INDEX AC system 179 Creep 169,462 Acoustic gauge 180 Crinkling of struts 50 Acoustoelasticity 192 Crossed set-up 182 Active gauge 172,176,178-9 Cross-sensitivity 173 Airy stress function 263.265 Crushing stress 37 Allowable working load 73 Cyclic stress-strain 455 Alternating stress amplitude 447 Cylinders,residual stresses in 87 Annular rings 208 Cylindrical components 239 Area,principal moments of 4 Area,product moment of 3 Area,second moment of 3-10 Dark field 182 Auto frettage 89 Ayrton and Perry 42 DC system 179 De Forrest 168 Deflections,unsymmetrical members 15 Deviatoric stress 251 Balanced circuit 173 Diaphragms 193 Banded method 313 Directions cosine 223 Basquin's law 457 Disc Beams,curved 509 circular,solid 119 Bending,of beams 509-16 plastic yielding of 94 Bending,unsymmetrical 1 rotating 117 Birefringence 183 uniform strength 125 Body force stress 220 with central hole 122 Boundary condition,application 316,349 Discretisation 305 Boundary stress 185 Distortion 311 Bredt-Batho theory 147.150 Dummy gauge 172,175-6 Brittle lacquers 167 Dye-etchant 169 Buckling of struts 30 Dynamic strain 171 Built-up girders 52 Eccentric loading Calibration 69,169,186 of struts 42 Capacitance gauge 180 to collapse 85 Carrier frequency system 180 Ellipse Cartesian stress 220 momental 11 Case-hardened shafts 79 of second moments of area 9 Circular plates 193 Ellis 168 Circular polarisation 188 Endurance limit 423 Clarke 168 Equilibrium 319 Coffin-Manson Law 457 Equilibrium Collapse 64 cartesian coordinates 236 Columns 30 cylindrical coordinates 239 Combined circle (Mohr)228 Equivalent length 35 Combined diagram 229 Equivalent length (of Struts)35 Compatibility 261,321 Euler theory 31 Compensation .187 Extensometers 180 Conjugate diameters 13 Contact stress 382 Corkscrew rule 12 Factor,load 41,65,166 Correspondence table 347 Fatigue 446 Crack detection 169 Fatigue crack growth 486.489 Crack tip plasticity 482.488 Finite element analysis 302 537
INDEX AC system 179 Acoustic gauge 180 Acoustoelasticity 192 Active gauge 172, 176, 178-9 Airy stress function 263, 265 Allowable working load 73 Alternating stress amplitude 447 Annular rings 208 Area, principal moments of 4 Area, product moment of 3 Area, second moment of 3- 10 Auto frettage 89 Ayrton and Perry 42 Balanced circuit 173 Banded method 313 Basquin’s law 457 Beams, curved 509 Bending, of beams 509-16 Bending, unsymmetrical 1 Birefringence 183 Body force stress 220 Boundary condition, application 3 16, 349 Boundary stress 185 Bredt-Batho theory 147, 150 Brittle lacquers 167 Buckling of struts 30 Built-up girders 52 Calibration 69, 169, 186 Capacitance gauge 180 Carrier frequency system 180 Cartesian stress 220 Case-hardened shafts 79 Circular plates 193 Circular polarisation 188 Clarke 168 Coffin-Manson Law 457 Collapse 64 Columns 30 Combined circle (Mohr) 228 Combined diagram 229 Compatibility 261, 321 Compensation 187 Conjugate diameters 13 Contact stress 382 Corkscrew rule 12 Correspondence table 347 Crack detection 169 Crack tip plasticity 482, 488 Creep 169,462 Crinkling of struts 50 Crossed set-up 182 Cross-sensitivity 173 Crushing stress 37 Cyclic stress-strain 455 Cylinders, residual stresses in 87 Cylindrical components 239 Dark field 182 DC system 179 De Forrest 168 Deflections, unsymmetrical members 15 Deviatoric stress 251 Diaphragms 193 Directions cosine 223 Disc circular, solid 119 plastic yielding of 94 rotating 117 uniform strength 125 with central hole 122 Discretisation 305 Distortion 3 1 1 Dummy gauge 172, 175-6 Dye-etchant 169 Dynamic strain 171 Eccentric loading of struts 42 to collapse 85 momenta1 11 of second moments of area 9 Ellipse Ellis 168 Endurance limit 423 Equilibrium 319 Equilibrium Cartesian coordinates 236 cylindrical coordinates 239 Equivalent length 35 Equivalent length (of Struts) 35 Euler theory 31 Extensometers 180 Factor, load 41,65, 166 Fatigue 446 Fatigue crack growth 486,489 Finite element analysis 302 537
538 Index Finite element mesh 308 Neuber's rule 425 Finite element method 300 Notch sensitivity 424 Fixed-ended struts 33 Null balance 173 Flexural stiffness 193,197 Foil gauge 171,173 Fracture mechanics 472 Oblique plane,stress on 224 Fringe order 185-6 Octahedral planes 249 Fringe pattern181-2,184-192,420,481 Octahedral shear stress 250 Fringe value 185-6 Octahedral stress 249 Frontal method 315 Overspeeding 95 Frozen stress technique 190 Full bridge circuit 173 Parallel set-up 183 Partitioning 349 Gauge Perry-Robertson 29,39 acoustic 180 Photoelastic coating 190 electrical resistance 171-180 Photoelasticity strain 171-80 reflection 190 factor 172 transmission 181 Girder,built-up 50,52 Piezo-resistive gauge 180 Graphical procedure,stress 228-9 Plane polarisation 182 Grid technique 192 Plane strain 254 Griffith's criterion 475 Plane stress 254 Plastic bending 64 Plastic deformation Half-bridge 172-3 discs 94 Hetenyi 84 thick cylinder 87 Holography 192 Plastic hinge 71 Hydrostatic stress 249,251 Plastic limit design 71 Plastic torsion 75,79 Pneumatic gauge 180 Idealisation 305 Polariscope 182 Inductance gauge 180 Polariser 182 Initial curvature 41 Principal axes 2 Interference 181,184 Principal second moments of area 4 Isochromatic 185 Principal strain 228 Isoclinic 188 Principal stress 228,247 Product second moment of area 3 Johnson parabolic formula 36 Quarter-bridge 173 Quarter-wave plates 187 Land's circle of moments of area 7 Larson-Miller parameter 468 Laterally loaded struts 46 Radial stress117-23,125-8,193-9 Light field 182 Radius of gyration 28 Load factor 41,73 Rankine-Gordon theory 38 Rectangular plates 213 Reduced modulus 82 Reflection polariscope 190 Manson-Haferd parameter 469 Reflective coating 190 Material fringe value 185-6 Refraction 183 Maximum compressive stress 381,385,387 Replica technique 192 Mean stress 252,451 Residual stresses 73.79.84.86.95-6.394 Membrane 152 Resistivity 172 Modulus,reduced 82 Rotating cylinders 124 Mohr's circle of second moments of area 6 Rotating discs Mohr's strain circle 228 and rings 117 Mohr's stress circle 228 collapse 94 Moire 192 Rotating hollow discs 122 Momental ellipse 11,13 Rotating uniform strength discs 125 Monochromatic light 185 Ruge and Simmons 171
538 Index Finite element mesh 308 Finite element method 300 Fixed-ended struts 33 Flexural stiffness 193. 197 Foil gauge 171, 173 Fracture mechanics 47 Fringe order 185-6 Fringe pattern 181-2, Fringe value 185-6 Frontal method 3 15 Frozen stress technique Full bridge circuit 173 84- 192,420,481 190 Gauge acoustic 180 electrical resistance strain 171-80 factor 172 17 1 - 180 Girder, built-up 50, 52 Graphical pmedure, stress 228-9 Grid technique 192 Griffith’s criterion 475 Half-bridge 172-3 Het6nyi 84 Holography 192 Hydrostatic stress 249, 251 Idealisation 305 Inductance gauge 180 Initial curvature 41 Interference 181, 184 Isochromatic 185 Isoclinic 188 Johnson parabolic formula 36 Land’s circle of moments of area 7 Larson-Miller parameter 468 Laterally loaded struts 46 Light field 182 Load factor 41, 73 Manson-Haferd parameter 469 Material fringe value 185-6 Maximum compressive stress 381, 385,387 Mean stress 252.45 1 Membrane 152 Modulus. reduced 82 Mohr’s circle of second moments of area Mohr’s strain circle 228 Mohr’s stress circle 228 Moir6 192 Momenta1 ellipse 1 I, 13 Monochromatic light 185 6 Neuber’s rule 425 Notch sensitivity 424 Null balance 173 Oblique plane, stress on 224 Octahedral planes 249 Octahedral shear stress 250 Octahedral stress 249 Overspeeding 95 Parallel set-up 183 Partitioning 349 Perry-Robertson 29.39 Photoelastic coating 190 Photoelasticity reflection 190 transmission 18 1 Piezo-resistive gauge 180 Plane polarisation 182 Plane strain 254 Plane stress 254 Plastic bending 64 Plastic deformation discs 94 thick cylinder 87 Plastic hinge 71 Plastic limit design 71 Plastic torsion 75, 79 Pneumatic gauge 180 Polariscope 182 Polariser 182 Principal axes 2 Principal second moments of area 4 Principal strain 228 Principal stress 228, 247 Product second moment of area 3 Quarter-bridge 173 Quarter-wave plates 187 Radial stress 117-23, 125-8, 193-9 Radius of gyration 28 Rankine-Gordon theory 38 Rectangular plates 213 Reduced modulus 82 Reflection polariscope 190 Reflective coating 190 Refraction 183 Replica technique 192 Residual stresses 73.79.84.86.95-6.394 Resistivity 172 Rotating cylinders 124 Rotating discs and rings 117 collapse 94 Rotating hollow discs 122 Rotating uniform strength discs 125 Ruge and Simmons 171
Index 539 Safety factor 41,65,166 Struts 28 Saint-Venant 420 Sand heap analogy 78 Second moment of area 2-10 ellipse of 9 Tangential stress 193,199 principle 4 Tardy compensation 187 product 3 Temperature stresses 126 Semi-conductor gauges 180 Temporary birefringence 183 Senarment 187 Tensor notation 235 Shape factor 65 Thermal stresses 126 unsymmetrical sections 67.69 Thin membranes 194 Shear flow 147 Thin shells 517-18 Shear stress 224 Threshold strain 167 Sherby-Dom parameter 469 Timoshenko142,144,146,212,214 Skew loading 2 Torsion of cellular sections 150 Slendemness ration 28 Torsion of non-circular sections 141 Smith-Southwell theory 42 Torsion of open sections 143,150 Southwell 42 Torsion of rectangular sections 142 Specific resistance 172 Torsion of square closed of closed section 141 Stern 168 Torsion of thin-walled closed sections 147 Straight line formula 36 Torsion of thin-walled stiffened sections 151 Strain Torsion section modulus 144 deviatoric 251,253 Torsional rigidity 150 invariants 247 Toughness 473 threshold 167 Transformation 259,326 Strain circle 228 Transverse sensitivity 173 Strain gauge 171 Triangular plane membrane element 343 Strain hardening 63-4,80 Twist,angle of 141-7,149-52 Stress body force 220 boundary 185 Unbalanced bridge 173 cartesian 220 Uniform strength discs 125 concentration 86 Unsymmetrical bending I concentration factor 408 Unsymmetrical,section struts 49 concentration factor (evaluation)413 crushing 37 deviatoric 246,251 direct 224 Validity limit (Euler)37 equations of equilibrium 236 Virtual work 323 freezing technique 190 Viscoelasticity 521 hydrostatic 249-51 Voight-Kelvin 522 invariants 243-4 mean 252,447,451 radial 193,199 Warping 153,310 range 447 relaxation 470 Webb's approximation 44 Wheatstone bridge 172 separation 190 Wilson-Stokes equation 423 shear 224 Wire gauge 171 tangential 193,199 three-dimensional 220 trajectory 189 yield 61 X-rays 192 Stress concentration,effects 453 Stress intensity factor 477 stresscoat 168 Yield stress 61
Index 539 Safety factor 41, 65, 166 Saint-Venant 420 Sand heap analogy 78 Second moment of area 2- 10 ellipse of 9 principle 4 product 3 Semi-conductor gauges 180 Senarment 187 Shape factor 65 Shear flow 147 Shear stress 224 Sherby-Dom parameter 469 Skew loading 2 Slenderness ration 28 Smith-Southwell theory 42 Southwell 42 Specific resistance 172 Stem 168 Straight line formula 36 Strain deviatoric 251, 253 invariants 247 threshold 167 Strain circle 228 Strain gauge 171 Strain hardening 63-4, 80 Stress unsymmetrical sections 67,69 body force 220 boundary 185 Cartesian 220 concentration 86 concentration factor 408 concentration factor (evaluation) 41 3 crushing 37 deviatoric 246, 251 direct 224 equations of equilibrium 236 freezing technique 190 hydrostatic 249-51 invariants 243-4 mean 252,447,451 radial 193, 199 range 447 relaxation 470 separation 190 shear 224 tangential 193, 199 three-dimensional 220 trajectory 189 yield 61 Stress concentration, effects 453 Stress intensity factor 477 stresscoat 168 Struts 28 Tangential stress 193, 199 Tardy compensation 187 Temperature stresses 126 Temporary birefringence 183 Tensor notation 235 Thermal stresses 126 Thin membranes 194 Thin shells 517-18 Threshold strain 167 Timoshenko 142, 144, 146,212,214 Torsion of cellular sections 150 Torsion of non-circular sections 141 Torsion of open sections Torsion of rectangular sections 142 Torsion of square closed of closed section Torsion of thin-walled closed sections Torsion of thin-walled stiffened sections Torsion section modulus 144 Torsional rigidity 150 Toughness 473 Transformation 259, 326 Transverse sensitivity 173 Triangular plane membrane element 343 Twist, angle of 141 -7, 149-52 143, 150 141 147 151 Unbalanced bridge 173 Uniform strength discs 125 Unsymmetrical bending 1 Unsymmetrical, section struts 49 Validity limit (Euler) 37 Virtual work 323 Viscoelasticity 521 Voight-Kelvin 522 Warping 153,310 Webb’s approximation 44 Wheatstone bridge 172 Wilson-Stokes equation 423 Wire gauge 171 X-rays 192 Yield stress 61