viii Contents 6.22 Reflective coating technique 190 6.23 Other methods of strain measurement 192 Bibliography 192 7 Circular Plates and Diaphragms 193 Summary 193 A.CIRCULAR PLATES 195 7.1 Stresses 195 7.2 Bending moments 197 7.3 General equation for slope and deflection 198 7.4 General case of a circular plate or diaphragm subjected to combined uniformly distributed load q(pressure)and central concentrated load F 199 7.5 Uniformly loaded circular plate with edges clamped 200 7.6 Uniformly loaded circular plate with edges freely supported 202 7.7 Circular plate with central concentrated load F and edges clamped 203 7.8 Circular plate with central concentrated load F and edges freely supported 205 7.9 Circular plate subjected to a load F distributed round a circle 206 7.10 Application to the loading of annular rings 208 7.11 Summary of end conditions 208 7.12 Stress distributions in circular plates and diaphragms subjected to lateral pressures 209 7.13 Discussion of results-limitations of theory 211 7.14 Other loading cases of practical importance 212 B.BENDING OF RECTANGULAR PLATES 213 7.15 Rectangular plates with simply supported edges carrying uniformly distributed loads 213 7.16 Rectangular plates with clamped edges carrying uniformly distributed loads 214 Examples 215 Problems 218 8 Introduction to Advanced Elasticity Theory 220 8.1 Types of stress 220 8.2 The cartesian stress components:notation and sign convention 220 8.2.1 Sign conventions 221 8.3 The state of stress at a point 221 8.4 Direct,shear and resultant stresses on an oblique plane 224 8.4.1 Line of action of resultant stress 226 8.4.2 Line of action of normal stress 227... VI11 Contents 6.22 Rejective coating technique 6.23 Other methods of strain measurement Bibliography 7 Circular Plates and Diaphragms Summary A. CIRCULAR PLATES 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.1 1 7.12 7.13 7.14 Stresses Bending moments General equation for slope and dejection General case of a circular plate or diaphragm subjected to combined uniformly distributed load q (pressure) and central concentrated load F Uniformly loaded circular plate with edges clamped Uniformly loaded circular plate with edges freely supported Circular plate with central concentrated load F and edges clamped Circular plate with central concentrated load F and edges freely supported Circular plate subjected to a load F distributed round a circle Application to the loading of annular rings Summary of end conditions Stress distributions in circular plates and diaphragms subjected to lateral pressures Discussion of results - limitations of theory Other loading cases of practical importance B. BENDING OF RECTANGULAR PLATES 7.15 7.16 Rectangular plates with simply supported edges carrying uniformly distributed loads Rectangular plates with clamped edges carrying uniformly distributed loads Examples Problems 8 Introduction to Advanced Elasticity Theory 8.1 Types of stress 8.2 8.3 8.4 The Cartesian stress components: notation and sign convention 8.2.1 Sign conventions The state of stress at a point Direct, shear and resultant stresses on an oblique plane 8.4.1 8.4.2 Line of action of resultant stress Line of action of normal stress 190 192 192 193 193 195 195 197 198 199 200 202 203 205 206 208 208 209 21 1 212 213 213 214 215 218 220 220 220 22 1 22 1 224 226 227