Mechanics of Materials presents the theory and practice of mechanics of materials in a straight-forward, student-friendly manner that addresses the learning styles of today's students without sacrificing rigor or depth in the presentation of topics. From basic concepts of stress and strain to more advanced topics like beam deflections and combined loads, this book provides students with everything they need to embark on successful careers in materials and mechanical engineering. Laying an emphasis on critical thinking forms, this text focuses on helping learners develop practical skills, encouraging them to recognize fundamental concepts relevant to specific situations, identify equations needed to solve problems, and engage with literature in the field.
This International Adaptation has been thoroughly updated to use SI units. This edition strengthens the coverage by including methods such as moment area method and conjugate beam method for calculating deflection of beams, and a method for calculating shear stresses in beams of triangular cross section. Additionally, it includes Learning Assessments in a range of difficulty suitable for learners at various stages of development which elucidate and reinforce the course concepts.
Table of Contents
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)
