Advanced Mechanics of Materials

ARTHUR P. BORESI is Professor Emeritus in the Department of Civil andArchitectural Engineering at the University of Wyoming in Laramie. He is the coauthor of a number of books, including Statics and Dynamics, Approximate Solution Methods in Engineering Mechanics, and Advanced Mechanics of Materials.

• CHAPTER 1 INTRODUCTION 11.1 Review of Elementary Mechanics of Materials 11.2 Methods of Analysis 51.3 Stress–Strain Relations 81.4 Failure and Limits on Design 16Problems 22References 24CHAPTER 2 THEORIES OF STRESS AND STRAIN 252.1 Definition of Stress at a Point 252.2 Stress Notation 262.3 Symmetry of the Stress Array and Stress on an Arbitrarily Oriented Plane 282.4 Transformation of Stress, Principal Stresses, and Other Properties 312.5 Differential Equations of Motion of a Deformable Body 502.6 Deformation of a Deformable Body 542.7 Strain Theory, Transformation of Strain, and Principal Strains 552.8 Small-Displacement Theory 612.9 Strain Measurement and Strain Rosettes 70Problems 72References 78CHAPTER 3 LINEAR STRESS–STRAIN–TEMPERATURE RELATIONS 793.1 First Law of Thermodynamics, Internal-Energy Density, and Complementary Internal-Energy Density 793.2 Hooke’s Law: Anisotropic Elasticity 843.3 Hooke’s Law: Isotropic Elasticity 853.4 Equations of Thermoelasticity for Isotropic Materials 913.5 Hooke’s Law: Orthotropic Materials 93Problems 101References 103CHAPTER 4 INELASTIC MATERIAL BEHAVIOR 1044.1 Limitations on the Use of Uniaxial Stress–Strain Data 1044.2 Nonlinear Material Response 1074.3 Yield Criteria: General Concepts 1134.4 Yielding of Ductile Metals 1174.5 Alternative Yield Criteria 1264.6 General Yielding 129Problems 142References 146CHAPTER 5 APPLICATIONS OF ENERGY METHODS 1475.1 Principle of Stationary Potential Energy 1475.2 Castigliano’s Theorem on Deflections 1525.3 Castigliano’s Theorem on Deflections for Linear Load–Deflection Relations 1555.4 Deflections of Statically Determinate Structures 1635.5 Statically Indeterminate Structures 177Problems 187References 199CHAPTER 6 TORSION 2006.1 Torsion of a Prismatic Bar of Circular Cross Section 2006.2 Saint-Venant’s Semiinverse Method 2096.3 Linear Elastic Solution 2136.4 The Prandtl Elastic-Membrane (Soap-Film) Analogy 2166.5 Narrow Rectangular Cross Section 2196.6 Torsion of Rectangular Cross Section Members 2226.7 Hollow Thin-Wall Torsion Members and Multiply Connected Cross Sections 2286.8 Thin-Wall Torsion Members with Restrained Ends 2346.9 Numerical Solution of the Torsion Problem 2396.10 Inelastic Torsion: Circular Cross Sections 2436.11 Fully Plastic Torsion: General Cross Sections 250Problems 254References 262CHAPTER 7 BENDING OF STRAIGHT BEAMS 2637.1 Fundamentals of Beam Bending 2637.2 Bending Stresses in Beams Subjected to Nonsymmetrical Bending 2727.3 Deflections of Straight Beams Subjected to Nonsymmetrical Bending 2807.4 Effect of Inclined Loads 2847.5 Fully Plastic Load for Nonsymmetrical Bending 285Problems 287References 294CHAPTER 8 SHEAR CENTER FOR THIN-WALL BEAM CROSS SECTIONS 2958.1 Approximations for Shear in Thin-Wall Beam Cross Sections 2958.2 Shear Flow in Thin-Wall Beam Cross Sections 2968.3 Shear Center for a Channel Section 2988.4 Shear Center of Composite Beams Formed from Stringers and Thin Webs 3038.5 Shear Center of Box Beams 306Problems 312References 318CHAPTER 9 CURVED BEAMS 3199.1 Introduction 3199.2 Circumferential Stresses in a Curved Beam 3209.3 Radial Stresses in Curved Beams 3339.4 Correction of Circumferential Stresses in Curved Beams Having I, T, or Similar Cross Sections 3389.5 Deflections of Curved Beams 3439.6 Statically Indeterminate Curved Beams: Closed Ring Subjected to a Concentrated Load 3489.7 Fully Plastic Loads for Curved Beams 350Problems 352References 356CHAPTER 10 BEAMS ON ELASTIC FOUNDATIONS 35710.1 General Theory 35710.2 Infinite Beam Subjected to a Concentrated Load: Boundary Conditions 36010.3 Infinite Beam Subjected to a Distributed Load Segment 36910.4 Semiinfinite Beam Subjected to Loads at Its End 37410.5 Semiinfinite Beam with Concentrated Load Near Its End 37610.6 Short Beams 37710.7 Thin-Wall Circular Cylinders 378Problems 384References 388CHAPTER 11 THE THICK-WALL CYLINDER 38911.1 Basic Relations 38911.2 Stress Components at Sections Far from Ends for a Cylinder with Closed Ends 39211.3 Stress Components and Radial Displacement for Constant Temperature 39511.4 Criteria of Failure 39911.5 Fully Plastic Pressure and Autofrettage 40511.6 Cylinder Solution for Temperature Change Only 40911.7 Rotating Disks of Constant Thickness 411Problems 419References 422CHAPTER 12 ELASTIC AND INELASTIC STABILITY OF COLUMNS 42312.1 Introduction to the Concept of Column Buckling 42412.2 Deflection Response of Columns to Compressive Loads 42512.3 The Euler Formula for Columns with Pinned Ends 42812.4 Euler Buckling of Columns with Linearly Elastic End Constraints 43612.5 Local Buckling of Columns 44012.6 Inelastic Buckling of Columns 442Problems 450References 455CHAPTER 13 FLAT PLATES 45713.1 Introduction 45713.2 Stress Resultants in a Flat Plate 45813.3 Kinematics: Strain–Displacement Relations for Plates 46113.4 Equilibrium Equations for Small-Displacement Theory of Flat Plates 46613.5 Stress–Strain–Temperature Relations for Isotropic Elastic Plates 46913.6 Strain Energy of a Plate 47213.7 Boundary Conditions for Plates 47313.8 Solution of Rectangular Plate Problems 47613.9 Solution of Circular Plate Problems 486Problems 500References 501CHAPTER 14 STRESS CONCENTRATIONS 50214.1 Nature of a Stress Concentration Problem and the Stress Concentration Factor 50414.2 Stress Concentration Factors: Theory of Elasticity 50714.3 Stress Concentration Factors: Combined Loads 51514.4 Stress Concentration Factors: Experimental Techniques 52214.5 Effective Stress Concentration Factors 53014.6 Effective Stress Concentration Factors: Inelastic Strains 536Problems 539References 541CHAPTER 15 FRACTURE MECHANICS 54315.1 Failure Criteria and Fracture 54415.2 The Stationary Crack 55115.3 Crack Propagation and the Stress Intensity Factor 55515.4 Fracture: Other Factors 561Problems 564References 565CHAPTER 16 FATIGUE: PROGRESSIVE FRACTURE 56716.1 Fracture Resulting from Cyclic Loading 56816.2 Effective Stress Concentration Factors: Repeated Loads 57516.3 Effective Stress Concentration Factors: Other Influences 57516.4 Low Cycle Fatigue and the _–N Relation 580Problems 585References 588CHAPTER 17 CONTACT STRESSES 58917.1 Introduction 58917.2 The Problem of Determining Contact Stresses 59017.3 Geometry of the Contact Surface 59117.4 Notation and Meaning of Terms 59617.5 Expressions for Principal Stresses 59717.6 Method of Computing Contact Stresses 59817.7 Deflection of Bodies in Point Contact 60717.8 Stress for Two Bodies in Line Contact: Loads Normal to Contact Area 61117.9 Stresses for Two Bodies in Line Contact: Loads Normal and Tangent to Contact Area 613Problems 622References 623CHAPTER 18 CREEP: TIME-DEPENDENT DEFORMATION 62418.1 Definition of Creep and the Creep Curve 62418.2 The Tension Creep Test for Metals 62618.3 One-Dimensional Creep Formulas for Metals Subjected to Constant Stress and Elevated Temperature 62618.4 One-Dimensional Creep of Metals Subjected to Variable Stress and Temperature 63118.5 Creep Under Multiaxial States of Stress 64018.6 Flow Rule for Creep of Metals Subjected to Multiaxial States of Stress 64318.7 An Application of Creep of Metals 64918.8 Creep of Nonmetals 650References 654APPENDIX A AVERAGE MECHANICAL PROPERTIES OF SELECTED MATERIALS 657APPENDIX B SECOND MOMENT (MOMENT OF INERTIA) OF A PLANE AREA 660B.1 Moments of Inertia of a Plane Area 660B.2 Parallel Axis Theorem 661B.3 Transformation Equations for Moments and Products of Inertia 664Problems 666APPENDIX C PROPERTIES OF STEEL CROSS SECTIONS 668AUTHOR INDEX 673SUBJECT INDEX 676