Mechanics of Materials

Ansel C. Ugural, Ph.D., is Research Professor at New Jersey Institute of Technology. He has held various faculty and administrative positions at Fairleigh Dickinson University, and he taught at the University of Wisconsin. Ugural has considerable industrial experience in both full-time and consulting capacities.

• PREFACE viiLIST OF SYMBOLS xixChapter 1 INTRODUCTION 11.1 Mechanics of Materials 21.2 Scope of the Book 31.3 Methods of Analysis 41.4 Engineering Design 51.5 Review of Static Equilibrium 61.6 Internal Force Resultants 101.7 Problem Formulation and Solution 131.8 Application to Simple Structures 15Chapter Summary 26References 27Chapter 2 CONCEPT OF STRESS 282.1 Introduction 292.2 Internal Axial Forces 292.3 Normal Stress 312.4 Bearing Stress in Connections 372.5 Shearing Stress 382.6 Stresses in Simple Structures 432.7 Allowable Stress and Factor of Safety 522.8 Design of Bars for Axial Loading 562.9 Case Studies 602.10 Stress under General Loading 68Chapter Summary 77References 78Chapter 3 STRAIN AND MATERIAL PROPERTIES 793.1 Introduction 803.2 Deformation 803.3 Strain 813.4 Components of Strain 843.5 Materials 893.6 Stress–Strain Diagrams 903.7 True Stress and True Strain 973.8 Elastic versus Plastic Behavior 983.9 Hooke’s Law 993.10 Poisson’s Ratio 1023.11 Generalized Hooke’s Law 1083.12 Strain Energy 1133.13 Impact Strength 1153.14 Fatigue 1163.15 Permanent Deformation 1193.16 General Properties of Materials 1213.17 Selecting Materials 122Chapter Summary 127References 129Chapter 4 AXIALLY LOADED MEMBERS 1304.1 Introduction 1314.2 Deformation of Axially Loaded Members 1314.3 Statically Indeterminate Structures 1434.4 Method of Superposition 1474.5 Thermal Deformation and Stress 1484.6 Stresses on Inclined Planes 1564.7 Saint-Venant’s Principle 1594.8 Stress Concentrations 1604.9 Ductility and Design 1644.10 Plastic Deformation and Residual Stress 165Chapter Summary 172References 173Chapter 5 TORSION 1745.1 Introduction 1755.2 Deformation of a Circular Shaft 1755.3 The Torsion Formula 1785.4 Axial and Transverse Shear Stresses 1805.5 Stresses on Inclined Planes 1835.6 Angle of Twist 1885.7 Statically Indeterminate Shafts 1965.8 Design of Circular Shafts 2025.9 Stress Concentrations 2065.10 Inelastic Torsion of Circular Shafts 2115.11 Torsion of Noncircular Solid Bars 2155.12 Thin-Walled Hollow Members 218Chapter Summary 228References 230Chapter 6 SHEAR AND MOMENT IN BEAMS 2316.1 Introduction 2326.2 Classification of Beams 2326.3 Calculation of Beam Reactions 2336.4 Shear Force and Bending Moment 2386.5 Load, Shear, and Moment Relationships 2436.6 Shear and Moment Diagrams 2456.7 Discontinuity Functions 259Chapter Summary 268References 270Chapter 7 STRESSES IN BEAMS 2717.1 Introduction 272PART A Pure Bending 2737.2 Beam Deformation in Pure Bending 2737.3 Assumptions of Beam Theory 2757.4 Normal Strain in Beams 2767.5 Normal Stress in Beams 2807.6 Stress Concentrations in Bending 285PART B Shear and Bending 2927.7 Shear Stresses in Beams 2927.8 Shear Stress Distribution in Rectangular Beams 2977.9 Shear Stresses in Beams of Circular Cross Section 2997.10 Shear Stress Distribution in Flanged Beams 3007.11 Comparison of Shear and Bending Stresses 3047.12 Design of Prismatic Beams 3087.13 Design of Beams of Constant Strength 311PART C Special Topics 3217.14 Composite Beams 3217.15 Reinforced Concrete Beams 3257.16 Unsymmetric Bending 3277.17 Shear Center 3327.18 Inelastic Bending 3347.19 Curved Beams 341Chapter Summary 356References 359Chapter 8 TRANSFORMATION OF STRESS AND STRAIN 3608.1 Introduction 3618.2 Plane Stress 3618.3 Principal Stresses 3678.4 Maximum Shear Stress 3688.5 Mohr’s Circle for Plane Stress 3708.6 Absolute Maximum Shear Stress 3838.7 Principal Stresses for a General State of Stress 3848.8 Thin-Walled Pressure Vessels 3858.9 Thick-Walled Pressure Vessels 3938.10 Plane Strain 4028.11 Mohr’s Circle for Plane Strain 4058.12 Measurement of Strain;Strain Rosette 4098.13 Relation Involving E, n, and G 412Chapter Summary 416References 418Chapter 9 COMBINED LOADINGS AND FAILURE CRITERIA 4199.1 Introduction 420PART A Combined Stresses 4219.2 Axial and Torsional Loads 4219.3 Direct Shear and Torsional Loads: Helical Springs 4279.4 Axial, Transverse, and Torsional Loads 4319.5 Transverse Shear and Bending MomentLoads: Principal Stresses in Beams 4379.6 Eccentric Axial Loads 440PARTB Failure Theories inDesign 4509.7 Material Failure 4509.8 Yield Criteria for Ductile Materials 4519.9 Fracture Criteria for Brittle Materials 4549.10 Design of Transmission Shafts 460Chapter Summary 468References 470Chapter 10 DEFLECTIONS OF BEAMS 47110.1 Introduction 47210.2 The Elastic Curve 47210.3 Boundary Conditions 47310.4 Method of Integration 47610.5 Use of Discontinuity Functions 48710.6 Method of Superposition 49310.7 Statically Indeterminate Beams 49610.8 Statically Indeterminate Beams—Method of Integration 49710.9 Statically Indeterminate Beams—Method of Superposition 50710.10 Moment–Area Method 51410.11 Statically Indeterminate Beams—Moment–Area Method 52510.12 Continuous Beams 527Chapter Summary 535References 536Chapter 11 BUCKLING OF COLUMNS 53711.1 Introduction 53811.2 Stability of Structures 53811.3 Pin-Ended Columns 54011.4 Columns with Other End Conditions 54211.5 Critical Stress: Classification of Columns 54711.6 Eccentric Loaded Columns and the Secant Formula 55811.7 Design of Columns for Centric Loading 56411.8 Design of Columns for Eccentric Loading 569Chapter Summary 574References 575Chapter 12 ENERGY METHODS AND IMPACT 57612.1 Introduction 57712.2 Strain Energy under Axial Loading 57712.3 Strain Energy in Circular Shafts 58012.4 Strain Energy in Beams 58112.5 Strain Energy for a General State of Stress 58412.6 Conservation of Energy 58912.7 Displacement under a Single Load by the Work–Energy Method 59012.8 Displacements by Castigliano’s Theorem 59312.9 Unit-Load Method 59912.10 Statically Indeterminate Structures 60212.11 Impact Loading 60912.12 Longitudinal and Bending Impact 610Chapter Summary 621References 623Chapter 13 FINITE ELEMENT ANALYSIS 62413.1 Introduction 62513.2 The Bar Element 62613.3 Two-Dimensional Bar Element 62713.4 Axial Force in the Bar Element 63013.5 Formulation of the Finite Element Method 63113.6 Beam Elements 644Chapter Summary 652References 653Appendix A PROPERTIES OF AREAS 655A.1 Centroid of an Area 655A.2 Moments of Inertia and Radius of Gyration 658A.3 Parallel-Axis Theorem 660A.4 Principal Moments of Inertia 662Appendix B TABLES 667B.1 Principal SI Units Used in Mechanics 668B.2 SI Prefixes 668B.3 Conversion Factors between U.S. Customary and SI Units 669B.4 Properties of Selected Engineering Materials 670B.5 Materials and Selected Members of Each Class 672B.6 Properties of Areas 674B.7 Properties of Selected Steel Pipe and Tubing 675B.8 Properties of Steel W Shapes, Wide-Flange Sections 676B.9 Properties of Steel S Shapes, American Standard I-Beams 678B.10 Properties of Steel C Shapes, American Standard Channels 680B.11 Properties of Steel L Shapes, Angles with Equal Legs 682B.12 Properties of Steel L Shapes, Angles with Unequal Legs 684B.13 Properties of Structural Lumber 686B.14 Deflections and Slopes of Beams 687B.15 Reactions and Deflections of Statically Indeterminate Beams 689Appendix C MATRIX ALGEBRA 690C.1 Definition of a Matrix 690C.2 Determinant of a Matrix 691C.3 Matrix Operations 693C.4 Simultaneous Linear Equations 695Appendix D FUNDAMENTALS OF ENGINEERING EXAMINATION 697ANSWERS TO SELECTED EVEN-NUMBERED PROBLEMS 698INDEX 711