Preface |
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xi | |
Author |
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xiii | |
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1 | (22) |
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1 | (7) |
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1.2 Bending of Symmetric Beams |
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8 | (6) |
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1.3 Torsion of Circular Members |
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14 | (9) |
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16 | (5) |
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List of Elementary Formulas |
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21 | (1) |
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22 | (1) |
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23 | (44) |
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2.1 The Stress at a Point |
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24 | (2) |
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2.2 Equations of Equilibrium |
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26 | (2) |
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2.3 Stress Vector (Traction) |
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28 | (1) |
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2.4 Stresses on an Inclined Plane |
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28 | (6) |
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2.5 Transformation of Stress |
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34 | (4) |
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38 | (9) |
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2.6.1 Principal Normal Stresses |
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38 | (4) |
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2.6.2 Principal Shear Stresses |
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42 | (5) |
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2.7 Stress Deviator Tensor |
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47 | (3) |
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50 | (2) |
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2.9 Mohr's Stress Circles |
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52 | (15) |
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58 | (7) |
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65 | (2) |
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67 | (38) |
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3.1 Displacement at a Point |
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67 | (2) |
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3.2 Normal and Shear Strains |
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69 | (8) |
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70 | (5) |
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75 | (2) |
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3.3 Compatibility Conditions |
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77 | (2) |
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79 | (1) |
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3.5 Transformation of Strain |
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79 | (6) |
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80 | (1) |
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81 | (4) |
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85 | (3) |
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3.6.1 Mathematical Strain |
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86 | (2) |
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88 | (4) |
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92 | (1) |
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3.9 Mohr's Circle of Strain |
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92 | (3) |
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95 | (10) |
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98 | (5) |
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103 | (2) |
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4 Stress--Strain Relations |
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105 | (64) |
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105 | (8) |
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106 | (4) |
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4.1.2 Incompressible Material |
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110 | (1) |
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4.1.3 Equations of Equilibrium in Terms of Displacements |
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110 | (3) |
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113 | (7) |
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4.2.1 Dilatational and Distortional Strain Energy Densities |
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117 | (2) |
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119 | (1) |
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120 | (18) |
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4.3.1 Static Tension Test |
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120 | (1) |
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4.3.2 Basic Stress--Strain Relations |
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121 | (2) |
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4.3.3 Models of Uniaxial Stress--Strain Relations |
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123 | (12) |
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4.3.4 True Stress and Strain |
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135 | (3) |
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138 | (15) |
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4.4.1 Maximum Shearing Stress Criterion |
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139 | (1) |
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4.4.2 Maximum Distortion Energy Criterion |
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140 | (5) |
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4.4.3 Yield Surfaces in Haigh--Wesregaard Stress Space |
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145 | (1) |
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4.4.4 Strain Hardening Rules |
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146 | (1) |
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4.4.4.1 Isotropic Hardening Rule |
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147 | (1) |
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4.4.4.2 Kinematic Hardening Rule |
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147 | (1) |
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4.4.4.3 Independent Hardening Rule |
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148 | (5) |
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4.5 Plastic Stress--Strain Relations |
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153 | (16) |
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4.5.1 Stress--Strain Relations for Perfectly Plastic Material |
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154 | (1) |
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4.5.2 Deformation Theory of Plasticity (J2---Material) |
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155 | (4) |
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159 | (8) |
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167 | (2) |
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5 Torsion of Prismatic Bars |
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169 | (58) |
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169 | (1) |
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5.2 Torsion of a Cylindrical Bar |
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170 | (9) |
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5.2.1 Elastic-Perfectly Plastic Material |
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171 | (5) |
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5.2.2 Work--Hardening Material |
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176 | (3) |
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5.3 Torsion of Noncircular Bars |
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179 | (1) |
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180 | (18) |
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5.4.1 Polynomial Solution |
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183 | (8) |
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5.4.2 Fourier Series Solutions |
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191 | (5) |
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5.4.3 Approximate Solution |
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196 | (2) |
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198 | (10) |
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200 | (2) |
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202 | (4) |
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5.5.3 Fully Plastic Torque |
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206 | (2) |
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208 | (9) |
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5.6.1 Torsion of Thin-Walled Members |
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211 | (3) |
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5.6.2 Torsion of Thin-Walled Tubes |
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214 | (3) |
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5.7 Torsion of Restrained Structural Sections |
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217 | (10) |
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220 | (5) |
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225 | (2) |
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6 Two-Dimensional Problems |
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227 | (74) |
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227 | (2) |
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229 | (2) |
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231 | (3) |
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234 | (11) |
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6.4.1 Cantilever Beam Loaded by a Concentrated Force |
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235 | (4) |
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6.4.2 Bending of a Simply Supported Beam by Uniform Load |
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239 | (4) |
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6.4.3 Cantilever Beam Subjected to Hydrostatic Pressure |
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243 | (2) |
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6.5 Saint-Venant's Principle |
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245 | (3) |
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6.6 Solutions in Polar Coordinates |
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248 | (4) |
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6.7 Solutions of the Compatibility Equation |
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252 | (23) |
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6.7.1 Axially Symmetric Problems |
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254 | (11) |
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265 | (5) |
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6.7.3 Semi-Infinite Solid |
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270 | (5) |
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6.8 Rotating Circular Disks |
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275 | (26) |
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277 | (3) |
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280 | (4) |
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6.8.3 Angular Rotation of a Thin Ring or Cylinder |
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284 | (1) |
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6.8.4 Disks of Variable Thickness |
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285 | (5) |
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6.8.5 Rotating Disk of Uniform Strength |
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290 | (1) |
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291 | (8) |
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299 | (2) |
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7 Other Elastoplastic Problems |
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301 | (50) |
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7.1 Thick-Walled Cylindrical Tubes |
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301 | (21) |
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7.1.1 Cylindrical Tube Subjected to Internal Pressure |
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303 | (3) |
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7.1.2 External Pressure Only |
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306 | (1) |
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7.1.3 Elastic-Plastic Expansion of a Cylinder Subjected to Internal Pressure |
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307 | (7) |
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314 | (1) |
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315 | (4) |
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7.1.6 Influence of Strain Hardening of the Material |
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319 | (3) |
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7.2 Thick-Walled Spherical Shell |
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322 | (10) |
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7.2.1 Spherical Shell Subjected to Internal Pressure |
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324 | (4) |
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7.2.2 Influence of Changes in Geometry of the Sphere |
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328 | (1) |
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7.2.3 Work-Hardening Material |
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329 | (3) |
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7.3 Stress Concentration Factors |
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332 | (8) |
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7.3.1 Infinite Plate Containing a Circular Hole |
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332 | (7) |
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7.3.2 Infinite Plate Containing an Elliptical Hole |
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339 | (1) |
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7.4 Structural Members Containing Cracks |
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340 | (11) |
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7.4.1 Plastic Zone near Crack Tip |
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343 | (2) |
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345 | (4) |
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349 | (2) |
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351 | (32) |
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8.1 Thermal Stresses in Uniform Circular Disks |
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356 | (5) |
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357 | (1) |
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357 | (1) |
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8.1.3 Combined Thermal and Rotational Stresses |
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358 | (3) |
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8.2 Thermal Stresses in Cylindrical Vessels |
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361 | (9) |
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8.2.1 Steady-State Heat Flow |
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363 | (4) |
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8.2.2 Thermal Stresses in Pressurized Vessels Subject to Steady-State Heat How |
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367 | (1) |
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8.2.3 Initiation of Ductile Yield |
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368 | (1) |
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8.2.4 Elastic-Plastic Expansion |
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368 | (2) |
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8.3 Thermal Stresses in Thick-Walled Spherical Shell |
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370 | (13) |
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8.3.1 Steady-State Temperature Distribution in Spherical Vessels |
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372 | (1) |
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8.3.2 Initiation of Yield |
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373 | (1) |
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8.3.3 Elastic-Plastic Expansion |
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374 | (2) |
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8.3.4 Combined Steady-State Heat Flow and Internal Pressure |
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376 | (2) |
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378 | (3) |
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381 | (2) |
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9 Three-Dimensional Problems |
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383 | (74) |
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9.1 Elongation of a Prismatic Bar due to Its Own Weight |
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383 | (5) |
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9.2 3D Axisymmetric Deformations of Solids |
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388 | (5) |
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9.2.1 Polar Coordinates and Legendre Functions |
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390 | (3) |
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9.3 Rotation of a Circular Disk |
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393 | (3) |
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9.4 Force at a Point in an Infinite Solid |
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396 | (5) |
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9.5 Stress Concentration around a Spherical Cavity |
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401 | (3) |
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9.6 Concentrated Force on Boundary of a Semi-Infinite Solid |
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404 | (4) |
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9.7 Uniform Load Distributed over a Part of the Boundary of a Semi-Infinite Solid |
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408 | (3) |
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9.7.1 Uniform Load Distributed over a Circular Area of Radius a |
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409 | (1) |
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9.7.2 Uniform Pressure Distributed over Squares and Rectangles |
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410 | (1) |
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9.8 Contact Problems in Three Dimensions |
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411 | (22) |
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9.8.1 Solution Depending on One Harmonic Function |
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412 | (3) |
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9.8.2 General Solution of 3D Contact Problems |
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415 | (5) |
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9.8.3 Contact Problems for Solids Containing Cavities |
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420 | (8) |
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9.8.4 Contact between Two Spherical Bodies: Hertz Problem |
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428 | (5) |
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9.9 A Semi-Infinite Plane Cut or Crack in an Infinite Body |
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433 | (15) |
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9.9.1 Plane Crack Problem |
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433 | (2) |
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9.9.2 Symmetric Normal Loads |
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435 | (4) |
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9.9.3 Antisymmetric Shear Loading Normal to Crack Edge |
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439 | (4) |
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9.9.4 Antisymmetric Shear Loading Parallel to Crack-Edge |
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443 | (5) |
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9.10 Deformation of a Circular Cylinder |
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448 | (9) |
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9.10.1 Pressure Band of Finite Length Acting on a Long Cylinder |
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451 | (1) |
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452 | (2) |
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454 | (3) |
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10 Three-Dimensional Thermal Stresses |
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457 | (62) |
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457 | (2) |
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10.2 Thin Circular Disk (Plane Stress) |
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459 | (1) |
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10.3 Long Circular Cylinder (Plane Strain) |
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460 | (6) |
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462 | (2) |
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10.3.2 Cylinder with a Concentric Central Hole |
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464 | (2) |
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10.4 Thermal Stresses in a Sphere |
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466 | (3) |
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467 | (1) |
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10.4.2 Sphere with a Spherical Hole at the Center |
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468 | (1) |
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10.5 Thermoelastic Displacement Potential |
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469 | (5) |
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471 | (1) |
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10.5.2 Plane Stress (Thin Plate) |
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471 | (3) |
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10.6 Structural Members Containing Flaws or Cracks |
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474 | (45) |
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474 | (9) |
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10.6.2 External Circular Crack |
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483 | (4) |
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487 | (2) |
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10.6.3.1 Symmetrical Case: Constant Temperature on Crack Surface |
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489 | (3) |
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10.6.3.2 Skew-Symmetric Case: Insulated Elliptical Crack |
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492 | (3) |
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10.6.3.3 Symmetrical Case: Polynomial Temperature Specified on Crack Surface |
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495 | (3) |
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10.6.3.4 Skew-Symmetric Case: Polynomial Temperature Gradient Specified on Crack Surface |
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498 | (5) |
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10.6.4 Semi-Infinite Plane Crack |
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503 | (12) |
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515 | (2) |
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517 | (2) |
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11 Solutions to Selected Problems |
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519 | (20) |
Index |
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539 | |