Advanced Mechanics of Materials and Applied Elasticity (International Series in the Physical and Chemical Engineering Sciences)

The Leading Practical Guide to Stress Analysis--Updated with State-of-the-Art Methods, Applications, and Problems This widely acclaimed exploration of real-world stress analysis reflects advanced methods and applications used in today's mechanical, civil, marine, aeronautical engineering, and engineering mechanics/science environments. Practical and systematic, Advanced Mechanics of Materials and Applied Elasticity, Sixth Edition, has been updated with many new examples, figures, problems, MATLAB solutions, tables, and charts. The revised edition balances discussions of advanced solid mechanics, elasticity theory, classical analysis, and computerized numerical approaches that facilitate solutions when problems resist analysis. It illustrates applications with case studies, worked examples, and problems drawn from modern applications, preparing readers for both advanced study and practice. Readers will find updated coverage of analysis and design principles, failure criteria, fracture mechanics, compound cylinders, rotating disks, 3-D Mohr's circles, energy and variational methods, buckling of stepped columns, common shell types, inelastic materials behavior, and more. The text addresses the use of new materials in bridges, buildings, automobiles, submarines, ships, aircraft, and spacecraft. It offers significantly expanded coverage of stress concentration factors and contact stress developments. This book aims to help the student Review fundamentals of statics, solids mechanics, stress, and modes of load transmission Master stress analysis and design principles through hands-on practice that illuminates their connections Understand plane stress, stress transformations, deformations, and strains Analyze a body's load-carrying capacity based on strength, stiffness, and stability Explore failure criteria and material behavior under diverse conditions, and predict component deformation or buckling Learn and apply the theory of elasticity Solve problems related to beam bending, torsion of noncircular bars, and axisymmetrically loaded components, plates, or shells Use the numerical finite element method to economically solve complex problems Characterize the plastic behavior of materials Conforming with current policy and standards, quantities are defined in both SI and U.S. units. Throughout the text, SI-based problems are provided, and sign conventions are consistent with vector mechanics. Register your product for convenient access to downloads, updates, and/or corrections as they become available. Cover Half Title Title Page Copyright Page Contents Preface Acknowledgments About the Authors List of Symbols Chapter 1: Analysis of Stress 1.1 Introduction 1.1.1 Mechanics of Materials and Theory of Elasticity 1.1.2 Historical Development 1.2 Scope of the Book 1.3 Analysis and Design 1.3.1 Role of Analysis in Design 1.3.2 Selection of Factor of Safety 1.3.3 Case Studies 1.4 Conditions of Equilibrium 1.5 Definition and Components of Stress 1.5.1 Sign Convention 1.5.2 Equality of Shearing Stresses 1.5.3 Some Special Cases of Stress 1.6 Internal Force Resultant and Stress Relations 1.6.1 Basic Formulas for Stress 1.6.2 Combined Stresses 1.7 Stresses on Inclined Sections 1.7.1 Axially Loaded Members 1.8 Variation of Stress within a Body 1.8.1 Equations of Equilibrium 1.9 Plane-Stress Transformation 1.9.1 Stress Tensor 1.9.2 Polar Representations of State of Plane Stress 1.9.3 Cartesian Representation of State of Plane Stress 1.10 Principal Stresses and Maximum In-Plane Shear Stress 1.11 Mohr’s Circle for Two-Dimensional Stress 1.12 Three-Dimensional Stress Transformation 1.13 Principal Stresses in Three Dimensions 1.13.1 Invariants for Three-Dimensional Stress 1.14 Normal and Shear Stresses on an Oblique Plane 1.14.1 Octahedral Stresses 1.15 Mohr’s Circles in Three Dimensions 1.15.1 Absolute Maximum Shear Stress 1.15.2 Equations of Three Mohr’s Circles for Stress 1.16 Boundary Conditions in Terms of Surface Forces 1.17 Indicial Notation References Problems Chapter 2: Strain and Material Properties 2.1 Introduction 2.2 Deformation 2.2.1 Superposition 2.3 Strain Defined 2.3.1 Plane Strain 2.3.2 Three-Dimensional Strain 2.3.3 Eulerian and Lagrangian Coordinates 2.3.4 Large Strains 2.4 Equations of Compatibility 2.5 State of Strain at a Point 2.5.1 Transformation of Two-Dimensional Strain 2.5.2 Transformation of Three-Dimensional Strain 2.5.3 Invariants in Three-Dimensional Strain 2.5.4 Mohr’s Circle for Plane Strain 2.6 Engineering Materials 2.6.1 General Properties of Some Common Materials 2.7 Stress-Strain Diagrams 2.7.1 Ductile Materials in Tension 2.7.2 Geometry Change of Specimen 2.7.3 True Stress and True Strain 2.7.4 Brittle Materials in Tension 2.7.5 Materials in Compression 2.7.6 Materials in Shear 2.7.7 Short-Time Effects of Temperature on Stress-Strain Properties 2.8 Elastic versus Plastic Behavior 2.9 Hooke’s Law and Poisson’s Ratio 2.9.1 Volume Change 2.9.2 Deflection of Axially Loaded Members 2.10 Generalized Hooke’s Law 2.11 Orthotropic Materials 2.11.1 Generalized Hook’s Law for Orthotropic Material 2.12 Measurement of Strain: Strain Gage 2.12.1 Strain Rosette of Three Gages 2.12.2 Rectangular and Delta Strain Rosettes 2.13 Strain Energy 2.13.1 Strain Energy Density for Normal and Shear Stresses 2.13.2 Strain Energy Density for Three-Dimensional Stresses 2.14 Strain Energy in Common Structural Members 2.14.1 Strain Energy for Axially Loaded Bars 2.14.2 Strain Energy of Circular Bars in Torsion 2.14.3 Strain Energy for Beams in Bending 2.15 Components of Strain Energy 2.16 Saint-Venant’s Principle 2.16.1 Confirmation of Saint-Venant’s Rule References Problems Chapter 3: Problems in Elasticity 3.1 Introduction 3.2 Fundamental Principles of Analysis 3.2.1 Three-Dimensional Problems 3.2.2 Two-Dimensional Problems Part A: Formulation and Methods of Solution 3.3 Plane Strain Problems 3.4 Plane Stress Problems 3.4.1 Stress–Strain Relations for Orthotropic Materials 3.5 Comparison of Two-Dimensional Isotropic Problems 3.6 Airy’s Stress Function 3.6.1 Generalized Plane Strain Problems 3.6.2 Antiplane Shear Deformations 3.7 Solution of Elasticity Problems 3.7.1 Polynomial Solutions 3.8 Thermal Stresses 3.8.1 Equations of Thermoelasticity 3.9 Basic Relations in Polar Coordinates 3.9.1 Equations of Equilibrium 3.9.2 Stress Function 3.9.3 Strain-Displacement Relations 3.9.4 Hooke’s Law 3.9.5 Transformation Equations 3.9.6 Compatibility Equation Part B: Stress Concentrations 3.10 Stresses Due to Concentrated Loads 3.10.1 Compression of a Wedge (Fig. 3.10a) 3.10.2 Bending of a Wedge (Fig. 3.10b) 3.10.3 Concentrated Load on a Straight Boundary (Fig. 3.11a) 3.11 Stress Distribution Near a Concentrated Load Acting on a Beam 3.11.1 Accuracy of Results 3.12 Stress Concentration Factors 3.12.1 Circular Hole in a Large Plate in Simple Tension 3.12.2 Circular Hole in a Large Plate in Biaxial Tension 3.12.3 Elliptic Hole in a Large Plate in Tension 3.12.4 Graphs for Stress Concentration Factors Part C: Contact Mechanics 3.13 Contact Stresses and Deflections 3.13.1 Hertz Theory 3.13.2 Johnson–Kendall–Roberts Theory 3.14 Spherical and Cylindrical Contacts 3.14.1 Two Spheres in Contact 3.14.2 Two Parallel Cylinders in Contact 3.15 Contact Stress Distribution 3.15.1 Two Spheres in Contact (Figure 3.18a) 3.15.2 Two Parallel Cylinders in Contact (Figure 3.20a) 3.16 General Contact References Problems Chapter 4: Failure Criteria 4.1 Introduction 4.1.1 Failure Part A: Static Loading 4.2 Failure by Yielding 4.2.1 Creep: Time-Dependent Deformation 4.4 Yield and Fracture Criteria 4.5 Maximum Shearing Stress Theory 4.6 Maximum Distortion Energy Theory 4.6.1 Yield Surfaces for Triaxial Stress 4.7 Octahedral Shearing Stress Theory 4.8 Comparison of the Yielding Theories 4.9 Maximum Principal Stress Theory 4.10 Mohr’s Theory 4.11 Coulomb–Mohr Theory 4.12 Introduction to Fracture Mechanics 4.12.1 Stress-Intensity Factors 4.13 Fracture Toughness Part B: Repeated and Dynamic Loadings 4.3 Failure by Fracture 4.3.1 Types of Fracture in Tension 4.14 Fatigue: Progressive Fracture 4.14.1 Fatigue Tests 4.14.2 Estimating the Endurance Limit and Fatigue Strength 4.15 Failure Criteria for Metal Fatigue 4.15.1 Uniaxial State of Stress 4.15.2 Comparison of Fatigue Failure Criteria 4.15.3 Design for Uniaxial Stress 4.15.4 Combined State of Stress 4.16 Fatigue Life 4.17 Impact Loads 4.17.1 Strain Rate 4.17.2 Basic Assumptions of Impact Analysis 4.18 Longitudinal and Bending Impact 4.18.1 Freely Falling Weight 4.18.2 Horizontally Moving Weight 4.19 Ductile–Brittle Transition References Problems Chapter 5: Bending of Beams 5.1 Introduction Part A: Exact Solutions 5.2 Pure Bending of Beams of Symmetrical Cross Section 5.2.1 Kinematic Relationships 5.2.2 Timoshenko Beam Theory 5.3 Pure Bending of Beams of Asymmetrical Cross Section 5.3.1 Stress Distribution 5.3.2 Transformation of Inertia Moments 5.4 Bending of a Cantilever of Narrow Section 5.4.1 Comparison of the Results with the Elementary Theory Results 5.5 Bending of a Simply Supported Narrow Beam 5.5.1 Use of Stress Functions 5.5.2 Comparison of the Results with the Elementary Theory Results Part B: Approximate Solutions 5.6 Elementary Theory of Bending 5.6.1 Assumptions of Elementary Theory 5.6.2 Method of Integration 5.7 Normal and Shear Stresses 5.7.1 Rectangular Cross Section 5.7.2 Various Cross Sections 5.7.3 Beam of Constant Strength 5.8 Effect of Transverse Normal Stress 5.9 Composite Beams 5.9.1 Transformed Section Method 5.9.2 Equation of Neutral Axis 5.9.3 Stresses in the Transformed Beam 5.9.4 Composite Beams of Multi Materials 5.10 Shear Center 5.10.1 Thin-Walled Open Cross Sections 5.10.2 Arbitrary Solid Cross Sections 5.11 Statically Indeterminate Systems 5.11.1 The Method of Superposition 5.12 Energy Method for Deflections 5.12.1 Form Factor for Shear Part C: Curved Beams 5.13 Elasticity Theory 5.13.1 Equations of Equilibrium and Compatibility 5.13.2 Boundary Conditions 5.13.3 Stress Distribution 5.13.4 Deflections 5.14 Curved Beam Formula 5.14.1 Basic Assumptions 5.14.2 Location of the Neutral Axis 5.14.3 Tangential Stress 5.14.4 Winkler’s Formula 5.15 Comparison of the Results of Various Theories 5.15.1 Correction of σθ for Beams with Thin-Walled Cross Sections 5.16 Combined Tangential and Normal Stresses References Problems Chapter 6: Torsion of Prismatic Bars 6.1 Introduction 6.2 Elementary Theory of Torsion of Circular Bars 6.2.1 Shearing Stress 6.2.2 Angle of Twist 6.2.3 Axial and Transverse Shear Stresses 6.3 Stresses on Inclined Planes 6.3.1 Stress Transformation 6.3.2 Transmission of Power by Shafts 6.4 General Solution of the Torsion Problem 6.4.1 Geometry of Deformation 6.4.2 Equations of Equilibrium 6.4.3 Equations of Compatibility 6.5 Prandtl’s Stress Function 6.5.1 Boundary Conditions 6.5.2 Force and Moments over the Ends 6.5.3 Circular Cross Section 6.6 Prandtl’s Membrane Analogy 6.6.1 Equation of Equilibrium 6.6.2 Shearing Stress and Angle of Twist 6.7 Torsion of Narrow Rectangular Cross Section 6.7.1 Thin-Walled Open Cross Sections 6.8 Torsion of Multiply Connected Thin-Walled Sections 6.8.1 Shearing Stress 6.8.2 Angle of Twist 6.9 Fluid Flow Analogy and Stress Concentration 6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section 6.10.1 Torsional and Lateral Shears 6.10.2 Boundary Conditions 6.10.3 Long Beams Under Torsion 6.10.4 Angle of Twist 6.11 Torsion Bar Springs 6.12 Curved Circular Bars 6.12.1 Helical Springs References Problems Chapter 7: Numerical Methods 7.1 Introduction Part A: Finite Difference Analysis 7.2 Finite Differences 7.2.1 Central Differences 7.3 Finite Difference Equations 7.4 Curved Boundaries 7.5 Boundary Conditions Part B: Finite Element Analysis 7.6 Fundamentals 7.7 The Bar Element 7.7.1 Equilibrium Method 7.7.2 Energy Method 7.8 Arbitrarily Oriented Bar Element 7.8.1 Coordinate Transformation 7.8.2 Force Transformation 7.8.3 Displacement Transformation 7.8.4 Governing Equations 7.9 Axial Force Equation 7.10 Force-Displacement Relations for a Truss 7.10.1 The Assembly Process 7.11 Beam Element 7.12 Properties of Two-Dimensional Elements 7.12.1 Displacement Matrix 7.12.2 Strain, Stress, and Elasticity Matrices 7.13 General Formulation of the Finite Element Method 7.13.1 Outline of General Finite Element Analysis 7.14 Triangular Finite Element 7.14.1 Element Nodal Forces 7.15 Case Studies in Plane Stress 7.16 Computational Tools References Problems Chapter 8: Thick-Walled Cylinders and Rotating Disks 8.1 Introduction 8.1.1 Basic Relations 8.2 Thick-Walled Cylinders Under Pressure 8.2.1 Special Cases 8.2.2 Closed-Ended Cylinder 8.3 Maximum Tangential Stress 8.4 Application of Failure Theories 8.5 Compound Cylinders: Press or Shrink Fits 8.6 Rotating Disks of Constant Thickness 8.6.1 Annular Disk 8.6.2 Solid Disk 8.7 Disk Flywheels 8.7.1 Design Factors 8.7.2 Stresses and Displacement 8.8 Rotating Disks of Variable Thickness 8.9 Rotating Disks of Uniform Stress 8.10 Thermal Stresses in Thin Disks 8.10.1 Annular Disk 8.10.2 Solid Disk 8.11 Thermal Stress in Long Circular Cylinders 8.11.1 Solid Cylinder 8.11.2 Cylinder with a Central Circular Hole 8.11.3 Special Case 8.12 Finite Element Solution 8.12.1 Axisymmetric Element References Problems Chapter 9: Beams on Elastic Foundations 9.1 Introduction 9.2 General Theory 9.3 Infinite Beams 9.4 Semi-Infinite Beams 9.5 Finite Beams 9.6 Classification of Beams 9.7 Beams Supported by Equally Spaced Elastic Elements 9.8 Simplified Solutions for Relatively Stiff Beams 9.9 Solution by Finite Differences 9.10 Applications 9.10.1 Grid Configurations of Beams References Problems Chapter 10: Applications of Energy Methods 10.1 Introduction Part A: Energy Principles 10.2 Work Done in Deformation 10.3 Reciprocity Theorem 10.4 Castigliano’s Theorem 10.4.1 Application to Bars and Beams 10.4.2 Application to Trusses 10.4.3 Use of a Fictitious Load 10.5 Unit- or Dummy-Load Method 10.6 Crotti–Engesser Theorem 10.7 Statically Indeterminate Systems Part B: Variational Methods 10.8 Principle of Virtual Work 10.8.1 Variation in Strain Energy 10.8.2 Virtual Work Done by Forces 10.9 Principle of Minimum Potential Energy 10.10 Deflections by Trigonometric Series 10.10.1 Strain Energy 10.10.2 Virtual Work 10.11 Rayleigh–Ritz Method References Problems Chapter 11: Stability of Columns 11.1 Introduction 11.2 Critical Load 11.2.1 Equilibrium Method 11.2.2 Energy Method 11.3 Buckling of Pin-Ended Columns 11.3.1 Modes of Buckling 11.4 Deflection Response of Columns 11.4.1 Effects of Large Deflections 11.4.2 Effects of Imperfections 11.4.3 Effects of Inelastic Behavior 11.5 Columns with Different End Conditions 11.6 Critical Stress: Classification of Columns 11.6.1 Long Columns 11.6.2 Short Columns 11.6.3 Intermediate Columns: Inelastic Buckling 11.7 Design Formulas for Columns 11.8 Imperfections in Columns 11.9 Local Buckling of Columns 11.10 Eccentrically Loaded Columns: Secant Formula 11.10.1 Simplified Formula for Short Columns 11.11 Energy Methods Applied to Buckling 11.12 Solution by Finite Differences 11.13 Finite Difference Solution for Unevenly Spaced Nodes References Problems Chapter 12: Plastic Behavior of Materials 12.1 Introduction 12.2 Plastic Deformation 12.2.1 Slip Action: Dislocation 12.3 Idealized Stress–Strain Diagrams 12.3.1 True Stress–True Strain Relationships 12.4 Instability in Simple Tension 12.5 Plastic Axial Deformation and Residual Stress 12.6 Plastic Deflection of Beams 12.7 Analysis of Perfectly Plastic Beams 12.7.1 Shape Factor 12.7.2 Plastic Hinge 12.8 Collapse Load of Structures: Limit Design 12.8.1 Collapse Mechanism 12.8.2 Ultimate Load by the Energy Method 12.9 Elastic–Plastic Torsion of Circular Shafts 12.9.1 Yield Torque 12.9.2 Elastic–Plastic Torque 12.9.3 Ultimate Torque 12.9.4 Residual Rotation and Stress 12.10 Plastic Torsion: Membrane Analogy 12.10.1 Membrane–Roof Analogy 12.10.2 Sand Hill Analogy 12.11 Elastic–Plastic Stresses in Rotating Disks 12.11.1 Initial Yielding 12.11.2 Partial Yielding 12.11.3 Complete Yielding 12.12 Plastic Stress–Strain Relations 12.13 Plastic Stress–Strain Increment Relations 12.14 Stresses in Perfectly Plastic Thick-Walled Cylinders 12.14.1 Complete Yielding 12.14.2 Partial Yielding References Problems Chapter 13: Stresses in Plates and Shells 13.1 Introduction Part A: Bending of Thin Plates 13.2 Basic Assumptions 13.3 Strain–Curvature Relations 13.4 Stress, Curvature, and Moment Relations 13.5 Governing Equations of Plate Deflection 13.6 Boundary Conditions 13.7 Simply Supported Rectangular Plates 13.8 Axisymmetrically Loaded Circular Plates 13.9 Deflections of Rectangular Plates by the Strain-Energy Method 13.10 Sandwich Plates 13.10.1 Design of Sandwich Beams and Plates 13.11 Finite Element Solution 13.11.1 Strain, Stress, and Elasticity Matrices 13.11.2 Displacement Function 13.11.3 Stiffness Matrix 13.11.4 External Nodal Forces Part B: Membrane Stresses in Thin Shells 13.12 Theories and Behavior of Shells 13.13 Simple Membrane Action 13.14 Symmetrically Loaded Shells of Revolution 13.14.1 Equations of Equilibrium 13.14.2 Conditions of Compatibility 13.15 Some Typical Cases of Shells of Revolution 13.15.1 Spherical Shell 13.15.2 Conical Shell 13.15.3 Circular Cylindrical Shell 13.16 Thermal Stresses in Compound Cylinders 13.17 Cylindrical Shells of General Shape References Problems Appendix A: Problem Formulation and Solution A.1 Basic Method A.1.1 Numerical Accuracy A.1.2 Daily Planning Appendix B: Solution of the Stress Cubic Equation B.1 Principal Stresses B.1.1 Direction Cosines Appendix C: Moments of Composite Areas C.1 Centroid C.2 Moments of Inertia C.2.1 Parallel Axis Theorem C.2.2 Principal Moments of Inertia Appendix D: Tables and Charts D.1 Charts of Stress Concentration Factors Appendix E: Introduction to MATLAB Answers to Selected Problems Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z This systematic exploration of real-world stress analysis has been completely updated to reflect state-of-the-art methods and applications now used in aeronautical, civil, and mechanical engineering, and engineering mechanics. Distinguished by its exceptional visual interpretations of solutions, Advanced Mechanics of Materials and Applied Elasticity offers in-depth coverage for both students and engineers. The authors carefully balance comprehensive treatments of solid mechanics, elasticity, and computer-oriented numerical methods–preparing readers for both advanced study and professional practice in design and analysis.