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 120

2.2 Changes in Lengths of Axially Loaded Members 120

2.3 Changes in Lengths under Nonuniform Conditions 128

2.4 Statically Indeterminate Structures 142

2.5 Thermal Effects, Misfits, and Prestrains 155

2.6 Stresses on Inclined Sections 174

2.7 Strain Energy 186

*2.8 Impact Loading 197

*2.9 Repeated Loading and Fatigue 205

*2.10 Stress Concentrations 207

*2.11 Nonlinear Behavior 214

*2.12 Elastoplastic Analysis 218

Chapter Summary and Review 225

Problems 227

* Specialized and/or advanced topics

3.1 Introduction 274

3.2 Torsional Deformations of a Circular Bar 274

3.3 Circular Bars of Linearly Elastic Materials 277

3.4 Nonuniform Torsion 290

3.5 Stresses and Strains in Pure Shear 302

3.6 Relationship Between Moduli of Elasticity E and G 309

3.7 Transmission of Power by Circular Shafts 311

3.8 Statically Indeterminate Torsional Members 315

3.9 Strain Energy in Torsion and Pure Shear 319

3.10 Torsion of Noncircular Prismatic Shafts 326

3.11 Thin-Walled Tubes 336

*3.12 Stress Concentrations in Torsion 344

Chapter Summary and Review 349

Problems 352

*Specialized and/or advanced topics

4 Shear Forces and Bending Moments

4.1 Introduction 377

4.2 Types of Beams, Loads, and Reactions 378

4.3 Shear Forces and Bending Moments 388

4.4 Relationships Among Loads, Shear Forces, and Bending

Moments 396

4.5 Shear-Force and Bending-Moment Diagrams 400

Chapter Summary and Review 427

poblems 429

5.1 Introduction 446

5.2 Pure Bending and Nonuniform Bending 446

5.3 Curvature of a Beam 447

5.4 Longitudinal Strains in Beams 449

5.5 Normal Stresses in Beams (Linearly Elastic Materials) 453

5.6 Design of Beams for Bending Stresses 466

5.7 Nonprismatic Beams 476

5.8 Shear Stresses in Beams of Rectangular Cross Section 480

5.9 Shear Stresses in Beams of Circular Cross Section 488

5.10 Shear Stresses in the Webs of Beams with Flanges 491

*5.11 Built-Up Beams and Shear Flow 498

*5.12 Beams with Axial Loads 502

*5.13 Stress Concentrations in Bending 509

Chapter Summary and Review 514

Problems 518

*Specialized and/or advanced topics

6 Stresses in Beams (Advanced Topics)

6.1 Introduction 554

6.2 Composite Beams 554

6.3 Transformed-Section Method 563

6.4 Doubly Symmetric Beams with Inclined Loads 571

6.5 Bending of Unsymmetric Beams 578

6.6 The Shear-Center Concept 589

6.7 Shear Stresses in Beams of Thin-Walled Open Cross Sections 590

6.8 Shear Stresses in Wide-Flange Beams 593

6.9 Shear Centers of Thin-Walled Open Sections 597

*6.10 Elastoplastic Bending 605

Chapter Summary and Review 614

Problems 616

*Specialized or Advanced Topics

7 Analysis of Stress and Strain

7.1 Introduction 640

7.2 Plane Stress 640

7.3 Principal Stresses and Maximum Shear Stresses 648

7.4 Mohr’s Circle for Plane Stress 656

7.5 Hooke’s Law for Plane Stress 669

7.6 Triaxial Stress 675

7.7 Plane Strain 679

Chapter Summary and Review 694

Problems 697

8 Applications of Plane Stress

(Pressure Vessels, Beams, and Combined Loadings

8.1 Introduction 720

8.2 Spherical Pressure Vessels 720

8.3 Cylindrical Pressure Vessels 726

8.4 Maximum Stresses in Beams 733

8.5 Combined Loadings 741

Chapter Summary and Review 766

Problems 768

9 Deflections of Beams

9.1 Introduction 788

9.2 Differential Equations of the Deflection Curve 788

9.3 Deflections by Integration of the Bending-Moment

Equation 793

9.4 Deflections by Integration of the Shear-Force and Load

Equations 804

9.5 Method of Superposition 809

9.6 Moment-Area Method 818

9.7 Nonprismatic Beams 826

9.8 Strain Energy of Bending 831

*9.9 Castigliano’s Theorem 836

*9.10 Deflections Produced by Impact 848

*9.11 Temperature Effects 850

Chapter Summary and Review 854

Problems 856

*Advanced topics

10 Statically Indeterminate Beams

10.1 Introduction 884

10.2 Types of Statically Indeterminate Beams 884

10.3 Analysis by the Differential Equations of the Deflection

Curve 887

10.4 Method of Superposition 893

*10.5 Temperature Effects 907

*10.6 Longitudinal Displacements at the Ends of a Beam 914

Chapter Summary and Review 917

Problems 919

*Advanced topics

11 Columns

11.1 Introduction 934

11.2 Buckling and Stability 934

11.3 Columns with Pinned Ends 942

11.4 Columns with Other Support Conditions 951

11.5 Columns with Eccentric Axial Loads 960

11.6 The Secant Formula for Columns 965

11.7 Elastic and Inelastic Column Behavior 970

11.8 Inelastic Buckling 972

11.9 Design Formulas for Columns 977

Chapter Summary and Review 993

Problems 996