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