1 Tension, Compression, and Shear

1.1 Introduction to Mechanics of Materials 2

1.2 Problem-Solving Approach 2

1.3 Statics Review 3

1.4 Normal Stress and Strain 22

1.5 Mechanical Properties of Materials 31

1.6 Elasticity, Plasticity, and Creep 38

1.7 Linear Elasticity, Hooke’s Law, and Poisson’s Ratio 44

1.8 Shear Stress and Strain 50

1.9 Allowable Stresses and Allowable Loads 63

1.10 Design For Axial Loads and Direct Shear 70

Chapter Summary and Review 74

Problems 77

2 Axially Loaded Members

2.1 Introduction 124

2.2 Changes in Lengths of Axially Loaded Members 124

2.3 Changes in Lengths under Nonuniform Conditions 132

2.4 Statically Indeterminate Structures 146

2.5 Thermal Effects, Misfits, and Prestrains 159

2.6 Stresses on Inclined Sections 178

2.7 Strain Energy 190

*2.8 Impact Loading 201

*2.9 Repeated Loading and Fatigue 209

*2.10 Stress Concentrations 211

*2.11 Nonlinear Behavior 218

*2.12 Elastoplastic Analysis 222

Chapter Summary and Review 229

Problems 231

* Specialized and/or advanced topics

3.1 Introduction 282

3.2 Torsional Deformations of a Circular Bar 282

3.3 Circular Bars of Linearly Elastic Materials 285

3.4 Nonuniform Torsion 298

3.5 Stresses and Strains in Pure Shear 310

3.6 Relationship Between Moduli of Elasticity E and G 317

3.7 Transmission of Power by Circular Shafts 319

3.8 Statically Indeterminate Torsional Members 323

3.9 Strain Energy in Torsion and Pure Shear 327

3.10 Torsion of Noncircular Prismatic Shafts 334

3.11 Thin-Walled Tubes 344

*3.12 Stress Concentrations in Torsion 352

Chapter Summary and Review 357

Problems 360

*Specialized and/or advanced topics

4 Shear Forces and Bending Moments

4.1 Introduction 390

4.2 Types of Beams, Loads, and Reactions 390

4.3 Shear Forces and Bending Moments 400

4.4 Relationships Among Loads, Shear Forces, and Bending

Moments 408

4.5 Shear-Force and Bending-Moment Diagrams 412

Chapter Summary and Review 439

Problems 441

5.1 Introduction 460

5.2 Pure Bending and Nonuniform Bending 460

5.3 Curvature of a Beam 461

5.4 Longitudinal Strains in Beams 463

5.5 Normal Stresses in Beams (Linearly Elastic Materials) 467

5.6 Design of Beams for Bending Stresses 480

5.7 Nonprismatic Beams 490

5.8 Shear Stresses in Beams of Rectangular Cross Section 494

5.9 Shear Stresses in Beams of Circular Cross Section 502

5.10 Shear Stresses in the Webs of Beams with Flanges 505

*5.11 Built-Up Beams and Shear Flow 512

*5.12 Beams with Axial Loads 516

*5.13 Stress Concentrations in Bending 523

Chapter Summary and Review 528

Problems 532

*Specialized and/or advanced topics

6 Stresses in Beams (Advanced Topics)

6.1 Introduction 570

6.2 Composite Beams 570

6.3 Transformed-Section Method 579

6.4 Doubly Symmetric Beams with Inclined Loads 587

6.5 Bending of Unsymmetric Beams 594

6.6 The Shear-Center Concept 605

6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 606

6.8 Shear Stresses in Wide-Flange Beams 609

6.9 Shear Centers of Thin-Walled Open Sections 613

*6.10 Elastoplastic Bending 621

Chapter Summary and Review 630

Problems 632

*Specialized or Advanced Topics

7 Analysis of Stress and Strain

7.1 Introduction 658

7.2 Plane Stress 658

7.3 Principal Stresses and Maximum Shear Stresses 666

7.4 Mohr’s Circle for Plane Stress 674

7.5 Hooke’s Law for Plane Stress 687

7.6 Triaxial Stress 693

7.7 Plane Strain 697

Chapter Summary and Review 712

Problems 715

8 Applications of Plane Stress

(Pressure Vessels, Beams, and Combined Loadings

8.1 Introduction 740

8.2 Spherical Pressure Vessels 740

8.3 Cylindrical Pressure Vessels 746

8.4 Maximum Stresses in Beams 753

8.5 Combined Loadings 761

Chapter Summary and Review 786

Problems 788

9 Deflections of Beams

9.1 Introduction 812

9.2 Differential Equations of the Deflection Curve 812

9.3 Deflections by Integration of the Bending-Moment

Equation 817

9.4 Deflections by Integration of the Shear-Force and Load

Equations 828

9.5 Method of Superposition 833

9.6 Moment-Area Method 842

9.7 Nonprismatic Beams 850

9.8 Strain Energy of Bending 855

*9.9 Castigliano’s Theorem 860

*9.10 Deflections Produced by Impact 872

*9.11 Temperature Effects 874

Chapter Summary and Review 878

Problems 880

*Advanced topics

10 Statically Indeterminate Beams

10.1 Introduction 910

10.2 Types of Statically Indeterminate Beams 910

10.3 Analysis by the Differential Equations of the Deflection

Curve 913

10.4 Method of Superposition 919

*10.5 Temperature Effects 933

*10.6 Longitudinal Displacements at the Ends of a Beam 940

Chapter Summary and Review 943

Problems 945

*Advanced topics

11 Columns

11.1 Introduction 964

11.2 Buckling and Stability 964

11.3 Columns with Pinned Ends 972

11.4 Columns with Other Support Conditions 981

11.5 Columns with Eccentric Axial Loads 990

11.6 The Secant Formula for Columns 995

11.7 Elastic and Inelastic Column Behavior 1000

11.8 Inelastic Buckling 1002

Chapter Summary and Review 1008

Problems 1011