Mechanics of materials : an integrated learning system

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 29
2.1 Displacement, Deformation,
and the Concept of Strain 29
2.2 Normal Strain 30
2.3 Shear Strain 37
2.4 Thermal Strain 41
Chapter 3 Mechanical Properties
of Materials 45
3.1 The Tension Test 45
3.2 The Stress–Strain Diagram 48
3.3 Hooke’s Law 56
3.4 Poisson’s ratio 56
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 77
Chapter 5 Axial Deformation 83
5.1 Introduction 83
5.2 Saint-Venant’s Principle 84
5.3 Deformations in Axially Loaded Bars 86
5.4 Deformations in a System of Axially
Loaded Bars 95
5.5 Statically Indeterminate Axially
Loaded Members 103
5.6 Thermal Effects on Axial Deformation 119
5.7 Stress Concentrations 129
Chapter 6 Torsion 135
6.1 Introduction 135
6.2 Torsional Shear Strain 137
6.3 Torsional Shear Stress 138
6.4 Stresses on Oblique Planes 140
6.5 Torsional Deformations 142
6.6 Torsion Sign Conventions 143
6.7 Gears in Torsion Assemblies 154
6.8 Power Transmission 161
6.9 Statically Indeterminate Torsion
Members 166
6.10 Stress Concentrations in Circular Shafts
Under Torsional Loadings 183
6.11 Torsion of Noncircular Sections 186
6.12 Torsion of Thin-Walled Tubes:
Shear Flow 189
Chapter 7 Equilibrium of Beams 193
7.1 Introduction 193
7.2 Shear and Moment in Beams 195
7.3 Graphical Method for Constructing Shear
and Moment Diagrams 205
7.4 Discontinuity Functions to represent
Load, Shear, and Moment 224
Chapter 8 Bending 237
8.1 Introduction 237
8.2 Flexural Strains 239
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8.3 Normal Stresses in Beams 240
8.4 Analysis of Bending Stresses
in Beams 254
8.5 Introductory Beam Design for
Strength 265
8.6 Flexural Stresses in Beams of
Two Materials 270
8.7 Bending Due to an Eccentric Axial
Load 282
8.8 Unsymmetric Bending 292
8.9 Stress Concentrations Under
Flexural Loadings 302
8.10 Bending of Curved Bars 306
Chapter 9 Shear Stress In Beams 319
9.1 Introduction 319
9.2 resultant Forces Produced by
Bending Stresses 319
9.3 The Shear Stress Formula 325
9.4 The First Moment of Area, Q 329
9.5 Shear Stresses in Beams of rectangular
Cross Section 331
9.6 Shear Stresses in Beams of Circular
Cross Section 338
9.7 Shear Stresses in Webs of
Flanged Beams 338
9.8 Shear Flow in Built-Up Members 346
9.9 Shear Stress and Shear Flow in
Thin-Walled Members 356
9.10 Shear Centers of Thin-Walled
Open Sections 373
Chapter 10 Beam Deflections 391
10.1 Introduction 391
10.2 Moment–Curvature relationship 392
10.3 The Differential Equation of the
Elastic Curve 392
10.4 Determining Deflections by Integration
of a Moment Equation 396
10.5 Determining Deflections by Integration
of Shear-Force or Load Equations 410
10.6 Determining Deflections by Using
Discontinuity Functions 413
10.7 Determining Deflections by the
Method of Superposition 423
Chapter 11 Statically Indeterminate
Beams 445
11.1 Introduction 445
11.2 Types of Statically Indeterminate
Beams 445
11.3 The Integration Method 447
11.4 Use of Discontinuity Functions for Statically
Indeterminate Beams 454
11.5 The Superposition Method 461
Chapter 12 Stress Transformations 479
12.1 Introduction 479
12.2 Stress at a General Point in an Arbitrarily
Loaded Body 480
12.3 Equilibrium of the Stress Element 482
12.4 Plane Stress 483
12.5 Generating the Stress Element 483
12.6 Equilibrium Method for Plane Stress
Transformations 488
12.7 General Equations of Plane Stress
Transformation 491
12.8 Principal Stresses and Maximum Shear
Stress 499
12.9 Presentation of Stress Transformation
results 506
12.10 Mohr’s Circle for Plane Stress 513
12.11 General State of Stress at a Point 532
Chapter 13 Strain Transformations 540
13.1 Introduction 540
13.2 Plane Strain 541
13.3 Transformation Equations for Plane
Strain 542
13.4 Principal Strains and Maximum
Shearing Strain 547
13.5 Presentation of Strain Transformation
results 548
13.6 Mohr’s Circle for Plane Strain 552
13.7 Strain Measurement and
Strain rosettes 555
13.8 Generalized Hooke’s Law
for Isotropic Materials 560
13.9 Generalized Hooke’s Law
for Orthotropic Materials 576
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Chapter 14 Pressure Vessels 585
14.1 Introduction 585
14.2 Thin-Walled Spherical Pressure Vessels 586
14.3 Thin-Walled Cylindrical Pressure
Vessels 588
14.4 Strains in Thin-Walled Pressure
Vessels 591
14.5 Stresses in Thick-Walled Cylinders 598
14.6 Deformations in Thick-Walled
Cylinders 606
14.7 Interference Fits 609
Chapter 15 Combined Loads 616
15.1 Introduction 616
15.2 Combined Axial and Torsional Loads 616
15.3 Principal Stresses in a
Flexural Member 621
15.4 General Combined Loadings 634
15.5 Theories of Failure 656
Chapter 16 Columns 667
16.1 Introduction 667
16.2 Buckling of Pin-Ended Columns 670
16.3 The Effect of End Conditions
on Column Buckling 680
16.4 The Secant Formula 690
16.5 Empirical Column Formulas—
Centric Loading 696
16.6 Eccentrically Loaded Columns 707
Chapter 17 Energy Methods 715
17.1 Introduction 715
17.2 Work and Strain Energy 716
17.3 Elastic Strain Energy for
Axial Deformation 720
17.4 Elastic Strain Energy for Torsional
Deformation 722
17.5 Elastic Strain Energy for
Flexural Deformation 724
17.6 Impact Loading 728
17.7 Work–Energy Method for Single
Loads 746
17.8 Method of Virtual Work 750
17.9 Deflections of Trusses by the Virtual-Work
Method 755
17.10 Deflections of Beams by the Virtual-Work
Method 762
17.11 Castigliano’s Second Theorem 774
17.12 Calculating Deflections of Trusses by
Castigliano’s Theorem 776
17.13 Calculating Deflections of Beams by
Castigliano’s Theorem 781
Appendix A Geometric Properties
of an Area 790
A.1 Centroid of an Area 790
A.2 Moment of Inertia for an Area 794
A.3 Product of Inertia for an Area 799
A.4 Principal Moments of Inertia 801
A.5 Mohr’s Circle for Principal Moments
of Inertia 805
Appendix B Geometric Properties
of Structural Steel Shapes 809
Appendix C Table of Beam Slopes and
Deflections 821
Appendix D Average Properties
of Selected Materials 824
Appendix E Fundamental Mechanics of
Materials Equations 828
Answers to Odd Numbered
Problems 832
Index 847