Textbook
Mechanics of Materials: An Integrated Learning System, 3rd EditionJune 2012, ©2013

Philpot’s Mechanics of Materials: An Integrated Learning System, 3^{rd} 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.
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 SaintVenant’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 ThinWalled 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 BuiltUp Members 369
9.9 Shear Stress and Shear Flow in ThinWalled Members 382
9.10 Shear Centers of ThinWalled Open Sections 393
Chapter 10: Beam Deflections
10.1 Introduction 409
10.2 MomentCurvature 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 ShearForce 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 TwoDimensional 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: ThinWalled 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 PinEnded 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 WorkEnergy Method for Single Loads 769
17.8 Method of Virtual Work 774
17.9 Defl ections of Trusses by the VirtualWork Method 779
17.10 Defl ections of Beams by the VirtualWork 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
 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 ThinWalled Members
 9.10 Shear Centers of ThinWalled 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 36010 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.
 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 computerbased instruction with the addition of the MecMovies , a webbased application designed by the author to promote visual learning and a deep, intuitive understanding of the concepts.
 Problemsolving schema: The book and webbased features are designed to assist students in organizing and categorizing concepts and problemsolving 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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