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Chapter 1: Stress
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
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
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
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
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 128
5.7 Stress Concentrations 140
Chapter 6: Torsion
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
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
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
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 369
9.9 Shear Stress and Shear Flow in Thin-Walled Members 382
9.10 Shear Centers of Thin-Walled Open Sections 393
Chapter 10: Beam Deflections
10.1 Introduction 409
10.2 Moment-Curvature Relationship 410
10.3 The Differential Equation of the Elastic Curve 410
10.4 Deflections by Integration of a Moment Equation 414
10.5 Deflections by Integration of Shear-Force or Load Equations 429
10.6 Deflections Using Discontinuity Functions 433
10.7 Method of Superposition 443
Chapter 11: Statically Indeterminate Beams
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
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 562
Chapter 13: Strain Transformations
13.1 Introduction 569
13.2 Two-Dimensional or 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
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
15.1 Introduction 623
15.2 Combined Axial and Torsional Loads 623
15.3 Principal Stresses in a Flexural Member 629
15.4 General Combined Loadings 643
15.5 Theories of Failure 668
Chapter 16: Columns
16.1 Introduction 681
16.2 Buckling of Pin-Ended Columns 684
16.3 The Effect of End Conditions on Column Buckling 696
16.4 The Secant Formula 707
16.5 Empirical Column Formulas—Centric Loading 714
16.6 Eccentrically Loaded Columns 726
Chapter 17: Energy Methods
17.1 Introduction 737
17.2 Work and Strain Energy 738
17.3 Elastic Strain Energy for Axial Deformation 742
17.4 Elastic Strain Energy for Torsional Deformation 744
17.5 Elastic Strain Energy for Flexural Deformation 746
17.6 Impact Loading 751
17.7 Work-Energy Method for Single Loads 769
17.8 Method of Virtual Work 774
17.9 Defl ections of Trusses by the Virtual-Work Method 779
17.10 Defl ections of Beams by the Virtual-Work Method 786
17.11 Castigliano’s Second Theorem 800
17.12 Calculating Defl ections of Trusses by Castigliano’s Theorem 802
17.13 Calculating Defl ections of Beams by Castigliano’s Theorem 807
Appendix A Geometric Properties of an Area 819
A.1 Centroid of an Area 819
A.2 Moment of Inertia for an Area 823
A.3 Product of Inertia for an Area 828
A.4 Principal Moments of Inertia 831
A.5 Mohr’s Circle for Principal Moments of Inertia 835
Appendix B Geometric Properties of Structural Steel Shapes 839
Appendix C Table of Beam Slopes and Deflections 853
Appendix D Average Properties of Selected Materials 857
Answers to Odd Numbered Problems 861
Index 885