Mechanics of Materials, International Adaptation

TIMOTHY A. PHILPOT was an Associate Professor in the Department of Civil, Architectural, and Environmental Engineering at the Missouri University of Science and Technology (formerly known as the University of Missouri–Rolla). He received his B.S. degree from the University of Kentucky in 1979, his M.Engr. degree from Cornell University in 1980, and his Ph.D. degree from Purdue University in 1992. In the 1980s, he worked as a structural engineer in the offshore construction industry in New Orleans, London, Houston, and Singapore. He joined the faculty at Murray State University in 1986 and Missouri S&T in 1999. He passed away unexpectedly in 2017. Dr. Philpot's primary areas of teaching and research were in engineering mechanics and the development of interactive, multimedia educational software for the introductory engineering mechanics courses. JEFFERY S. THOMAS is an Associate Teaching Professor in the Department of Civil, Architectural, and Environmental Engineering at Missouri University of Science and Technology (formerly known as the University of Missouri-Rolla). He received his B.S. (1995) and M.S. (1996) degrees in mechanical engineering and his Ph.D. (2009) in engineering mechanics from Missouri S&T. He has been on the faculty at Missouri S&T since 1996 and has assisted in the joint engineering program between Missouri S&T and Missouri State University since 2014. His educational research has focused on computer-based assessments, online content delivery, and measurement of student engagement. He is a licensed professional engineer and a member of the American Society for Engineering Education.

1 Stress 1

1.1 Introduction 1

1.2 Normal Stress Under Axial Loading 2

1.3 Direct Shear Stress 8

1.4 Bearing Stress 14

1.5 Stresses on Inclined Sections 18

1.6 Equality of Shear Stresses on Perpendicular Planes 20

2 Strain 31

2.1 Displacement, Deformation, and the Concept of Strain 31

2.2 Normal Strain 32

2.3 Shear Strain 37

2.4 Thermal Strain 41

3 Mechanical Properties of Materials 49

3.1 The Tension Test 49

3.2 The Stress-Strain Diagram 52

3.3 Hooke's Law 61

3.4 Poisson's Ratio 62

4 Design Concepts 77

4.1 Introduction 77

4.2 Types of Loads 78

4.3 Safety 79

4.4 Allowable Stress Design 80

4.5 Load and Resistance Factor Design 87

5 Axial Deformation 97

5.1 Introduction 97

5.2 Saint-Venant's Principle 98

5.3 Deformations in Axially Loaded Bars 100

5.4 Deformations in a System of Axially Loaded Bars 107

5.5 Statically Indeterminate Axially Loaded Members 114

5.6 Thermal Effects on Axial Deformation 125

5.7 Stress Concentrations 132

6 Torsion 149

6.1 Introduction 149

6.2 Torsional Shear Strain 151

6.3 Torsional Shear Stress 152

6.4 Stresses on Oblique Planes 154

6.5 Torsional Deformations 156

6.6 Torsion Sign Conventions 158

6.7 Gears in Torsion Assemblies 167

6.8 Power Transmission 172

6.9 Statically Indeterminate TorsionMembers 176

6.10 Stress Concentrations in Circular Shafts Under Torsional Loadings 188

6.11 Torsion of Noncircular Sections 191

6.12 Torsion of Thin-Walled Tubes: Shear Flow 195

7 Equilibrium of Beams 209

7.1 Introduction 209

7.2 Shear and Moment in Beams 211

7.3 Graphical Method for Constructing Shear and Moment Diagrams 222

7.4 Discontinuity Functions to Represent Load, Shear, and Moment 239

8 Bending 257

8.1 Introduction 257

8.2 Flexural Strains 259

8.3 Normal Stresses in Beams 260

8.4 Analysis of Bending Stresses in Beams 272

8.5 Introductory Beam Design for Strength 279

8.6 Flexural Stresses in Beams of Two Materials 284

8.7 Bending Due to an Eccentric Axial Load 295

8.8 Unsymmetric Bending 301

8.9 Stress Concentrations Under Flexural Loadings 311

8.10 Bending of Curved Bars 314

9 Shear Stress In Beams 339

9.1 Introduction 339

9.2 Resultant Forces Produced by Bending Stresses 339

9.3 The Shear Stress Formula 344

9.4 The First Moment of Area, Q 350

9.5 Shear Stresses in Beams of Rectangular Cross Section 352

9.6 Shear Stresses in Beams of Circular Cross Section 357

9.7 Shear Stresses in Beams of Triangular Cross Section 359

9.8 Shear Stresses in Webs of Flanged Beams 363

9.9 Shear Flow in Built-Up Members 366

9.10 Shear Stress and Shear Flow in Thin-Walled Members 375

9.11 Shear Centers of Thin-Walled Open Sections 393

10 Beam Deflections 421

10.1 Introduction 421

10.2 Moment-Curvature Relationship 422

10.3 The Differential Equation of the Elastic Curve 422

10.4 Determining Deflections by Integration of a Moment Equation 426

10.5 Determining Deflections by Integration of Shear-Force or Load Equations 438

10.6 Determining Deflections by Using Discontinuity Functions 441

10.7 Determining Deflections by the Method of Superposition 448

10.8 Determining Deflections by Using Moment Area Method 464

10.9 Determining Deflections by Using Conjugate Beam Method 466

11 Statically Indeterminate Beams 483

11.1 Introduction 483

11.2 Types of Statically Indeterminate Beams 483

11.3 The Integration Method 485

11.4 Use of Discontinuity Functions for Statically Indeterminate Beams 491

11.5 The Superposition Method 496

12 Stress Transformations 519

12.1 Introduction 519

12.2 Stress at a General Point in an Arbitrarily Loaded Body 519

12.3 Equilibrium of the Stress Element 522

12.4 Plane Stress 523

12.5 Generating the Stress Element 524

12.6 Equilibrium Method for Plane Stress Transformations 527

12.7 General Equations of Plane Stress Transformation 530

12.8 Principal Stresses and Maximum Shear Stress 536

12.9 Presentation of Stress Transformation Results 543

12.10 Mohr's Circle for Plane Stress 550

12.11 General State of Stress at a Point 566

13 Strain Transformations 587

13.1 Introduction 587

13.2 Plane Strain 588

13.3 Transformation Equations for Plane Strain 589

13.4 Principal Strains and Maximum Shearing Strain 593

13.5 Presentation of Strain Transformation Results 594

13.6 Mohr's Circle for Plane Strain 598

13.7 Strain Measurement and Strain Rosettes 600

14 Pressure Vessels 609

14.1 Introduction 609

14.2 Thin-Walled Spherical Pressure Vessels 610

14.3 Thin-Walled Cylindrical Pressure Vessels 613

14.4 Strains in Thin-Walled Pressure Vessels 617

14.5 Stresses in Thick-Walled Cylinders 619

14.6 Deformations in Thick-Walled Cylinders 627

14.7 Interference Fits 630

15 Combined Loads 641

15.1 Introduction 641

15.2 Combined Axial and Torsional Loads 641

15.3 Principal Stresses in a Flexural Member 644

15.4 General Combined Loadings 653

15.5 Theories of Failure 669

16 Columns 691

16.1 Introduction 691

16.2 Buckling of Pin-Ended Columns 694

16.3 The Effect of End Conditions on Column Buckling 702

16.4 The Secant Formula 712

16.5 Empirical Column Formulas--Centric Loading 717

16.6 Eccentrically Loaded Columns 725

17 Energy Methods 743

17.1 Introduction 743

17.2 Work and Strain Energy 744

17.3 Elastic Strain Energy for Axial Deformation 748

17.4 Elastic Strain Energy for Torsional Deformation 750

17.5 Elastic Strain Energy for Flexural Deformation 752

17.6 Impact Loading 756

17.7 Work-Energy Method for Single Loads 770

17.8 Method of Virtual Work 773

17.9 Deflections of Trusses by the Virtual-Work Method 778

17.10 Deflections of Beams by the Virtual-Work Method 786

17.11 Castigliano's Second Theorem 795

17.12 Calculating Deflections of Trusses by Castigliano's Theorem 797

17.13 Calculating Deflections of Beams by Castigliano's Theorem 803

Appendix A Geometric Properties of an Area 823

A.1 Centroid of an Area 823

A.2 Moment of Inertia for an Area 826

A.3 Product of Inertia for an Area 830

A.4 Principal Moments of Inertia 833

A.5 Mohr's Circle for Principal Moments of Inertia 837

Appendix B Geometric Properties of Structural Steel Shapes 841

Appendix C Table of Beam Slopes and Deflections 847

Appendix D Average Properties of Selected Materials 851

Appendix E Generalized Hooke's Law for Isotropic and Orthotropic Materials 855

E.1 Generalized Hooke's Law for Isotropic Materials 855

E.2 Generalized Hooke's Law for Orthotropic Materials 872

Appendix F Fundamental Mechanics of Materials Equations 877

Answers To Odd Numbered Problems (Available Online)