A Concise Introduction to Elastic Solids : An Overview of the Mechanics of Elastic Materials and Structures

This book provides an introduction to fundamental concepts of solid mechanics for the uninitiated. It also includes a concise review of fundamentals for those who have been away from the field for a time or are studying for a final exam or engineering license exam. The coverage ranges from fundamental definitions through constitutive equations, axial loading, torsion, bending, thermal effects, stability, pressure vessels, plates and shells, computational mechanics, and fibrous composite materials. Preface 7 Acknowledgements 8 Contents 9 About the Author 13 1 Mechanics of Solids 15 1.1 Fundamentals 15 1.2 Early History 16 References 21 2 Stress 22 2.1 Cauchy Stress 22 2.2 Plane Stress 23 2.3 Stress Transformation 24 2.4 Principal Stresses 25 2.5 Pure Shear Stress 26 2.6 Stress Tensor 27 2.7 Units of Stress 27 2.8 Exercises 27 Appendix: Solutions 28 References 30 3 Strain 31 3.1 Normal Strain 31 3.2 Engineering Shear Strain 31 3.3 Strain–Displacement Relationships 33 3.4 Tensor Shear Strain 33 3.5 Strain Transformation 34 3.6 Poisson’s Ratio 34 3.7 Plane Strain 35 3.8 Exercises 35 Appendix: Solutions 36 Reference 37 4 Constitutive Equations 38 4.1 Normal Stress–Strain Response 38 4.2 Shear Stress–Strain Response 39 4.3 E, G, ν Relationship 40 4.4 Exercises 40 Appendix: Solutions 41 References 42 5 Equilibrium 43 5.1 Newton’s Second Law 43 5.2 Exercises 44 Appendix: Solutions 44 Reference 45 6 Axial Loading 46 6.1 Axial Stress 46 6.2 Axial Strain 46 6.3 Change in Length 46 6.4 Stress–Strain Diagram 47 6.5 Nonlinear Response 47 6.6 Exercises 48 Appendix: Solutions 49 7 Torsion of Cylindrical Bars 50 7.1 Shear Strain 50 7.2 Torque 51 7.3 Angle of Twist 51 7.4 Maximum Shear Stress 52 7.5 Non-circular, Prismatic Bars 53 7.6 Exercises 53 Appendix: Solutions 53 8 Beam Bending 56 8.1 Pure Bending 56 8.2 Bending Moments 56 8.3 Beam Curvature and Strains 58 8.4 Stresses Due to Beam Bending 59 8.5 Exercises 61 Appendix: Solutions 61 9 Beam Subjected to Transverse Loading 64 9.1 Equilibrium 64 9.2 Stresses in Beams Under Transverse Loading 65 9.2.1 Normal Stress 65 9.2.2 Shear Stress 66 9.3 Exercises 67 Appendix: Solutions 68 10 Beam Deflections 70 10.1 General Considerations 70 10.2 Deflection Equations 70 10.3 Statically Indeterminate Beams 73 10.4 Exercises 73 Appendix: Solutions 73 Reference 75 11 Thermal Effects 76 11.1 Thermal Strains 76 11.2 Thermal Stresses 76 11.3 Exercises 77 Appendix: Solutions 77 12 Stability 80 12.1 Euler Buckling 80 12.2 Exercises 83 Appendix: Solutions 83 References 84 13 Thin-Walled Pressure Vessels 85 13.1 Spherical Pressure Vessel 85 13.2 Cylindrical Pressure Vessel 86 13.3 Exercises 87 Appendix: Solutions 87 14 Plates and Shells 90 14.1 Plates 90 14.2 Plate in Cylindrical Bending 93 14.3 Circular Plate Under Symmetrical Loading 94 14.4 Circular Plate with Clamped Edge 95 14.5 Circular Plate with Simply Supported Edge 96 14.6 Shells 96 14.7 Exercises 97 Appendix: Solutions 98 References 100 15 Computational Mechanics 102 15.1 Finite Element Methods 102 15.2 The Value of π 103 15.3 Torsion of a Square Bar by Finite Elements 104 15.4 Exercises 105 Appendix: Solutions 105 References 107 16 Fibrous Composite Materials 108 16.1 Laminated Composites 110 16.2 Plane Stress of Orthotropic Material 111 16.3 Classical Lamination Theory 111 16.4 Effective Laminate Properties 116 16.5 Effective Axial Modulus 119 16.6 Effective Inplane Poisson’s Ratio 120 16.7 Effective Shear Modulus 120 16.8 Effective Coefficient of Thermal Expansion 121 16.9 Effective Coefficient of Mutual Influence 124 16.10 Exercises 124 Appendix: Solutions 124 References 126 Appendix 127 Outline placeholder 0 A.1 Trigonometric Identities 127 A.2 Derivatives of Trigonometric Functions 127 A.3 Moment of Inertia 128 A.4 Partial Derivatives 128 A.5 Biharmonic Operator \nabla^{4} 128 A.6 Matrix Notation 128 A.7 Matrix Determinate 129 A.8 Matrix Inverse 129 A.9 Tensors 130 A.10 Tensor Transformations 131 A.11 Vector Transformation 132 A.12 Second-Order Tensor Transformation 133 Index 134 Front Matter....Pages i-xvi Mechanics of Solids....Pages 1-7 Stress....Pages 9-17 Strain....Pages 19-25 Constitutive Equations....Pages 27-31 Equilibrium....Pages 33-35 Axial Loading....Pages 37-40 Torsion of Cylindrical Bars....Pages 41-46 Beam Bending....Pages 47-54 Beam Subjected to Transverse Loading....Pages 55-60 Beam Deflections....Pages 61-66 Thermal Effects....Pages 67-70 Stability....Pages 71-75 Thin-Walled Pressure Vessels....Pages 77-81 Plates and Shells....Pages 83-94 Computational Mechanics....Pages 95-100 Fibrous Composite Materials....Pages 101-119 Back Matter....Pages 121-131