

14.4 Impact Loading 730

14.5 Principle of Virtual Work 740

14.6 Method of Virtual Forces Applied to Trusses 744

14.7 Method of Virtual Forces Applied to Beams 752

14.8 Castigliano’s Theorem 762

14.9 Castigliano’s Theorem Applied to Trusses 764

14.10 Castigliano’s Theorem Applied to Beams 768

A GEOMETRIC PROPERTIES OF AN AREA 775

A.1 Centroid of an Area 775

A.2 Moment of Inertia for an Area 778

A.3 Product of Inertia for an Area 782

A.4 Moments of Inertia for an Area about Inclined Axes 784

A.5 Mohr’s Circle for Moments of Inertia 786

B GEOMETRICAL PROPERTIES OF STRUCTURAL SHAPES 792

C SLOPES AND DEFLECTIONS OF BEAMS 800

D REVIEW FOR THE FUNDAMENTALS OF ENGINEERING EXAM 802

ANSWERS 822

INDEX 844