INDEX A.C.system 443 reinforced 71 Acoustic gauge 444 Concrete columns 76,77 Acoustoelasticity 456 Constants,elastic 3,9,361,363,367 Active gauge 436,440,442,443 Continuous beams 115 Allowable stresses 308 Contraflexure 48 Area Crack detection 433 first moment of 67 Creep 15,432 second moment of 62,68 Criterion of failure 401 Auto frettage 233 Critical section ·72 Axis neutral 66 Crossed set-up 446 Cross-sensitivity 437 Curvature,radius of 62 Balanced circuit 437 Cylinders Balanced section 72 compound 224 Beams plastic yielding 223 bending stress in 64 thick 215 built-in 140-147 thin 198 cantilever97,98,101,109,110 continuous 115 Dark field 446 curved 284 D.C.system 443 shear stress in 154-166 De Forrest 432 Bending Deflections circular 66 bending 92-123 moment 41-56 impact 264 of beams 62-79 shear 269 plus direct stress 74 temperature effects 119 plus torsion 187 Delta rosette 382 simple theory of 64 Deviatoric stress 263 Birefringence 446 Dilatational stresses 386 Boundary stress 429 Direct integration method 97 Brittle materials 8,402,404,412 Distortion energy 385 Built-in beams 140-147 Distortional stresses 386 Bulk modulus 198.202 Double cantilever 146 Double integration method 89 Calibration 433 Ductile materials 8,14,402,404,411 Capacitance gauge 444 Ductility 4.8 Carriage spring 309 Dummy gauge 436,438 Carrier frequency system 444 Dye-etchant 433 Castigliano 255,266.269.303 Dynamic strain 434 Centroid 64,70 Eccentric loading 74 Circular shafts 176-190 Clapeyron's "three-moment"cquation 73 115 Economic section Close-coiled spring 299 Elastic constants 361.367 Combined modulus 29 Elastic limit 4 Complementary energy 257 Elastic modulus 3 Complex strain 361 Elasticity 3 Complex stress 326 Elongation 8 Composite beam 70 Encastred (encastre)beams 140-147 Compound bars 27 Endurance limit 17 Compound beams 70 Energy method 112 Compound shafts 182-184 Equivalent modulus 29 Compound tubes 224 Equivalent moment 187 Concrete 71 Equivalent torque 187,188 XXV
INDEX A.C. system 443 Acoustic gauge 444 Acoustoelasticity 456 Active gauge 436, 440, 442, 443 Allowable stresses 308 Area first moment of 67 second moment of 62, 68 Auto frettage 233 Axis neutral 66 Balanced circuit 437 Balanced section 72 Beams bending stress in 64 built-in 140-147 cantilever 97, 98, 101, 109, 110 continuous 115 curved 284 shear stress in 154166 circular 66 moment 41-56 of beams 62-79 plus direct stress 74 plus torsion 187 simple theory of 64 Bending Birefringence 446 Boundary stress 429 Brittle materials Built-in beams 140-147 Bulk modulus 198. 202 8, 402, 404, 412 Calibration 433 Capacitance gauge 444 Carriage spring 309 Carrier frequency system 444 Castigliano 255, 266, 269, 303 Centroid 64, 70 Circular shafts 176-190 Clapeyron’s “three-moment” equation 1 15 Close-coiled spring 299 Combined modulus 29 Complementary energy 257 Complex strain 361 Complex stress 326 Composite beam 70 Compound bars 27 Compound beams 70 Compound shafts 182-184 Compound tubes 224 Concrete 71 reinforced 71 Concrete columns 76, 77 Constants, elastic 3, 9, 361, 363, 267 Continuous beams 11 5 Contraflexure 48 Crack detection 433 Creep 15, 432 Criterion of failure 401 Critical section 72 Crossed set-up 446 Cross-sensitivity 437 Curvature, radius of 62 Cylinders compound 224 plastic yielding 223 thick 215 thin 198 Dark field 446 D.C. system 443 De Forrest 432 Deflections bending 92-123 impact 264 shear 269 temperature effects 119 Delta rosette 382 Deviatoric stress 263 Dilatational stresses 386 Direct integration method 97 Distortion energy 385 Distortional stresses 386 Double cantilever 146 Double integration method 89 Ductile materials 8, 14, 402, 404, 41 1 Ductility 4, 8 Dummy gauge 436, 438 Dye-etchant 433 Dynamic strain 434 Eccentric loading 74 Economic section 73 Elastic constants 361, 367 Elastic limit 4 Elastic modulus 3 Elasticity 3 Elongation 8 Encastred (encastre) beams 14&147 Endurance limit 17 Energy method 112 Equivalent modulus 29 Equivalent moment 187 Equivalent torque 187, 188 xxv
XXVi Index Factor Limit of proportionality 4 1oad13.414 Load of safety 12 alternating I Failure envelope 407 dead l Failure modes 416 fatigue I Failure theories 401 fluctuating l Fatigue 17 impact 1,265 Finite difference method 118 line 411 Fixed-ended beams 140-147 live 1 Fixing moment diagram 115,142,143 shock 1 Flitched beam 70 static 1 Foil gauge 435,437 Load factor 13 Force fits 229 Free length 30-34 Macaulay's method 102 Free-moment diagram 115,142,143 Masonry columns 76 Fringe order 449,450 Material fringe value 450 Fringe pattern 445-456 Maximum principal strain 361-387,404 Fringe value 449,450 Maximum principal stress 330-342.403 Frozen stress technique 454 Maximum shear plane 331 Full bridge circuit 436 Maximum shear stress 329,331,403 Maxwell failure theory 401.404 Gauge Maxwell reciprocal displacement 112 acoustic 444 McClintock method 378 electric resistance 433-444 Modulus strain 434444 buk198,203,363 Gauge factor 436 combined 29 Graphical procedure elasticity 3 stress 332 equivalent 29 thick cylinders 223 rigidity 12,13 Grid technique 456 section 62 Griffith 404 Young's 3 Guest 401 Modular ratio 71 Mohr's modified shear stress theory 404 Haigh 401 Mohr's strain circle 372 Half bridge 436 Mohr's stress circle 332,335 Helical spring Mohr's theory for slope and deflection 108,140,141 close-coiled 299 Moire 456 open-coiled 301 Moment Hogging of beams 42 bending41-56,62-79 Hollow shafts 182 fixing115,142,143 Holography 456 of area 66.68 Hooke's law 3 of resistance 73 Hydrostatic stress 386 Moments,equation of three 115 Hydrostatic stress line 413 Monochromatic light 449 Hysteresis loop 6 Movement of supports 146 Impact loads and stresses 264 Necking 5 Inclined loads 52 Neutral axis 64.66 Increasing loads 100 Neutral surface 67 Inductance gauge 444 Null balance 437 Inflexion,point of 48,146 Interference 445,448 Oblique plane Interference allowance 226 strain on 370 Isochromatic 449 stress on 326 Isoclinic 452 Octahedral shear stress 404 Open-coiled springs 301 Joint efficiency 205 Parallel axis theorem 70 Lame line 223 Parallel connection of shafts 183 Lame theory 217 Parallel set-up 446 Lateral restraint 366 Percentage elongation 8 Leaf spring 309 Percentage reduction in area 8 Light field 446 Permanent set 5
XXVl Index Factor load 13, 414 of safety 12 Failure envelope 407 Failure modes 416 Failure theories 401 Fatigue 17 Finite difference method 118 Fixed-ended beams 140-147 Fixing moment diagram Flitched beam 70 Foil gauge 435, 437 Force fits 229 Free length 30-34 Free-moment diagram 115, 142, 143 Fringe order 449, 450 Fringe pattern 445456 Fringe value 449, 450 Frozen stress technique 454 Full bridge circuit 436 Gauge 115, 142, 143 acoustic 444 electric resistance 433-444 strain 43-4 Gauge factor 436 Graphical procedure stress 332 thick cylinders 223 Grid technique 456 Griffith 404 Guest 401 Haigh 401 Half bridge 436 Helical spring close-coiled 299 open-coiled 301 Hogging of beams 42 Hollow shafts 182 Holography 456 Hooke’s law 3 Hydrostatic stress 386 Hydrostatic stress line 413 Hysteresis loop 6 Impact loads and stresses 264 Inclined loads 52 Increasing loads 100 Inductance gauge 444 Inflexion, point of 48, 146 Interference 445, 448 Interference allowance 226 Isochromatic 449 Isoclinic 452 Joint efficiency 205 Lame line 223 Lame theory 217 Lateral restraint 366 Leaf spring 309 Light field 446 Limit of proportionality 4 Load alternating 1 dead 1 fatigue 1 fluctuating 1 impact I, 265 line 411 live 1 shock 1 static 1 Load factor 13 Macaulay’s method 102 Masonry columns 76 Material fringe value 450 Maximum principal strain 361-387, 404 Maximum principal stress 330-342, 403 Maximum shear plane 331 Maximum shear stress 329, 331, 403 Maxwell failure theory 401, 404 Maxwell reciprocal displacement 112 McClintock method 378 Modulus bulk 198, 203, 363 combined 29 elasticity 3 equivalent 29 rigidity 12, 13 section 62 Young’s 3 Modular ratio 71 Mohr’s modified shear stress theory 404 Mohr’s strain circle 372 Mohr’s stress circle 332, 335 Mohr’s theory for slope and deflection Moirt 456 Moment 108, 140, 141 bending 41-56, 62-79 fixing 115, 142, 143 of area 66, 68 of resistance 73 Moments, equation of three 115 Monochromatic light 449 Movement of supports 146 Necking 5 Neutral axis 64, 66 Neutral surface 67 Null balance 437 Oblique plane strain on 370 stress on 326 Octahedral shear stress 404 Open-coiled springs 301 Parallel axis theorem 70 Parallel connection of shafts 183 Parallel set-up 446 Percentage elongation 8 Percentage reduction in area 8 Permanent set 5
Index xxVii Photoelastic coating 454 Shrink-fit cylinders 224.226 Photoelasticity 445 Specific resistance 435 reflection 454 Spiral spring 314 transmission 445 Spring Piezo-resistive gauge 444 carriage 309 Plane polarisation 446 close-coiled 299 Plastic deformation 5 helical 299 Pneumatic gauge 444 in parallel 306 Poisson's ratio 9-11 in series 305 Polar section modulus 181 open-coiled 301 Polar second moment of area 179 quarter--elliptic、312 Polariscope 446 semi-elliptic 309 Polariser 446 spiral 317 Pole point 54 stiffness 306 Principal planes 331 Stern 598 Principal strain 362,372 Stiffness of springs 306 Principal stress 331 Strain Principle of superposition 34,52,112 complex 361 Proof load 311 diametral 200 Proof stress 5 direct 2 Proof stress(springs)312 initial 16 Proportionality,limit of 4 lateral 9 Propped cantilever 130 micro 2 Pure shear 327 principal 362,372 rosette 378.381 Quarter bridge 436 shear11,180.371 Quarter-wave plates 451,452 threshold 431 volumetric 201,202 Rankine 401 Strain circle 372 Rectangular rosette 382 Strain energy Reflection polariscope 454 dilatational 262 Reflective coating 454 distortional 263 Relation between M.O.and w 94 in bending 260 Replica technique 456 in curved members 284 Resilience 257 in direct stress 257 modulus of 254 in shear 263 pr0of254,257 in springs 302,304 Resistivity 435 in torsion 184,261 Rosette strain gauge analysis 378,381 shear 263.385 Ruge and Simmons 435 total 385 volumetric 263,385 Safety factor 13,414,430 Strain gauge 378,434 Sagging 42 Strength,tensile 5 Saint-Venant 401 Stress Second moment of area 66,68 bending 65-79 Semi-conductor gauges 444 boundary 449 Senarment 45 circumferential 199 Series-connected shafts 182 complementary shear 155.237 Shafts,torsion of 176-190 complex 326 Shear deviatoric 263 complementary 155,327 direct 2 double 12 ho0p199.202 Shear centre 165 hydrostatic 386 Shear deflection 269 longitudinal 199 Shear distribution 156 proof 5.312 Shear force11,41-56.154-166 radial 198 Shear strain 11,180,371 separation 454 Shear strain energy 259,385 shear11.180.326 Shear stress 11.180.326 spherical 386 in bending 77,154 three-dimensional 338 in torsion 176 two-dimensional 10.326 Shells,thin 202-206 ultimate tensile 5 Shrinkage allowance 226 volumetric 363
Idex xxvii Photoelastic coating 454 Photoelasticity 445 reflection 454 transmission 445 Piezo-resistive gauge 444 Plane polarisation 446 Plastic deformation 5 Pneumatic gauge 444 Poisson's ratio 9-1 1 Polar section modulus 181 Polar second moment of area Polariscope 446 Polariser 446 Pole point 54 Principal planes 331 Principal strain 362, 372 Principal stress 33 1 Principle of superposition 34, 52, 112 Proof load 31 1 Proof stress 5 Proof stress (springs) 3 12 Proportionality, limit of 4 Propped cantilever 130 Pure shear 327 Quarter bridge 436 Quarter-wave plates 451, 452 Rankine 401 Rectangular rosette 382 Reflection polariscope 454 Reflective coating 454 Relation between M, Q, and w 94 Replica technique 456 Resilience 257 179 modulus of 254 proof 254, 257 Resistivity 435 Rosette strain gauge analysis Ruge and Simmons 435 Safety factor 13, 414, 430 Sagging 42 Saint-Venant 401 Second moment of area 66, 68 Semi-conductor gauges 444 Senarment 45 Series-connected shafts 182 Shafts, torsion of 176190 Shear complementary 155, 327 double 12 378, 381 Shear centre 165 Shear deflection 269 Shear distribution 156 Shear force 11, 41-56, 154-166 Shear strain 11, 180, 371 Shear strain energy 259, 385 Shear stress 11, 180, 326 in bending 77, 154 in torsion 176 Shells, thin 202-206 Shrinkage allowance 226 Shrink-fit cylinders 224. 226 Specific resistance 435 Spiral spring 3 I4 Spring carriage 309 close-coiled 299 helical 299 in parallel 306 in series 305 open-coiled 301 quarter-elliptic 3 12 semi-elliptic 309 spiral 317 stiffness 306 Stern 598 Stiffness of springs 306 Strain complex 361 diametral 200 direct 2 initial 16 lateral 9 micro 2 principal 362, 372 rosette 378, 381 shear I I, 180, 371 threshold 43 1 volumetric 20 I, 202 Strain circle 372 Strain energy dilatational 262 distortional 263 in bending 260 in curved members 284 in direct stress 257 in shear 263 in springs 302, 304 in torsion 184, 261 shear 263, 385 total 385 volumetric 263, 385 Strain gauge 378, 434 Strength, tensile 5 Stress bending 65-79 boundary 449 circumferential 199 complementary shear 155, 237 complex 326 deviatoric 263 direct 2 hoop 199,202 hydrostatic 386 longitudinal 199 proof 5, 312 radial 198 separation 454 shear 11. 180, 326 spherical 386 three-dimensional 338 two-dimensional IO, 326 ultimate tensile 5 volumetric 363
xXviii Index working 12 Tresca theory 401,403,412 yield 4.401 Twist,angle of 176-190 Stress concentration 14.413,515 Stress concentration factor 14 Unbalanced bridge 437 Stress freezing technique 454 Unit load method 268 Stress trajectory 453 Stresscoat 432 Volume change 201,203,364,365 Superposition,principle of 34,52,112 Volumetric strain 363,369 Volumetric strain energy 263,385 Tapered shaft 186 von Mises theory 401,404 Tardy compensaion 451 Temperature compensation 438 Wheatstone bridge 436 Temperature stresses 30-34,231,439 Wind-up angle 301,305 Temporary birefringence 446 Wire gauge 435 Tensile strength 5 Wire-wound thick cylinder 194 Tensile test 4 Wire-wound thin cylinder 206 Theory of failure 401-417 Thermal stresses 231 X-rays 456 Thick cylinders 215-251 Thin cylinders 198-207 Yield criteria 401 Threshold strain 431 Yield loci Thrust diagram 53 two-dimensional 406 Torsion three-dimensional 412 of shafts 176 Yield point 5 Torsional rigidity 182 Yield stress 4,401 Toughness 14 Yield theories 401-417 Transverse sensitivity 437 Young's modulus 3,361
xxviii Index working 12 yield 4, 401 Stress concentration 14, 413, 515 Stress concentration factor 14 Stress freezing technique 454 Stress trajectory 453 Stresscoat 432 Superposition, principle of 34, 52, 112 Tapered shaft 186 Tardy compensaion 451 Temperature compensation 438 Temperature stresses 3G34, 23 1, 439 Temporary birefringence 446 Tensile strength 5 Tensile test 4 Theory of failure 401417 Thermal stresses 231 Thick cylinders 215-251 Thin cylinders 198-207 Threshold strain 43 1 Thrust diagram 53 Torsion of shafts 176 Torsional rigidity 182 Toughness 14 Transverse sensitivity 437 Tresca theory 401, 403, 412 Twist, angle of 176190 Unbalanced bridge 437 Unit load method 268 Volume change 201, 203, 364, 365 Volumetric strain 363, 369 Volumetric strain energy 263, 385 von Mises theory 401, 404 Wheatstone bridge 436 Wind-up angle 301, 305 Wire gauge 435 Wire-wound thick cylinder 194 Wire-wound thin cylinder 206 X-rays 456 Yield criteria 401 Yield loci two-dimensional 406 three-dimensional 412 Yield point 5 Yield stress 4, 401 Yield theories 401417 Young’s modulus 3, 361
