Copyrighted Materials t0CrpUvy Press fort wwo INDEX Index Terms Links A A matrix 70 80 Amplification factor 302 Average stress criterion 431 B Back calculation of engineering constants 451 example 451 B-matrix 70 80 Beams applied loads 203 bending 206 bending stiffness 206 207 208 209 210 boundary conditions 205 206 264 box-beams See Box-beams buckling. See Buckling of beams; Buckling of beams with shear deformation C-section beams.See C-beams centroid 203 with circular cross section.See Beams with circular cross section compliance 209 coordinate system 203 This page has been reformatted by Knovel to provide easier navigation
This page has been reformatted by Knovel to provide easier navigation. INDEX Index Terms Links A A matrix 70 80 Amplification factor 302 Average stress criterion 431 B Back calculation of engineering constants 451 example 451 B-matrix 70 80 Beams applied loads 203 bending 206 bending stiffness 206 207 208 209 210 boundary conditions 205 206 264 box-beams. See Box-beams buckling. See Buckling of beams; Buckling of beams with shear deformation C-section beams. See C-beams centroid 203 with circular cross section. See Beams with circular cross section compliance 209 coordinate system 203
Index Terms Links Beams(Cont.) coupling.See Coupling curvature 204 equilibrium 204 force-strain relationship 204 206 209 governing equations 203 I-beams.See I-beams internal forces 203 isotropic beams 206 L-beams.See L-beams neutral plane 213 See also Neutral plane orthotropic beams 207 rate of twist 204 rectangular solid cross section See Solid-section beams under axial load and bending reference plane 213 See also Reference plane replacement stiffness 210 restrained-warping-induced torque 263 318 339 354 sandwich.See Sandwich beams shear center.See Shear center shear deformation.See Beams with shear deformation;Sandwich beams shear force 203 stiffness 204 strain-displacement relationship 204 summary of equations 311 with symmetrical cross section 206 tensile stiffness 206 207 208 210 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Beams (Cont.) coupling. See Coupling curvature 204 equilibrium 204 force–strain relationship 204 206 209 governing equations 203 I-beams. See I-beams internal forces 203 isotropic beams 206 L-beams. See L-beams neutral plane 213 See also Neutral plane orthotropic beams 207 rate of twist 204 rectangular solid cross section See Solid-section beams under axial load and bending reference plane 213 See also Reference plane replacement stiffness 210 restrained-warping-induced torque 263 318 339 354 sandwich. See Sandwich beams shear center. See Shear center shear deformation. See Beams with shear deformation; Sandwich beams shear force 203 stiffness 204 strain-displacement relationship 204 summary of equations 311 with symmetrical cross section 206 tensile stiffness 206 207 208 210
Index Terms Links Beams (Cont.) thin-walled beams. See Closed-section beams under axial load and bending;Open- section beams under axial load and bending;Stiffened beams;Thin-walled beams under axial load,bending,and torsion;Torsion of thin-walled beams torque neutral surface 254 258 torsional stiffness 206 208 210 transversely loaded.See Transversely loaded beams;Transversely loaded beams with shear deformation T-section beams.See T-beams twist 203 vibration.See Vibration warping stiffness.See Warping stiffness Z-section beams.See Z-beams Beam element 397 Beam equations,summary of 311 Beams with circular cross section 454 455 458 Beams with shear deformation 313 See also Sandwich beams;Transversely loaded beams with shear deformation bending moment 319 bending stiffness 322 boundary conditions 321 buckling. See Buckling of beams with shear deformation This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Beams (Cont.) thin-walled beams. See Closed-section beams under axial load and bending; Opensection beams under axial load and bending; Stiffened beams; Thin-walled beams under axial load, bending, and torsion; Torsion of thin-walled beams torque neutral surface 254 258 torsional stiffness 206 208 210 transversely loaded. See Transversely loaded beams; Transversely loaded beams with shear deformation T-section beams. See T-beams twist 203 vibration. See Vibration warping stiffness. See Warping stiffness Z-section beams. See Z-beams Beam element 397 Beam equations, summary of 311 Beams with circular cross section 454 455 458 Beams with shear deformation 313 See also Sandwich beams; Transversely loaded beams with shear deformation bending moment 319 bending stiffness 322 boundary conditions 321 buckling. See Buckling of beams with shear deformation
Index Terms Links Beams with shear deformation (Cont. coordinate system 313 deflection 313 330 deformation 313 effects of shear deformation 359 equations,summary of 320 equilibrium 320 force-strain relationship 315 governing equations 314 I-beams 315 324 rate of twist 314 315 317 restrained-warping-induced torque 319 rotation of the cross-section 313 314 Saint-Venant torque 317 shear compliance 320 321 shear force 319 shear stiffness 320 321 322 325 strain-displacement relationship 315 strain energy 322 tensile stiffness 322 torsional stiffness 322 transverse shear strain 313 vibration 347 warping stiffness 322 Bending-bending coupling 73 Bending moment.See Moment Bending-shear coupling 73 Bending stiffness of beams with shear deformation 322 of box-beams 256 258 454 455 456 of C-beams 285 454 456 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Beams with shear deformation (Cont.) coordinate system 313 deflection 313 330 deformation 313 effects of shear deformation 359 equations, summary of 320 equilibrium 320 force–strain relationship 315 governing equations 314 I-beams 315 324 rate of twist 314 315 317 restrained-warping-induced torque 319 rotation of the cross-section 313 314 Saint-Venant torque 317 shear compliance 320 321 shear force 319 shear stiffness 320 321 322 325 strain–displacement relationship 315 strain energy 322 tensile stiffness 322 torsional stiffness 322 transverse shear strain 313 vibration 347 warping stiffness 322 Bending–bending coupling 73 Bending moment. See Moment Bending–shear coupling 73 Bending stiffness of beams with shear deformation 322 of box-beams 256 258 454 455 456 of C-beams 285 454 456
Index Terms Links Bending stiffness(Cont.) of circular cross-section beams 454 455 of closed-section beams 231 232 234 235 246 of I-beams 295 454 455 456 of L-beams 223 of open-section beams 230 231 232 234 235 236 of sandwich beams 327 328 333 334 of stiffened beams 289 ofT-beams 219 240 Bending stiffness parameter 100 Bending-twist coupling 72 76 Bernoulli-Navier hypothesis 203 227 267 313 Biaxial test 418 Bimoment 262 317 318 319 354 Boundary conditions 47 beams 205 206 264 beams with shear deformation 321 plates 92 101 113 145 sandwich plates 172 183 torsion of beams 264 Box-beams 255 272 300 bending stiffness 256 258 454 455 456 centroid 274 454 456 compliance 274 deflection 257 259 elongation 260 274 examples 255 257 272 304 local buckling 300 304 neutral surface 258 259 parameter of restraint 304 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Bending stiffness (Cont.) of circular cross-section beams 454 455 of closed-section beams 231 232 234 235 246 of I-beams 295 454 455 456 of L-beams 223 of open-section beams 230 231 232 234 235 236 of sandwich beams 327 328 333 334 of stiffened beams 289 of T-beams 219 240 Bending stiffness parameter 100 Bending–twist coupling 72 76 Bernoulli–Navier hypothesis 203 227 267 313 Biaxial test 418 Bimoment 262 317 318 319 354 Boundary conditions 47 beams 205 206 264 beams with shear deformation 321 plates 92 101 113 145 sandwich plates 172 183 torsion of beams 264 Box-beams 255 272 300 bending stiffness 256 258 454 455 456 centroid 274 454 456 compliance 274 deflection 257 259 elongation 260 274 examples 255 257 272 304 local buckling 300 304 neutral surface 258 259 parameter of restraint 304
Index Terms Links Box-beams (Cont.) reference surface 259 shear compliance 458 spring constant 304 stiffness 256 258 259 273 tensile stiffness 259 454 455 456 torque neutral surface 258 torsion 255 257 torsional stiffness 256 258 458 twist 257 259 274 warping stiffness 458 Bredt-Batho formula 253 Buckling amplification factor 302 Buckling constant 292 Buckling length.See Buckling of plates Buckling load parameter.See Load parameter Buckling load.See Buckling of:beams;beams with shear deformation; cylinders;plates;shells Buckling of beams 290 461 effective length factor 292 293 examples 294 298 304 305 flexural-torsional 291 force-strain relationship 291 lateral-torsional 296 local buckling 300 orthotropic beams 290 spring constant 301 Buckling of beams with shear deformation 334 equilibrium 335 339 examples 342 343 345 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Box-beams (Cont.) reference surface 259 shear compliance 458 spring constant 304 stiffness 256 258 259 273 tensile stiffness 259 454 455 456 torque neutral surface 258 torsion 255 257 torsional stiffness 256 258 458 twist 257 259 274 warping stiffness 458 Bredt–Batho formula 253 Buckling amplification factor 302 Buckling constant 292 Buckling length. See Buckling of plates Buckling load parameter. See Load parameter Buckling load. See Buckling of: beams; beams with shear deformation; cylinders; plates; shells Buckling of beams 290 461 effective length factor 292 293 examples 294 298 304 305 flexural–torsional 291 force–strain relationship 291 lateral–torsional 296 local buckling 300 orthotropic beams 290 spring constant 301 Buckling of beams with shear deformation 334 equilibrium 335 339 examples 342 343 345
Index Terms Links Buckling of beams with shear deformation(Cont.) flexural 335 flexural-torsional 341 lateral-torsional 345 shear deformation effects 359 torsional 339 Buckling of cylinders 387 buckled shape 389 buckling pattern 387 390 examples 387 391 with orthotropic wall 390 with sandwich wall 393 Buckling of plates 112 under biaxial load 112 118 187 buckled shape 122 125 127 136 buckling length 135 buckling load 123 125 136 with built-in and simply supported edges 118 equilibrium 132 examples 115 116 121 126 130 examples,long plates 133 138 139 examples,sandwich plates 186 188 195 face wrinkling 190 with free edge 124 under linearly varying load 140 load parameter 112 119 long plates with various edge supports 132 potential energy 118 125 potential of external forces 113 principle of stationary potential energy 113 118 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Buckling of beams with shear deformation (Cont.) flexural 335 flexural–torsional 341 lateral–torsional 345 shear deformation effects 359 torsional 339 Buckling of cylinders 387 buckled shape 389 buckling pattern 387 390 examples 387 391 with orthotropic wall 390 with sandwich wall 393 Buckling of plates 112 under biaxial load 112 118 187 buckled shape 122 125 127 136 buckling length 135 buckling load 123 125 136 with built-in and simply supported edges 118 equilibrium 132 examples 115 116 121 126 130 examples, long plates 133 138 139 examples, sandwich plates 186 188 195 face wrinkling 190 with free edge 124 under linearly varying load 140 load parameter 112 119 long plates with various edge supports 132 potential energy 118 125 potential of external forces 113 principle of stationary potential energy 113 118
Index Terms Links Buckling of plates(Cont.) Ritz method 113 118 183 188 with rotationally restrained edges 127 sandwich plates 185 shear load,under 140 with simply supported edges 112 strain energy 112 under uniaxial load 122 123 124 Buckling of shells 384 buckled shape 386 389 buckling pattern 386 387 390 391 examples 387 391 C C-beams 284 bending stiffness 285 454 456 centroid 285 454 456 coordinate system 285 deflection 286 examples 284 287 shear center 286 457 shear compliance 459 tensile stiffness 285 454 456 torsional stiffness 286 457 twist 286 288 warping stiffness 288 457 Center of mass 309 310 Center of gravity 203 213 Center of twist 252 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Buckling of plates (Cont.) Ritz method 113 118 183 188 with rotationally restrained edges 127 sandwich plates 185 shear load, under 140 with simply supported edges 112 strain energy 112 under uniaxial load 122 123 124 Buckling of shells 384 buckled shape 386 389 buckling pattern 386 387 390 391 examples 387 391 C C-beams 284 bending stiffness 285 454 456 centroid 285 454 456 coordinate system 285 deflection 286 examples 284 287 shear center 286 457 shear compliance 459 tensile stiffness 285 454 456 torsional stiffness 286 457 twist 286 288 warping stiffness 288 457 Center of mass 309 310 Center of gravity 203 213 Center of twist 252
Index Terms Links Centroid 203 of box-beams 274 454 456 of C-beams 285 454 456 of closed-section beams 231 232 234 235 of I-beams 295 454 455 456 of L-beams 223 of open-section beams 230 231 232 234 235 236 of sandwich beams 328 of solid-section beams 213 of stiffened beams 289 of T-beams 219 240 of thin-walled beams with arbitrary layup 271 Characteristic length 431 434 Circular frequency 141 See also Vibration of beams 306 350 352 463 of plates 141 196 Closed-section beams under axial load and bending 243 See also Box beams bending stiffness 231 232 234 235 246 centroid 231 232 234 235 compatibility condition 245 compliance 247 coordinate system 243 269 displacements 243 force-strain relationship 247 267 neutral surface 453 tensile stiffness 231 232 234 235 247 transversely loaded 278 282 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Centroid 203 of box-beams 274 454 456 of C-beams 285 454 456 of closed-section beams 231 232 234 235 of I-beams 295 454 455 456 of L-beams 223 of open-section beams 230 231 232 234 235 236 of sandwich beams 328 of solid-section beams 213 of stiffened beams 289 of T-beams 219 240 of thin-walled beams with arbitrary layup 271 Characteristic length 431 434 Circular frequency 141 See also Vibration of beams 306 350 352 463 of plates 141 196 Closed-section beams under axial load and bending 243 See also Box beams bending stiffness 231 232 234 235 246 centroid 231 232 234 235 compatibility condition 245 compliance 247 coordinate system 243 269 displacements 243 force-strain relationship 247 267 neutral surface 453 tensile stiffness 231 232 234 235 247 transversely loaded 278 282
Index Terms Links Compliance See also Shear compliance of beams 209 of closed-section beams 247 254 266 273 274 constraint on 56 58 example 21 of isotropic material 12 14 21 35 42 of generally anisotropic material 9 29 30 36 of laminates 71 74 76 77 81 of monoclinic material 12 32 in new reference plane 81 of open-section beams 266 of orthotropic material 12 14 34 41 under plane-strain 30 32 33 34 under plane-stress 39 41 42 of solid-section beams 212 214 250 transformation 53 of transversely isotropic material 12 14 20 35 42 of woven fabric 44 Conservation of energy 145 323 Constitutive equations. See Stress-strain relationship, Force-strain relationship Continuity condition 48 Conversion factors 467 Coordinate system of beams 203 211 313 of C-beams 221 of closed section beams 243 265 267 268 of isotropic material 20 of laminates 63 66 This page has been reformatted by Knovel to provide easier navigation
Index Terms Links This page has been reformatted by Knovel to provide easier navigation. Compliance See also Shear compliance of beams 209 of closed-section beams 247 254 266 273 274 constraint on 56 58 example 21 of isotropic material 12 14 21 35 42 of generally anisotropic material 9 29 30 36 of laminates 71 74 76 77 81 of monoclinic material 12 32 in new reference plane 81 of open-section beams 266 of orthotropic material 12 14 34 41 under plane-strain 30 32 33 34 under plane-stress 39 41 42 of solid-section beams 212 214 250 transformation 53 of transversely isotropic material 12 14 20 35 42 of woven fabric 44 Conservation of energy 145 323 Constitutive equations. See Stress–strain relationship, Force–strain relationship Continuity condition 48 Conversion factors 467 Coordinate system 3 of beams 203 211 313 of C-beams 221 of closed section beams 243 265 267 268 of isotropic material 20 of laminates 63 66
