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Mechanics of Materials: An Integrated Learning System, 3rd Edition

June 2012, ©2013
Mechanics of Materials: An Integrated Learning System, 3rd Edition (EHEP002335) cover image

Philpot’s Mechanics of Materials: An Integrated Learning System, 3rd Edition, helps engineering students visualize key mechanics of materials concepts better than any text available, following a sound problem solving methodology while thoroughly covering all the basics. The third edition retains seamless integration with the author’s award winning MecMovies software.  More than 40% of the problems are new and/or revised. New coverage is included on sheer stress in beams as well as energy methods. Content has also been revised throughout the text to provide students with the latest information in the field.

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Chapter 1: Stress

1.1 Introduction 1

1.2 Normal Stress Under Axial Loading 2

1.3 Direct Shear Stress 7

1.4 Bearing Stress 12

1.5 Stresses on Inclined Sections 22

1.6 Equality of Shear Stresses on Perpendicular Planes 24

Chapter 2: Strain

2.1 Displacement, Deformation, and the Concept of Strain 31

2.2 Normal Strain 32

2.3 Shear Strain 39

2.4 Thermal Strain 43

Chapter 3: Mechanical Properties of Materials

3.1 The Tension Test 47

3.2 The Stress–Strain Diagram 50

3.3 Hooke’s Law 58

3.4 Poisson’s Ratio 58

Chapter 4: Design Concepts

4.1 Introduction 69

4.2 Types of Loads 70

4.3 Safety 71

4.4 Allowable Stress Design 72

4.5 Load and Resistance Factor Design 83

Chapter 5: Axial Deformation

5.1 Introduction 89

5.2 Saint-Venant’s Principle 90

5.3 Deformations in Axially Loaded Bars 92

5.4 Deformations in a System of Axially Loaded Bars 101

5.5 Statically Indeterminate Axially Loaded Members 109

5.6 Thermal Effects on Axial Deformation 128

5.7 Stress Concentrations 140

Chapter 6: Torsion

6.1 Introduction 147

6.2 Torsional Shear Strain 149

6.3 Torsional Shear Stress 150

6.4 Stresses on Oblique Planes 152

6.5 Torsional Deformations 154

6.6 Torsion Sign Conventions 155

6.7 Gears in Torsion Assemblies 168

6.8 Power Transmission 175

6.9 Statically Indeterminate Torsion Members 182

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 201

6.11 Torsion of Noncircular Sections 204

6.12 Torsion of Thin-Walled Tubes:

Shear Flow 207

Chapter 7: Equilibrium of Beams

7.1 Introduction 213

7.2 Shear and Moment in Beams 215

7.3 Graphical Method for Constructing Shear and Moment Diagrams 227

7.4 Discontinuity Functions to Represent Load, Shear, and Moment 248

Chapter 8: Bending

8.1 Introduction 261

8.2 Flexural Strains 263

8.3 Normal Stresses in Beams 264

8.4 Analysis of Bending Stresses in Beams 279

8.5 Introductory Beam Design for Strength 292

8.6 Flexural Stresses in Beams of Two Materials 297

8.7 Bending Due to Eccentric Axial Load 310

8.8 Unsymmetric Bending 322

8.9 Stress Concentrations Under Flexural Loadings 332

Chapter 9: Shear Stress in Beams

9.1 Introduction 337

9.2 Resultant Forces Produced by Bending Stresses 337

9.3 The Shear Stress Formula 345

9.4 The First Moment of Area Q 349

9.5 Shear Stresses in Beams of Rectangular Cross Section 351

9.6 Shear Stresses in Beams of Circular Cross Section 358

9.7 Shear Stresses in Webs of Flanged Beams 358

9.8 Shear Flow in Built-Up Members 369

9.9 Shear Stress and Shear Flow in Thin-Walled Members 382

9.10 Shear Centers of Thin-Walled Open Sections 393

Chapter 10: Beam Deflections

10.1 Introduction 409

10.2 Moment-Curvature Relationship 410

10.3 The Differential Equation of the Elastic Curve 410

10.4 Deflections by Integration of a Moment Equation 414

10.5 Deflections by Integration of Shear-Force or Load Equations 429

10.6 Deflections Using Discontinuity Functions 433

10.7 Method of Superposition 443

Chapter 11: Statically Indeterminate Beams

11.1 Introduction 469

11.2 Types of Statically Indeterminate Beams 469

11.3 The Integration Method 471

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 478

11.5 The Superposition Method 486

Chapter 12: Stress Transformations

12.1 Introduction 507

12.2 Stress at a General Point in an Arbitrarily Loaded Body 508

12.3 Equilibrium of the Stress Element 510

12.4 Plane Stress 511

12.5 Generating the Stress Element 511

12.6 Equilibrium Method for Plane Stress Transformations 517

12.7 General Equations of Plane Stress Transformation 520

12.8 Principal Stresses and Maximum Shear Stress 528

12.9 Presentation of Stress Transformation Results 535

12.10 Mohr’s Circle for Plane Stress 543

12.11 General State of Stress at a Point 562

Chapter 13: Strain Transformations

13.1 Introduction 569

13.2 Two-Dimensional or Plane Strain 570

13.3 Transformation Equations for Plane Strain 571

13.4 Principal Strains and Maximum Shearing Strain 576

13.5 Presentation of Strain Transformation Results 578

13.6 Mohr’s Circle for Plane Strain 581

13.7 Strain Measurement and Strain Rosettes 585

13.8 Generalized Hooke’s Law for Isotropic Materials 591

Chapter 14: Thin-Walled Pressure Vessels

14.1 Introduction 607

14.2 Spherical Pressure Vessels 608

14.3 Cylindrical Pressure Vessels 610

14.4 Strains in Pressure Vessels 613

Chapter 15: Combined Loads

15.1 Introduction 623

15.2 Combined Axial and Torsional Loads 623

15.3 Principal Stresses in a Flexural Member 629

15.4 General Combined Loadings 643

15.5 Theories of Failure 668

Chapter 16: Columns

16.1 Introduction 681

16.2 Buckling of Pin-Ended Columns 684

16.3 The Effect of End Conditions on Column Buckling 696

16.4 The Secant Formula 707

16.5 Empirical Column Formulas—Centric Loading 714

16.6 Eccentrically Loaded Columns 726

Chapter 17: Energy Methods

17.1 Introduction 737

17.2 Work and Strain Energy 738

17.3 Elastic Strain Energy for Axial Deformation 742

17.4 Elastic Strain Energy for Torsional Deformation 744

17.5 Elastic Strain Energy for Flexural Deformation 746

17.6 Impact Loading 751

17.7 Work-Energy Method for Single Loads 769

17.8 Method of Virtual Work 774

17.9 Defl ections of Trusses by the Virtual-Work Method 779

17.10 Defl ections of Beams by the Virtual-Work Method 786

17.11 Castigliano’s Second Theorem 800

17.12 Calculating Defl ections of Trusses by Castigliano’s Theorem 802

17.13 Calculating Defl ections of Beams by Castigliano’s Theorem 807

Appendix A Geometric Properties of an Area 819

A.1 Centroid of an Area 819

A.2 Moment of Inertia for an Area 823

A.3 Product of Inertia for an Area 828

A.4 Principal Moments of Inertia 831

A.5 Mohr’s Circle for Principal Moments of Inertia 835

Appendix B Geometric Properties of Structural Steel Shapes 839

Appendix C Table of Beam Slopes and Deflections 853

Appendix D Average Properties of Selected Materials 857

Answers to Odd Numbered Problems 861

Index 885

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  • Additional material on shear stress in beams:  Two new sections have been added in Chapter 9 to discuss additional topics related to shear stress in beams.  These sections are:
    • 9.9 Shear Stress and Shear Flow in Thin-Walled Members
    • 9.10 Shear Centers of Thin-Walled Open Sections
  • New coverage of energy methods:  Chapter 17 – Energy Methods has been developed to discuss the application of work and strain energy principles, virtual work principles, and Castigliano’s Theorem to solid mechanics problems.
  • Updated coverage to match the latest design standards:  Design equations in Chapter 16 for the critical buckling stress of structural steel columns have been updated to conform to the latest provisions of ANSI/AISC 360-10 Specification for Structural Steel Buildings.
  • New and revised homework problems:  More than 40% of the problems are new or revised, broadening the variety of problems available for many topics.
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  • Focuses On Visual Learning: The illustrations use color, shading, perspective, and dimension to clearly convey concepts while striving to place these concepts in the context of real world components and objects.  These illustrations have been prepared by an engineer and educator (the author), to train future engineers.
  • MecMovies: The text integrates computer-based instruction with the addition of the MecMovies , a web-based application designed by the author to promote visual learning and a deep, intuitive  understanding of the concepts.
  • Problem-solving schema: The   book and web-based features are designed to assist students in organizing and categorizing concepts and problem-solving procedures. 
  • Style and clarity of examples: This textbook places great emphasis on the presentation and quality of example problems.  The author’s commentary explains why various steps are taken and describes the rationale for each step in a solution process while the accompanying illustrations help build the mental imagery needed to transfer the concepts to differingsituations.
  • Homework philosophy: This textbook includes over 1,300 homework problems in a range of difficulty.
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Mechanics of Materials: An Integrated Learning System, 3rd Edition
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July 2012, ©2013
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