1. Introduction1 1.1 Types of Linearity 1 1.1.1Linear Shapes-The Elastic Line . .1 1.1.2Linear Displacement (Plane Sections) 2 1.1.3Linear Stress Strain Behavior (Hooke's Law)3 1.1.4Geometric Linearity 4 1.1.5Linear Tangent Transformation 4 1.2 Displacements-Vectors and Tensors 5 1.3 Finite Linear Transformation. 6 1.4 Symmetric and Asymmetric Components9 1.4.1 Asymmetric Transformation 9 1.4.2 Symmetric Transformation10 1.5 Principal or Eigenvalue Representation13 1.6 Eield Theory17 1.7 Problems and Question19 2.Strain and Stress 23 2.1Deformation (Relative Displacement) 23 2.2 The Strain Tensor 24 2.3 The Stress Tensor28 2.4 Components at an Arbitrary Orientation 30 (Tensor Transformation) 2.4.1Invariants and Principal Orientation 33 2.5 Isotropic and Deviatoric Components 37 2.6 Principal Space and the Octahedral Representation 39 2.7 Two-Dimensional Stress or Strain 42 2.8 Mohr's Circle for a Plane Tensor 46 2.9 Mohr's Circle in Three Dimensions 50 2.10Equilibrium of a Differential Element53 2.11Other Orthogonal Coordinate Systems 55 2.11.1 Cylindrical Coordinates 57 2.11.2 Spherical Coordinates 58 2.11.3 Plane Polar Coordinates58 2.12 Summary 59 2.13 Problems and Questions61 3.Stress-Strain Relationships (Rheology) 65 3.1 Linear Elastic Behavior 65 3.2 Linear Viscous Behavior 72 3.3 Simple Viscoelastic Behavior 74 3.4 Fitting Laboratory Data with Viscoelastic Models 80 3.5 Elastic-Viscoelastic Analogy 83 3.6 Elasticity and Plasticity 86 3.7 Yield of Ductile Materials87 3.8 Yield (Slip) of Brittle Materials 90 3.9 Problems and Questions93 4. Strategies for Elastic Analysis and Design. .99 4.1 Rational Mechanics 99 4.2 Boundary Conditions 101 4.3Tactics for Analysis102 4.3.1Direct Determination of Displacements 102 4.3.2 Direct Determination of Stresses . 103 4.4 St. Venant's Principle105 4.5 Two- Dimensional Stress Formulation. 106 4.6 Types of Partial Differential Field Equations108 4.7 Properties of Elliptic Equation? . 109 4.8 The Conjugate Relationship Between Mean112 Stress and Rotation 4.9 The Deviatoric Field and Photoelasticity 120 4.10 Solutions by Potentials123 4.11 Problems and Questions124 5. Linear Free Fields127 5.1 Isotropic Stress127 5.2 Uniform Stress 128 5.3 Geostatic Fields 130 5-4 Uniform Acceleration of the Half-space 133 5.5 Pure Bending of Prismatic Bars135 5.6 Pure Bending of Plates140 5.7 Problems and Questions142 6. Two-Dimensional Solutions for Straight145 and Circular Beams 6.1The Classic Stress-Function Approach145 6.2 Airy's Stress Function in Cartesian Coordinates 146 6.3 Polynomial Solutions and Straight Beams 148 6.4Polar Coordinates and Airy's Stress Function 157 6.5 Simplified Analysis of Curved Beams 162 6.6 Pure bending of a Beam of Circular Arc165 6.7 Circular Beams with End Loads 171 6.8 Concluding Remarks174 6.9 Problems and Questions175 7. Ring, Holes, and Inverse Problems 181 7.1Lames Solution for Rings under Pressure181 7.2Small Circular Holes in Plates, Tunnels, and Inclusions.. 187 7.2.1sotropic Field.187 7.2.2Deviatoric Field194 7.2.3 General Biaxial Field197 7.3 Harmonic Holes and the Inverse Problem 198 7.3.1Design Condition 198 7.4 Harmonic Holes for Free Fields . 203 7.4.1Harmonic Holes for Biaxial Fields203 7.4.2Harmonic Holes for Gradient Fields 209 7.5 Neutral Holes 213 7.6 Solution Tactics for Neutral Holes-Examples 220 7.6.1Isotropic Field222 7.6.2 Deviatoric Field 223 7.6.3 General Biaxial Field 225 7.6.4 Gradient Fields with an Isotropic Component226 7.6.5 Summary 229 7.7 Rotating Disks and Rings233 7.7.1Disk of Constant Thickness233 7.7.2 Variable Thickness and the Inverse Problem236 7.8 Problems and Questions 238 8. Wedges and the Half-Space 243 8.1 Concentrated Loadings at the Apex243 8.2 Uniform Loading Cases251 8.3 Uniform Loading over a Finite Width256 8.4 Nonuniform Loadings on the Half-Space257 8.5 Line Loads within the Half-Space259 8.6 Diametric Loading of a Circular Disk 261 8.7 Wedges with Constant Body Forces 263 8.8 Corner Effects-Eigenfunction Strategy 270 8.9 Problems and Questions .272 9. Torsion 291 9.1Elementary (Linear) Solution291 9.2 St. Venant's Formulation (Noncircular Cross-Sections) 292 9.2.1 Solutions by St. Venant 295 9.3 Prandtl's Stress Function. 297 9.4 Membrane Analogy301 9.5Thin-Walled Tubes of Arbitrary Shape 307 9.6 Hydrodynamic Analogy and Stress Concentration311 9.7 Problems and Questions .315 10. Concepts of Plasticity321 10.1Plastic Material Behavior321 10.2 Plastic Structural Behavior323 10.3Plasticity Field Equations324 10.4 Example-Thick Ring.326 10.5Limit Load by a Work Calculation 329 10.6Theorems of Limit Analysis 332 10.7 The Lower-Bound Theorem332 10.8The Upper-Bound Theorem 335 10.9Example-the Bearing Capacity (Indentation) Problem.. 337 10.9.1 Circular Mechanisms 337 10.9.2 Sliding Block Mechanisms 339 10.10Problems and Questions 341 11.One-Dimensional Plasticity for Design347 11.1 Plastic Bending347 11.2 Plastic Hinges 352 11.3Limit Load (Collapse) of Beams 354 11.4Limit Analysis of Frames and Arches357 11.5Limit Analysis of Plates361 11.6 Plastic Torsion 369 11.6.1 Sand-Hill and Roof Analogies370 11.6.2 Sections with Holes and Keyways372 11.7 Combined Torsion with Tension and/or Bending375 11.8 Problems and Questions 378 12.Slip-Line Analysis .389 12.1 Mohr-Coulomb Criterion (Revisited). 389 12.2 Lateral Pressures and the Retaining Wall Problem 394 12.3 Graphic Analysis and Minimization 399 12.4 Slip-Line Theory. 402 12.5 Purely Cohesive Materials405 12.6 Weightless Material 407 12.7 Retaining Wall Solution for = 0 (EPS Material) 408 12.8 Comparison to the Coulomb Solution412 12.9 Other Special Cases: Slopes and Footings 414 12.10 Solutions for Weightless Mohr-Coulomb Materials.417 12.11 The General Case .422 12.12 An Approximate Coulomb Mechanism 425 12.13 Problems and Questions430 Index 437