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 12
1.5 Stresses on Inclined Sections 22
1.6 Equality of Shear Stresses on Perpendicular Planes 24
Chapter 2 Strain 31
2.1 Displacement, Deformation, and the Concept of Strain 31
2.2 Normal Strain 32
2.3 Shear Strain 39
2.4 Thermal Strain 43
Chapter 3 Mechanical Properties of Materials 47
3.1 The Tension Test 47
3.2 The Stress-Strain Diagram 50
3.3 Hooke's Law 58
3.4 Poisson's Ratio 58
Chapter 4 Design Concepts 69
4.1 Introduction 69
4.2 Types of Loads 70
4.3 Safety 71
4.4 Allowable Stress Design 72
4.5 Load and Resistance Factor Design 83
Chapter 5 Axial Deformation 89
5.1 Introduction 89
5.2 Saint-Venant's Principle 90
5.3 Deformations in Axially Loaded Bars 92
5.4 Deformations in a System of Axially Loaded Bars 101
5.5 Statically Indeterminate Axially Loaded Members 109
5.6 Thermal Effects on Axial Deformation 129
5.7 Stress Concentrations 141
Chapter 6 Torsion 147
6.1 Introduction 147
6.2 Torsional Shear Strain 149
6.3 Torsional Shear Stress 150
6.4 Stresses on Oblique Planes 152
6.5 Torsional Deformations 154
6.6 Torsion Sign Conventions 155
6.7 Gears in Torsion Assemblies 168
6.8 Power Transmission 175
6.9 Statically Indeterminate Torsion Members 182
6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 201
6.11 Torsion of Noncircular Sections 204
6.12 Torsion of Thin-Walled Tubes: Shear Flow 207
Chapter 7 Equilibrium of Beams 213
7.1 Introduction 213
7.2 Shear and Moment in Beams 215
7.3 Graphical Method for Constructing Shear and Moment Diagrams 227
7.4 Discontinuity Functions to Represent Load, Shear, and Moment 248
Chapter 8 Bending 261
8.1 Introduction 261
8.2 Flexural Strains 263
8.3 Normal Stresses in Beams 264
8.4 Analysis of Bending Stresses in Beams 279
8.5 Introductory Beam Design for Strength 292
8.6 Flexural Stresses in Beams of Two Materials 297
8.7 Bending Due to Eccentric Axial Load 310
8.8 Unsymmetric Bending 322
8.9 Stress Concentrations Under Flexural Loadings 332
Chapter 9 Shear Stress in Beams 337
9.1 Introduction 337
9.2 Resultant Forces Produced by Bending Stresses 337
9.3 The Shear Stress Formula 345
9.4 The First Moment of Area Q 349
9.5 Shear Stresses in Beams of Rectangular Cross Section 351
9.6 Shear Stresses in Beams of Circular Cross Section 358
9.7 Shear Stresses in Webs of Flanged Beams 358
9.8 Shear Flow in Built-Up Members 368
9.9 Shear Stress and Shear Flow in Thin-Walled Members 381
9.10 Shear Centers of Thin-Walled Open Sections 392
Chapter 10 Beam Defl ections 409
10.1 Introduction 409
10.2 Moment-Curvature Relationship 410
10.3 The Differential Equation of the Elastic Curve 410
10.4 Defl ections by Integration of a Moment Equation 414
10.5 Defl ections by Integration of Shear-Force or Load Equations 429
10.6 Defl ections Using Discontinuity Functions 433
10.7 Method of Superposition 443
Chapter 11 Statically Indeterminate Beams 469
11.1 Introduction 469
11.2 Types of Statically Indeterminate Beams 469
11.3 The Integration Method 471
11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 478
11.5 The Superposition Method 486
Chapter 12 Stress Transformations 507
12.1 Introduction 507
12.2 Stress at a General Point in an Arbitrarily Loaded Body 508
12.3 Equilibrium of the Stress Element 510
12.4 Plane Stress 511
12.5 Generating the Stress Element 511
12.6 Equilibrium Method for Plane Stress Transformations 517
12.7 General Equations of Plane Stress Transformation 520
12.8 Principal Stresses and Maximum Shear Stress 528
12.9 Presentation of Stress Transformation Results 535
12.10 Mohr's Circle for Plane Stress 543
12.11 General State of Stress at a Point 561
Chapter 13 Strain Transformations 569
13.1 Introduction 569
13.2 Plane Strain 570
13.3 Transformation Equations for Plane Strain 571
13.4 Principal Strains and Maximum Shearing Strain 576
13.5 Presentation of Strain Transformation Results 578
13.6 Mohr's Circle for Plane Strain 581
13.7 Strain Measurement and Strain Rosettes 585
13.8 Generalized Hooke's Law for Isotropic Materials 591
Chapter 14 Thin-Walled Pressure Vessels 607
14.1 Introduction 607
14.2 Spherical Pressure Vessels 608
14.3 Cylindrical Pressure Vessels 610
14.4 Strains in Pressure Vessels 613
Chapter 15 Combined Loads 623
15.1 Introduction 623
15.2 Combined Axial and Torsional Loads 623
15.3 Principal Stresses in a Flexural Member 628
15.4 General Combined Loadings 643
15.5 Theories of Failure 668
Chapter 16 Columns 681
16.1 Introduction 681
16.2 Buckling of Pin-Ended Columns 684
16.3 The Effect of End Conditions on Column Buckling 695
16.4 The Secant Formula 706
16.5 Empirical Column Formulas-Centric Loading 712
16.6 Eccentrically Loaded Columns 723
Chapter 17 Energy Methods 733
17.1 Introduction 733
17.2 Work and Strain Energy 734
17.3 Elastic Strain Energy for Axial Deformation 738
17.4 Elastic Strain Energy for Torsional Deformation 740
17.5 Elastic Strain Energy for Flexural Deformation 742
17.6 Impact Loading 747
17.7 Work-Energy Method for Single Loads 765
17.8 Method of Virtual Work 770
17.9 Deflections of Trusses by the Virtual-Work Method 775
17.10 Deflections of Beams by the Virtual-Work Method 782
17.11 Castigliano's Second Theorem 796
17.12 Calculating Deflections of Trusses by Castigliano's Theorem 798
17.13 Calculating Deflections of Beams by Castigliano's Theorem 803
Appendix A Geometric Properties of an Area 813
A.1 Centroid of an Area 813
A.2 Moment of Inertia for an Area 817
A.3 Product of Inertia for an Area 822
A.4 Principal Moments of Inertia 825
A.5 Mohr's Circle for Principal Moments of Inertia 829
Appendix B Geometric Properties of Structural Steel Shapes 833
Appendix C Table of Beam Slopes and Deflections 841
Appendix D Average Properties of Selected Materials 845
Answers to Odd Numbered Problems 849
Index 871
