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1 Introduction2

1-1 Engineering and the Mechanics of Materials4

1-2 Units and Numbers5

International System of Units5

U.S.Customary Units5

Use of Numbers6

1-3 Review of Statics6

Free-Body Diagrams6

Equilibrium8

Structures10

CONTENTS11

About the Authors11

Preface13

Centroids15

Distributcd Forces17

Problems21

2 Measures of Stress and Strain28

2-1 Stresses30

Traction,Normal Stress,and Shear Stress30

Average Stresses31

2-2 Strains39

Extensional Strain39

Shear Strain41

Chapter Summary45

Problems46

3 Axially Loaded Bars60

3-1 Stresses in Prismatic Bars62

Stresses on Perpendicular Planes62

Stresses on Oblique Planes68

3-2 Strains in Prismatic Bars72

Axial Strain andModulus ofElasticity72

Lateral Strain and Poisson s Ratio73

3-3 Statically Indeterminate Problems81

Example82

Flexibility and Stiffness Methods83

3-4 Nonprismatic Bars and Distributed Loads91

Bars with Gradually Varying Cross Sections91

Distributed Axial Loads93

3-5 Thermal Strains100

3-6 Material Behavior105

Axial Force Tests105

Other Aspects of Material Behavior110

3-7 Design Issues112

Allowable Stress113

Other Design Considerations113

Chapter Summary114

Problems117

4 Torsion136

4-1 Pure Shear Stress138

State of Stress138

Shear Modulus138

Stresses on Oblique Planes139

4-2 Torsion of Prismatic Circular Bars141

Stresses and Strains141

Polar Moment of Inertia144

Positive Directions of the Torque and Angle of Twist146

4-3 Statically Indeterminate Problems149

4-4 Nonprismatic Bars and Distributed Loads150

Bars with Gradually Varying Cross Sections150

Distributed Torsional Loads153

4-5 Torsiotn of an Elastic-Perfectly Plastic Circular Bar156

4-6 Torsion of Thin-Walled Tubes160

Stress160

Angle of Twist163

Cross Sections167

4-7 Design Issues167

Allowable Stress168

Chapter Summary171

Problems174

5 States of Stress186

5-1 Components of Stress188

5-2 Transformations of Plane Stress191

Coordinate Transformations192

Maximum and Minimum Stresses197

Constructing the Circle206

5-3 Mohr s Circle for Plane Stress206

Why Mohr s Circle Works207

Determining Principal Stresses and the Maximum In-PlaneShear Stress208

5-4 Principal Stresses in Three Dimensions217

General State of Stress218

Triaxial Stress219

5-5 Design IssuesPressure Vessels221

Spherical Vessels221

Cylindrical Vessels223

Allowable Stress227

5-6 Tetrahedron Argument228

Determining the Traction228

Determining the Normal and Shear Stresses230

Chapter Summary233

Problems236

6 States of Strain248

6-1 Components of Strain250

6-2 Transformations of Plane Strain252

Strain Gauge Rosette254

Maximum and Minimum Strains257

6-3 Mohr s Circle for Plane Strain264

Constructing the Circle265

Determining Principal Strains and the Maximum In-Plane Shear Strain266

6-4 Stress-Strain Relations270

Linearly Elastic Materials270

lsotropic Materials271

Chapter Summary279

Problems284

7 Internal Forces and Moments in Beams292

7-1 Axial Force,Shear Force,and Bending Moment294

7-2 Shear Force and Bending Moment Diagrams298

7-3 Equations Relating Distributed Load,Shear Force,and Bending Moment305 Chapter Summary314

Problems315

8 Stresses in Beams322

8-1 Distribution of the Stress324

Normal Stress324

Geometry ofDeformation325

Relation between Normal Stress and Bending Moment328

Beams Subiected to ArbitraryLoads330

8-2 Design Issues338

Cross Sections338

Allowable Stress340

8-3 Composite Beams343

8-4 Elastic-Perfectly Plastic Beams347

8-5 Unsymmetric Cross Sections355

Moment Exerted about a Principal Axis355

Moment Exerted about an Arbitrary Axis358

Shear Stress362

8-6 Distribution of the Average Stress363

Shear Formula363

Rectangular Cross Section366

8-7 Thin-Walled Cross Sections371

8-8 Shear Center377

Chapter Summary385

Problems390

9 Deflections of Beams404

Differential Equation406

9-1 Determination of the Deflection406

Boundary Conditions408

9-2 Statically Indeterminate Beams414

Difierential Equation419

9-3 Deflections Using the Fourth-Order Equation419

Boundary Conditions420

9-4 Method of Superposition424

Chapter Summary429

Problems430

10 Buckling of Columns438

10-1 Euler Buckling Load440

10-2 Other End Conditions447

Analysis of the Deflection447

Effective Length458

10-3 Eccentric Loads461

Analysis of the Deflection461

Secant Formula464

Chapter Summary467

Problems469

11 Energy Methods476

11-1 Work and Energy478

Work478

Strain Energy480

Applications482

11-2 Castigliano s Second Theorem489

Derivation489

Applications491

Chapter Summary496

Problems498

12 Criteria for Failure and Fracture502

12-1 Failure504

Overloads504

Repeated Loads512

12-2 Stress Concentrations520

Axially Loaded Bars520

Torsion521

Bending524

12-3 Fracture527

Overloads and Fast Crack Growth528

Repeated Loads and Slow Crack Growth535

Chapter Summary539

Problems542

Appendices549

A Results from Mathematics549

B Material Properties555

C Centroids and Moments of Inertia559

C-1 Centroids of Areas559

C-2 Composite Areas563

C-3 Moments of Inertia of Areas566

C-4 Parallel Axis Theorems570

C-5 Rotated and Principal Axes577

Problems583

D Properties of Areas589

E Deflections and Slopes of Prismatic Beams593

F Isotropic Stress-Strain Relations599

G Answers to Even-Numbered Problems605

Index623