Textbook

# Mechanics of Materials, 3rd Edition

## Description

The core concepts of equilibrium, force-temperature-deformation behavior of materials, and geometry of deformation are central to a students understanding of mechanics of materials. The third edition of Roy Craig’s Mechanics of Materials maintains its signature clear focus on these core concepts while showing students how to approach and solve problems with his four-step problem solving methodology.

With newly revised and updated homework problems, this edition brings on an award-winning software program, MD Solids, to reinforce visualization using animations, tutorials, and examples. In addition, new chapter summary tables help readers check their understanding of key concepts and key equations to increase student retention.

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1 INTRODUCTION TO MECHANICS OF MATERIALS 1

1.1 What Is Mechanics of Materials? 1

(Includes Color-Photo Insert)

1.2 The Fundamental Equations of Deformable-Body Mechanics 4

1.3 Problem-Solving Procedures 6

1.4 Review of Static Equilibrium; Equilibrium of Deformable Bodies 8

1.5 Problems 17

Chapter 1 Review 21

2 STRESS AND STRAIN; INTRODUCTION TO DESIGN 22

2.1 Introduction 22

2.2 Normal Stress 23

2.3 Extensional Strain; Thermal Strain 31

2.4 Stress-Strain Diagrams; Mechanical Properties of Materials 37

2.5 Elasticity and Plasticity; Temperature Effects 45

2.6 Linear Elasticity; Hooke’s Law and Poisson’s Ratio 48

2.7 Shear Stress and Shear Strain; Shear Modulus 51

2.8 Introduction to Design—Axial Loads and Direct Shear 57

2.9 Stresses on an Inclined Plane in an Axially Loaded Member 65

2.10 Saint-Venant’s Principle 67

2.11 Hooke’s Law for Plane Stress; The Relationship Between E and G 69

2.12 General Definitions of Stress and Strain 72

*2.13 Cartesian Components of Stress; Generalized Hooke’s Law for Isotropic Materials 82

*2.14 Mechanical Properties of Composite Materials 87

2.15 Problems 89

Chapter 2 Review 113

3 AXIAL DEFORMATION 118

3.1 Introduction 118

3.2 Basic Theory of Axial Deformation 118

3.3 Examples of Nonuniform Axial Deformation 126

3.4 Statically Determinate Structures 136

3.5 Statically Indeterminate Structures 143

3.6 Thermal Effects on Axial Deformation 152

3.7 Geometric ‘‘Misfits’’ 163

3.8 Displacement-Method Solution of Axial-Deformation Problems 168

*3.9 Force-Method Solution of Axial- Deformation Problems 180

*3.10 Introduction to the Analysis of Planar Trusses 189

*3.11 Inelastic Axial Deformation 197

3.12 Problems 209

Chapter 3 Review 234

4 TORSION 237

4.1 Introduction 237

4.2 Torsional Deformation of Circular Bars 238

4.3 Torsion of Linearly Elastic Circular Bars 241

4.4 Stress Distribution in Circular Torsion Bars; Torsion Testing 249

4.5 Statically Determinate Assemblages of Uniform Torsion Members 253

4.6 Statically Indeterminate Assemblages of Uniform Torsion Members 258

*4.7 Displacement-Method Solution of Torsion Problems 266

4.8 Power-Transmission Shafts 272

*4.9 Thin-Wall Torsion Members 275

*4.10 Torsion of Noncircular Prismatic Bars 280

*4.11 Inelastic Torsion of Circular Rods 284

4.12 Problems 290

Chapter 4 Review 307

5 EQUILIBRIUM OF BEAMS 309

5.1 Introduction 309

5.2 Equilibrium of Beams Using Finite Free-Body Diagrams 314

5.3 Equilibrium Relationships Among Loads Shear Force and Bending Moment 318

5.4 Shear-Force and Bending-Moment Diagrams: Equilibrium Method 321

5.5 Shear-Force and Bending-Moment Diagrams: Graphical Method 326

*5.6 Discontinuity Functions to Represent Loads Shear and Moment 333

5.7 Problems 340

Chapter 5 Review 348

6 STRESSES IN BEAMS 351

6.1 Introduction 351

6.2 Strain-Displacement Analysis 354

6.3 Flexural Stress in Linearly Elastic Beams 360

6.4 Design of Beams for Strength 369

6.5 Flexural Stress in Nonhomogeneous Beams 375

*6.6 Unsymmetric Bending 383

*6.7 Inelastic Bending of Beams 392

6.8 Shear Stress and Shear Flow in Beams 402

6.9 Limitations on the Shear-Stress Formula 408

6.10 Shear Stress in Thin-Wall Beams 411

6.11 Shear in Built-Up Beams 421

*6.12 Shear Center 425

6.13 Problems 432

Chapter 6 Review 460

7 DEFLECTION OF BEAMS 463

7.1 Introduction 463

7.2 Differential Equations of the Deflection Curve 464

7.3 Slope and Deflection by Integration—Statically Determinate Beams 470

7.4 Slope and Deflection by Integration—Statically Indeterminate Beams 483

*7.5 Use of Discontinuity Functions to Determine Beam Deflections 488

7.6 Slope and Deflection of Beams: Superposition Method 495

*7.7 Slope and Deflection of Beams: Displacement Method 513

7.8 Problems 520

Chapter 7 Review 539

8 TRANSFORMATION OF STRESS AND STRAIN; MOHR’S CIRCLE 541

8.1 Introduction 541

8.2 Plane Stress 542

8.3 Stress Transformation for Plane Stress 544

8.4 Principal Stresses and Maximum Shear Stress 551

8.5 Mohr’s Circle for Plane Stress 557

8.6 Triaxial Stress; Absolute Maximum Shear Stress 564

8.7 Plane Strain 571

8.8 Transformation of Strains in a Plane 572

8.9 Mohr’s Circle for Strain 576

8.10 Measurement of Strain; Strain Rosettes 582

*8.11 Analysis of Three-Dimensional Strain 587

8.12 Problems 588

Chapter 8 Review 601

9.1 Introduction 604

9.2 Thin-Wall Pressure Vessels 605

9.3 Stress Distribution in Beams 611

9.4 Stresses Due to Combined Loads 616

9.5 Problems 625

Chapter 9 Review 633

10 BUCKLING OF COLUMNS 635

10.1 Introduction 635

10.2 The Ideal Pin-Ended Column; Euler Buckling Load 638

10.3 The Effect of End Conditions on Column Buckling 644

*10.5 Imperfections in Columns 657

*10.6 Inelastic Buckling of Ideal Columns 658

10.7 Design of Centrally Loaded Columns 662

10.8 Problems 668

Chapter 10 Review 681

11 ENERGY METHODS 683

11.1 Introduction 683

11.2 Work and Strain Energy 684

11.4 Work-Energy Principle for Calculating Deflections 697

11.5 Castigliano’s Second Theorem; The Unit-Load Method 702

*11.6 Virtual Work 713

*11.7 Strain-Energy Methods 717

*11.8 Complementary-Energy Methods 722

11.10 Problems 737

Chapter 11 Review 751

12 SPECIAL TOPICS RELATED TO DESIGN 753

12.1 Introduction 753

12.2 Stress Concentrations 753

*12.3 Failure Theories 760

*12.4 Fatigue and Fracture 768

12.5 Problems 772

Chapter 12 Review 777

A NUMERICAL ACCURACY; APPROXIMATIONS A-1

A.1 Numerical Accuracy; Significant Digits A-1

A.2 Approximations A-2

B SYSTEMS OF UNITS B-1

B.1 Introduction B-1

B.2 SI Units B-1

B.3 U.S. Customary Units; Conversion of Units B-3

C GEOMETRIC PROPERTIES OF PLANE AREAS C-1

C.1 First Moments of Area; Centroid C-1

C.2 Moments of Inertia of an Area C-4

C.3 Product of Inertia of an Area C-8

C.4 Area Moments of Inertia About Inclined Axes; Principal Moments of Inertia C-10

D SECTION PROPERTIES OF SELECTED STRUCTURAL SHAPES D-1

D.1 Properties of Steel Wide-Flange (W) Shapes (U.S. Customary Units) D-2

D.2 Properties of Steel Wide-Flange (W) Shapes (SI Units) D-3

D.3 Properties of American Standard (S) Beams (U.S. Customary Units) D-4

D.4 Properties of American Standard (C) Channels (U.S. Customary Units) D-5

D.5 Properties of Steel Angle Sections—Equal Legs (U.S. Customary Units) D-6

D.6 Properties of Steel Angle Sections—Unequal Legs (U.S. Customary Units) D-7

D.7 Properties of Standard-Weight Steel Pipe (U.S. Customary Units) D-8

D.8 Properties of Structural Lumber (U.S. Customary Units) D-9

D.9 Properties of Aluminum Association Standard I-Beams (U.S. Customary Units) D-10

D.10 Properties of Aluminum Association Standard Channels (U.S. Customary Units) D-11

E DEFLECTIONS AND SLOPES OF BEAMS; FIXED-END ACTIONS E-1

E.1 Deflections and Slopes of Cantilever Uniform Beams E-1

E.2 Deflections and Slopes of Simply Supported Uniform Beams E-3

E.3 Fixed-End Actions for Uniform Beams E-4

F MECHANICAL PROPERTIES OF SELECTED ENGINEERING MATERIALS F-1

F.1 Specific Weight and Mass Density F-2

F.2 Modulus of Elasticity Shear Modulus of Elasticity and Poisson’s Ratio F-3

F.3 Yield Strength Ultimate Strength Percent Elongation in 2 Inches and Coefficient of Thermal Expansion F-4

G COMPUTATIONAL MECHANICS G-1

G.1 MDSolids G-1

ANSWERS TO SELECTED ODDNUMBERED PROBLEMS ANS-1

REFERENCES R-1

INDEX I-1

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## New To This Edition

• New chapter summary tables help readers confirm their grasp of the key concepts in each chapter, as well providing the key equation(s) that map to each of those concepts along with a guide to where the student can review the details
• MD Solids, an award-winning software package helps students gain visualization skills using animations, tutorials and other learning/problem-solving tools, along with numerous examples
• New and revised homework problems have been provided – approximately one third of the end of chapter problems are either new and/or revised
• Reorganization of Chapter 3, with the topic of statically indeterminate structures introduced in the 'classical' way, but integrating coverage of the Displacement Method while also offering a separate, optional section on force method. There is still a strong emphasis on the three distinct equations of deformable-body mechanics – equilibrium, force-deformation behavior, and geometry of behavior, but this coverage now focuses on procedures and then proceeds to flow charts
• Newly updated coverage of both wire rope and composites
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• Emphasis on the Three Key Concepts of Mechanics of Solids. Throughout the text, Craig utilizes a framework that helps students solve problems by identifying the key FUNDAMENTAL equations that may be considered, via the three key concepts OF:
• Equilibrium
• Force-Temperature-Deformation Behavior of Materials
• Geometry of Deformation
• Consistent four-step problem-solving procedure is utilized throughout the text , helping students to achieve greater accuracy while developing their skills
• Emphasis on logical and consistent sign conventions for problems in axial deformation, torsion, and bending
• Sound introductions of the displacement method and force method problem-solving procedures provide readers with a foundation for future courses in structures and/or Finite Element Analysis
• Emphasis on topics related to energy with an entire centralized coverage of all energy-related topics into one chapter (Chapter 11)
• Strong focus on design issues, including computer-assisted design and specified design-oriented problems
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Instructors Resources
Wiley Instructor Companion Site
MDSolids Software
Solutions Manual
Image Gallery
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Students Resources
Wiley Student Companion Site
MDSolids Software
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Purchase Options
Wiley E-Text
Mechanics of Materials, 3rd Edition
ISBN : 978-0-470-91200-3
864 pages