xii CONTENTS CONTENTS xii CHAPTER 4.TWO-DIMENSIONAL PROBLEMSIN POLAR COORDINATES GL.Stress Components in Curvilinear Coordinates,····,·,,·lg5 25.General Equations in Polar Coordinates.. 55 Problems,。·····‘ ··.197 4,44■▣，44 26.Stress Distribution Symmetrical about an Axis, 58 62.Solutions in Elliptie Coordinates. 197 27.Pure Bending of Curved Bar8.··..·······,,·+· 61 63.Elliptic Hole in a Plate under Simple Tension·,,·,,··.- 201 204 28.Strain Components in Polar Coordinates. 65 G4 Hyperbolic Boundaries,Notches。.,.,,,,,·。。.,. 206 29.Displacementa for Symmetrieal Stress Distributions. 66 65.Bipolar Co0 rdinate8.·.·。。,--·········-- 30.Rotating Disk3.· 69 GG.Solutions in Bipolar Coordinates.。.·,.,,·····。。. 208 31.Bending of a Curved Bar by a Force at the End . 73 Other Curvilinear Coordinates,,,·,···· ，，212 32.The Effect of Cireular Holes on Stress Distributions in Plates .. 33.Coneentrated Foree at a Point of a Straight Boundary 85 CHAPTER 8.ANALYSIS OF STRESS AND STRAIN IN THREE DIMEN. 34.Any Vertical Loading of a Straight Boundary 81 SIONS 35.Force Acting on the End of a Wedge...,:,···. 6 67.Specification of8 tress at a Point,。·。,,,,·,······衫 213 36.Concentrated Force Aeting on a Beam. 09 68.Principal Stresses. 214 37.Streases in a Cireular Disk. 44 107 69.Stress Ellipeoid and Stress-direetor Surface........... 215 38.Force at a Point of an Infinite Plate. 112 70,Determination of the Prineipal Stres8cw,。,,,+,····。, 217 39.General Solution of the Two-dimensional Problem in Polar Coordi- 71.Determination of the Maximum Shearing Stress 218 nates. ···。。116 72.Homogeneou3 Deformation,··········· 219 40.Applications of the General Solution in Polar Coordinates.....121 73.Strain at a Point......... 221 41.A Wedge1 oaded along the Faces,·,····。。·,,,·,,123 74.Principal Axes of Strain.... 4 224 Problem8,·。,,···,····125 75.otat50n..。·.。··,· 225 Problem. 227 CHAPr&R 5.THE PHOTOELASTIC METHOD 42.Photoelastic Stress Measurement..... 131 CHAPTER 9.GENERAL THEOREMS 43.Circular Polariscope. 135 76.Differential Equntion3 of Equilibrium,,,,,,。,·。。。·, 228 44.Examples of Photoelastic Stress Determination 138 77.Conditions of Compatibility.. 220 45.Determination of the Principal Stresscs.,,..,+···,·, 142 78.Determination of Displncementa 232 48.Three-dimensional Photoelasticity,,····。,,,,,..。l43 79.Equations of Equilibrium in Terms of Displacements 233 80.General Solution for the Displacements,,+.·。。。,·,,t 235 CHAPTER 6.STRAIN ENERGY METHODS 8l.The Principle of Superposition,,,············· 235 82.Uniqueness of Solution,,,·····。···,·,· 236 47.Strain Energy.· 48.Principle of Virtual Work 151 83.The Reciprocal Theorem. 239 49.Castigliano's Theorem. 162 84.Approximate Character of the Plane Stress Solutions. 241 50.Prineiple of Least Work 160 Problem8···.。 244 51.Applications of the Principle of Least Work-Rectangular Plates..167 52.Effective Width of Wide Beam Flanges··,·········,1T1 CHAPTER 10.ELEMENTARY PROBLEMS OF ELASTICITY IN THREE 53.Shear Lag。·。.,。,,,。。。。。。,,。。·。。·。。·177 DIMENSIONS Probiems......... 177 85.Uniform Stress..,,,·· 245 8G.Stretching of a Prismatical Bar by Tts Own Weight.。。。.,,,246 CHAPTER 7.TWO-DIMENSIONAL PROBLEMS IN CURVILINEAR COOR- 87.Twist of Circular Shafts of Constant Crogs Section...... 249 DINATES 88.Pure Bending of Prismatical Bars. 54.Functions of a Complex Variable................179 8般.Pure Bending of Plates··,··· ，+·。255 55.Analytie Funetions and Laplace's Equation ,......... 181 Problems. .··182 CHAPTER 11.TORSION OF PRISMATICAL BARS 56.Stress Functions in Terms of Harmonic and Complex Functions..183 90.Torgion of Prismatical Bars,.,,,,:·,.,。。···· 258 87.Displacement Corresponding to a Given8 tress Funetion,·,···1l86 91.Bars with Elliptical Cross Section................ 263 58.Stress and Displacement in Terms of Complex Potentials.....187 92.Other Elementary Solutions.................. 265 59.Resultant of Stress on a Curve.Boundary Conditions......190 g3.Membrane Analogy,。·,···· 268 60.Curvilinear Coordinates. --4192 94.Torsion of a Bar of Narrow Reetangular Cross Seetion..... 272