Chapter 1 STRESS 1

1.1 Introduction 1

1.2 Normal Stress Under Axial Loading 2

1.3 Direct Shear Stress 7

1.4 Bearing Stress 11

1.5 Stresses on Inclined Sections 19

1.6 Equality of Shear Stresses on Perpendicular Planes 21

Chapter 2 STRAIN 27

2.1 Displacement, Deformation, and the Concept of Strain 27

2.2 Normal Strain 28

2.3 Shear Strain 35

2.4 Thermal Strain 39

Chapter 3 MECHANICAL PROPERTIES OF MATERIALS 43

3.1 The Tension Test 43

3.2 The Stress–Strain Diagram 46

3.3 Hooke’s Law 54

3.4 Poisson’s Ratio 54

Chapter 4 DESIGN CONCEPTS 65

4.1 Introduction 65

4.2 Types of Loads 66

4.3 Safety 67

4.4 Allowable Stress Design 68

4.5 Load and Resistance Factor Design 79

Chapter 5 AXIAL DEFORMATION 85

5.1 Introduction 85

5.2 Saint-Venant’s Principle 86

5.3 Deformations in Axially Loaded Bars 88

5.4 Deformations in a System of Axially Loaded Bars 96

5.5 Statically Indeterminate Axially Loaded Members 105

5.6 Thermal Effects on Axial Deformation 122

5.7 Stress Concentrations 134

Chapter 6 TORSION 141

6.1 Introduction 141

6.2 Torsional Shear Strain 143

6.3 Torsional Shear Stress 144

6.4 Stresses on Oblique Planes 146

6.5 Torsional Deformations 148

6.6 Torsion Sign Conventions 149

6.7 Gears in Torsion Assemblies 162

6.8 Power Transmission 170

6.9 Statically Indeterminate Torsion Members 177

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 197

6.11 Torsion of Noncircular Sections 200

6.12 Torsion of Thin-Walled Tubes: Shear Flow 202

Chapter 7 EQUILIBRIUM OF BEAMS 207

7.1 Introduction 207

7.2 Shear and Moment in Beams 209

7.3 Graphical Method for Constructing Shear and Moment Diagrams 221

7.4 Discontinuity Functions to Represent Load, Shear, and Moment 242

Chapter 8 BENDING 255

8.1 Introduction 255

8.2 Flexural Strains 257

8.3 Normal Stresses in Beams 258

8.4 Analysis of Bending Stresses in Beams 273

8.5 Introductory Beam Design for Strength 286

8.6 Flexural Stresses in Beams of Two Materials 291

8.7 Bending Due to Eccentric Axial Load 305

8.8 Unsymmetric Bending 315

8.9 Stress Concentrations Under Flexural Loadings 324

Chapter 9 SHEAR STRESS IN BEAMS 329

9.1 Introduction 329

9.2 Resultant Forces Produced by Bending Stresses 329

9.3 The Shear Stress Formula 337

9.4 The First Moment of Area Q 341

9.5 Shear Stresses in Beams of Rectangular Cross Section 343

9.6 Shear Stresses in Beams of Circular Cross Section 350

9.7 Shear Stresses in Webs of Flanged Beams 350

9.8 Shear Flow in Built-Up Members 361

Chapter 10 BEAM DEFLECTIONS 375

10.1 Introduction 375

10.2 Moment-Curvature Relationship 376

10.3 The Differential Equation of the Elastic Curve 376

10.4 Deflections by Integration of a Moment Equation 380

10.5 Deflections by Integration of Shear-Force or Load Equations 395

10.6 Deflections Using Discontinuity Functions 399

10.7 Method of Superposition 409

Chapter 11 STATICALLY INDETERMINATE BEAMS 435

11.1 Introduction 435

11.2 Types of Statically Indeterminate Beams 435

11.3 The Integration Method 437

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 444

11.5 The Superposition Method 452

Chapter 12 STRESS TRANSFORMATIONS 469

12.1 Introduction 469

12.2 Stress at a General Point in an Arbitrarily Loaded Body 470

12.3 Equilibrium of the Stress Element 472

12.4 Two-Dimensional or Plane Stress 473

12.5 Generating the Stress Element 473

12.6 Equilibrium Method for Plane Stress Transformations 479

12.7 General Equations of Plane Stress Transformation 482

12.8 Principal Stresses and Maximum Shear Stress 490

12.9 Presentation of Stress Transformation Results 497

12.10 Mohr’s Circle for Plane Stress 505

12.11 General State of Stress at a Point 524

Chapter 13 STRAIN TRANSFORMATIONS 531

13.1 Introduction 531

13.2 Two-Dimensional or Plane Strain 532

13.3 Transformation Equations for Plane Strain 533

13.4 Principal Strains and Maximum Shearing Strain 538

13.5 Presentation of Strain Transformation Results 540

13.6 Mohr’s Circle for Plane Strain 543

13.7 Strain Measurement and Strain Rosettes 547

13.8 Generalized Hooke’s Law for Isotropic Materials 553

Chapter 14 THIN-WALLED PRESSURE VESSELS 567

14.1 Introduction 567

14.2 Spherical Pressure Vessels 568

14.3 Cylindrical Pressure Vessels 570

14.4 Strains in Pressure Vessels 573

Chapter 15 COMBINED LOADS 581

15.1 Introduction 581

15.2 Combined Axial and Torsional Loads 581

15.3 Principal Stresses in a Flexural Member 587

15.4 General Combined Loadings 601

15.5 Theories of Failure 626

Chapter 16 COLUMNS 639

16.1 Introduction 639

16.2 Buckling of Pin-Ended Columns 642

16.3 The Effect of End Conditions on Column Buckling 654

16.4 The Secant Formula 665

16.5 Empirical Column Formulas— Centric Loading 672

16.6 Eccentrically Loaded Columns 684

Appendix A GEOMETRIC PROPERTIES OF AN AREA 695

A.1 Centroid of an Area 695

A.2 Moment of Inertia for an Area 699

A.3 Product of Inertia for an Area 704

A.4 Principal Moments of Inertia 707

A.5 Mohr’s Circle for Principal Moments of Inertia 711

Appendix B GEOMETRIC PROPERTIES OF STRUCTURAL STEEL SHAPES 715

Appendix C TABLE OF BEAM SLOPES AND DEFLECTIONS 729

Appendix D AVERAGE PROPERTIES OF SELECTED MATERIALS 733

ANSWERS TO ODD NUMBERED PROBLEMS 737

INDEX 761