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عدد المساهمات : 19004 التقييم : 35512 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Intermediate Mechanics of Materials الخميس 14 يناير 2021, 9:13 pm | |
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أخوانى فى الله أحضرت لكم كتاب Intermediate Mechanics of Materials J.R. Barber
و المحتوى كما يلي :
Contents 1 Introduction . 1 1.1 The Engineering design process 1 1.2 Design optimization 2 1.2.1 Predicting the behaviour of the component . 3 1.2.2 Approximate solutions 5 1.3 Relative magnitude of different effects . 5 1.4 Formulating and solving problems 8 1.4.1 Use of procedures 8 1.4.2 Inverse problems . 10 1.4.3 Physical uniqueness and existence arguments . 11 1.5 Review of elementary mechanics of materials . 11 1.5.1 Definition of stress components 11 1.5.2 Transformation of stress components 13 1.5.3 Displacement and strain . 13 1.5.4 Hooke’s law 15 1.5.5 Bending of beams 17 1.5.6 Torsion of circular bars . 18 1.6 Summary . 18 Problems . 19 2 Material Behaviour and Failure 25 2.1 Transformation of stresses . 26 2.1.1 Review of two-dimensional results 27 2.1.2 Principal stresses in three dimensions . 30 2.2 Failure theories for isotropic materials . 36 2.2.1 The failure surface . 37 2.2.2 The shape of the failure envelope . 39 2.2.3 Ductile failure (yielding) 39 2.2.4 Brittle failure 51 2.3 Cyclic loading and fatigue . 63 2.3.1 Experimental data 64vi Contents 2.3.2 Statistics and the size effect 68 2.3.3 Factors influencing the design stress 74 2.3.4 Effect of combined stresses 78 2.3.5 Effect of a superposed mean stress 78 2.3.6 Summary of the design process 83 2.4 Summary . 87 Problems . 88 3 Energy Methods . 99 3.1 Work done on loading and unloading 100 3.2 Strain energy 101 3.3 Load-displacement relations . 103 3.3.1 Beams with continuously varying bending moments . 106 3.3.2 Axial loading and torsion . 107 3.3.3 Combined loading . 108 3.3.4 More general expressions for strain energy . 109 3.3.5 Strain energy associated with shear forces in beams . 109 3.4 Potential energy 110 3.5 The principle of stationary potential energy . 113 3.5.1 Potential energy due to an external force . 115 3.5.2 Problems with several degrees of freedom . 115 3.5.3 Non-linear problems . 118 3.6 The Rayleigh-Ritz method . 120 3.6.1 Improving the accuracy . 124 3.6.2 Improving the back of the envelope approximation 126 3.7 Castigliano’s first theorem . 131 3.8 Linear elastic systems . 135 3.8.1 Strain energy 136 3.8.2 Bounds on the coefficients . 138 3.8.3 Use of the reciprocal theorem 140 3.9 The stiffness matrix . 141 3.9.1 Structures consisting of beams . 142 3.9.2 Assembly of the stiffness matrix 146 3.10 Castigliano’s second theorem . 146 3.10.1 Use of the theorem . 148 3.10.2 Dummy loads . 151 3.10.3 Unit load method 154 3.10.4 Formal procedure for using Castigliano’s second theorem 155 3.10.5 Statically indeterminate problems 155 3.10.6 Three-dimensional problems . 159 3.11 Summary . 161 Problems . 162Contents vii 4 Unsymmetrical Bending 185 4.1 Stress distribution in bending . 185 4.1.1 Bending about the x-axis only 186 4.1.2 Bending about the y-axis only 187 4.1.3 Generalized bending . 188 4.1.4 Force resultants 189 4.1.5 Uncoupled problems . 190 4.1.6 Coupled problems . 192 4.2 Displacements of the beam . 195 4.3 Second moments of area . 199 4.3.1 Finding the centroid 199 4.3.2 The parallel axis theorem . 200 4.3.3 Thin-walled sections . 204 4.4 Further properties of second moments . 207 4.4.1 Coordinate transformation . 207 4.4.2 Mohr’s circle of second moments . 208 4.4.3 Solution of unsymmetrical bending problems in principal coordinates . 213 4.4.4 Design estimates for the behaviour of unsymmetrical sections 215 4.4.5 Errors due to misalignment 219 4.5 Summary . 220 Problems . 221 5 Non-linear and Elastic-Plastic Bending . 235 5.1 Kinematics of bending 235 5.2 Elastic-plastic constitutive behaviour 237 5.2.1 Unloading and reloading 238 5.2.2 Yield during reversed loading 239 5.2.3 Elastic-perfectly plastic material 240 5.3 Stress fields in non-linear and inelastic bending . 241 5.3.1 Force and moment resultants . 242 5.4 Pure bending about an axis of symmetry . 243 5.4.1 Symmetric problems for elastic-perfectly plastic materials 244 5.4.2 Fully plastic moment and shape factor . 249 5.5 Bending of a symmetric section about an orthogonal axis . 250 5.5.1 The fully plastic case . 251 5.5.2 Non-zero axial force 254 5.5.3 The partially plastic solution . 255 5.6 Unsymmetrical plastic bending . 258 5.7 Unloading, springback and residual stress 263 5.7.1 Springback and residual curvature 264 5.7.2 Reloading and shakedown . 268 5.8 Limit analysis in the design of beams 269 5.8.1 Plastic hinges . 269 5.8.2 Indeterminate problems . 270viii Contents 5.9 Summary . 272 Problems . 274 6 Shear and Torsion of Thin-walled Beams . 287 6.1 Derivation of the shear stress formula 288 6.1.1 Choice of cut and direction of the shear stress 292 6.1.2 Location and magnitude of the maximum shear stress 297 6.1.3 Welds, rivets and bolts 299 6.1.4 Curved sections . 301 6.2 Shear centre . 303 6.2.1 Finding the shear centre . 304 6.3 Unsymmetrical sections . 311 6.3.1 Shear stress for an unsymmetrical section 311 6.3.2 Determining the shear centre . 311 6.4 Closed sections 313 6.4.1 Determination of the shear stress distribution . 313 6.5 Pure torsion of closed thin-walled sections . 318 6.5.1 Torsional stiffness 319 6.5.2 Design considerations in torsion 322 6.6 Finding the shear centre for a closed section 323 6.6.1 Twist due to a shear force . 324 6.6.2 Multicell sections 327 6.7 Torsion of thin-walled open sections . 328 6.7.1 Loading of an open section away from its shear centre . 331 6.8 Summary . 334 Problems . 336 7 Beams on Elastic Foundations . 353 7.1 The governing equation . 354 7.1.1 Solution of the governing equation 355 7.2 The homogeneous solution . 356 7.2.1 The semi-infinite beam . 357 7.3 Localized nature of the solution . 361 7.4 Concentrated force on an infinite beam . 362 7.4.1 More general loading of the infinite beam 364 7.5 The particular solution 365 7.5.1 Uniform loading . 366 7.5.2 Discontinuous loads 367 7.6 Finite beams . 370 7.7 Short beams . 373 7.8 Summary . 375 Problems . 376Contents ix 8 Membrane Stresses in Axisymmetric Shells . 385 8.1 The meridional stress . 386 8.1.1 Choice of cut 389 8.2 The circumferential stress 391 8.2.1 The radii of curvature . 393 8.2.2 Sign conventions . 395 8.3 Self-weight 398 8.4 Relative magnitudes of different loads . 401 8.5 Strains and Displacements . 402 8.5.1 Discontinuities 404 8.6 Summary . 406 Problems . 407 9 Axisymmetric Bending of Cylindrical Shells . 419 9.1 Bending stresses and moments . 419 9.2 Deformation of the shell . 421 9.3 Equilibrium of the shell element 423 9.4 The governing equation . 424 9.4.1 Solution strategy . 426 9.5 Localized loading of the shell 429 9.6 Shell transition regions 430 9.6.1 The cylinder/cone transition . 433 9.6.2 Reinforcing rings 436 9.7 Thermal stresses . 437 9.8 The ASME pressure vessel code 439 9.9 Summary . 440 Problems . 441 10 Thick-walled Cylinders and Disks 449 10.1 Solution method . 449 10.1.1 Stress components and the equilibrium condition 450 10.1.2 Strain, displacement and compatibility 451 10.1.3 The elastic constitutive law 452 10.2 The thin circular disk . 454 10.3 Cylindrical pressure vessels 460 10.4 Composite cylinders, limits and fits . 464 10.4.1 Solution procedure . 464 10.4.2 Limits and fits . 468 10.5 Plastic deformation of disks and cylinders 468 10.5.1 First yield 470 10.5.2 The fully-plastic solution 470 10.5.3 Elastic-plastic problems . 472 10.5.4 Other failure modes 476 10.5.5 Unloading and residual stresses 476x Contents Problems . 479 11 Curved Beams . 487 11.1 The governing equation . 487 11.1.1 Rectangular and circular cross sections 489 11.1.2 The bending moment . 491 11.1.3 Composite cross sections 494 11.1.4 Axial loading . 494 11.2 Radial stresses . 499 11.3 Distortion of the cross section 502 11.4 Range of application of the theory . 504 11.5 Summary . 504 Problems . 505 12 Elastic Stability 511 12.1 Uniform beam in compression 512 12.2 Effect of initial perturbations . 517 12.2.1 Eigenfunction expansions . 520 12.3 Effect of lateral load (beam-columns) 521 12.4 Indeterminate problems . 525 12.5 Suppressing low-order modes 526 12.6 Beams on elastic foundations . 530 12.6.1 Axisymmetric buckling of cylindrical shells 532 12.6.2 Whirling of shafts 533 12.7 Energy methods 538 12.7.1 Energy methods in beam problems 540 12.7.2 The uniform beam in compression 541 12.7.3 Inhomogeneous problems . 543 12.8 Quick estimates for the buckling force . 545 12.9 Summary . 546 Problems . 547 A The Finite Element Method . 559 A.1 Approximation . 560 A.1.1 The ‘best’ approximation 560 A.1.2 Choice of weight functions 561 A.1.3 Piecewise approximations . 563 A.2 Axial loading 567 A.2.1 The structural mechanics approach . 567 A.2.2 Assembly of the global stiffness matrix 569 A.2.3 The nodal forces . 570 A.2.4 The Rayleigh-Ritz approach . 571 A.2.5 Direct evaluation of the matrix equation . 576 A.3 Solution of differential equations . 577 10.6 Summary . 478Contents xi A.4.1 Nodal forces and moments 584 A.5 Two and three-dimensional problems 587 A.6 Computational considerations 588 A.6.1 Data storage considerations 590 A.7 Use of the finite element method in design 590 A.8 Summary . 591 Problems . 592 B Properties of Areas . 599 C Stress Concentration Factors 603 D Answers to Even Numbered Problems 607 Index . Index Alternating stress, 79 Anisotropy, 36 Anticlastic curvature, 396 Antiplane shear, 52 Approximation, 560 piecewise approximation, 563 ASME pressure vessel code, 439 Axial loading, 254, 567 in the plastic range, 254 of curved beams, 494 Auxiliary problem, 140 Banded matrix, 142, 570, 588 Barber’s exception, 6 Beam-columns, 521 Bending of beams, 17, 185 et seq. in the plastic range, 241 et seq. curved beams, 488 on elastic foundations, 353 Bending of shells, 419 et seq. Boiler, 401, 437 Bolts, 299 Brake disc, 6, 458 Brittle fracture, 25, 51 Buckling, 322, 511 et seq. force, 516, 526, 530, 545 initial perturbations, 517 lateral loads, 521 mode suppression, 526 of shells, 532 Bulk modulus, 485 Castigliano’s first theorem, 131 Castigliano’s second theorem, 146 et seq. Centroid, 190, 199 et seq., 599–602 Circumferential stress, 391, 472, 489 Circumferential strain, 403, 421, 422 Closed section, 305, 313 torsion of, 318 Coefficient of thermal expansion, 7, 16, 439, 458 Column, 512 Collocation, 560 Collocation points, 561 Compatibility, 450, 451 Compatibility equation, 452 Complementary energy, 148 Complementary shear stress, 12, 291 Compliance matrix, 136 Composite cylinders, 464 et seq. Constitutive law, 450, 452 Constraints, 123 Contact pressure, 465 Coordinate transformation, 26–36, 146, 207, 393 Crack opening displacement, 53 Critical force, 515 Critical speed, 534 Cubic spline, 581 Cyclic loading, 63 et seq., 268 Curved beams, 487 et seq. Decay length, 361, 425 Degrees of freedom, 111, 113, 116, 120, 143, 560, 562, 582, 587 Design, 1, 74, 83, 123, 215, 269, 298, 401, 459, 535 against torsion, 322 use of finite element method, 590616 Index optimization, 3 Deviatoric strain energy, 45 Deviatoric stress, 44 Diametral interference, 466 Dilatation, 41, 45 Dirac delta function, 363 Direction cosines, 31 Discontinuities, 368, 404 Dislocations, 40 Distortion, 45 Displacement, 13, 451 Double integrals, 599 Ductile, 25, 39 Dummy loads, 151 Economics, 2 Eigenfunction, 517 series, 520 Eigenvalues, 32, 517 Elastic behaviour, 100 Elastic foundation, 353 modulus of, 354 Elastic instability, 511 et seq. Elastic-plastic behaviour, 237 Elastic-perfectly plastic, 240, 472 in a cylinder, 472 Embedded elastic beam, 246, 247 Endurance limit, 66 Energy methods, 99 et seq., 538 Engineering shear strain, 14 Equation of motion, 451 Equilibrium, 112, 288, 355, 363, 387, 390, 392, 423, 450, 451, 462, 578 Equivalent tensile stress, 47 Equivalent determinate problem, 18, 155, 159 Failure envelope, 38, 39, 48, 49, 60–62 Failure theories, 36 et seq. Failure surface, 37 Fatigue, 25, 63 et seq. low cycle, 67 Fatigue limit, 66 Flexible axis, 209 Fillet radius, 74 Finite element method, 125, 559 et seq. for beam problems, 579 First yield moment, 242 Flexural rigidity, 102, 106, 211, 354, 358, 518, 581 Floating beams, 374 Foundation modulus, 354 Fourier series, 124 Fourier transform, 366 Fracture, brittle, 25 Fracture mechanics, 52 Fracture toughness, 52, 54 Fully-plastic moment, 242, 249, 251 Generalized coordinates, 148 Goodman diagram, 80 Gradient factor, 71 Griffith criterion, 52, 53 Heat exchanger, 437, 439 Homogeneous equation, 514 Homogeneous solution, 356, 514, 518 Hooke’s law, 15, 403, 421, 422, 437, 450, 452 Hoop stress, 391 Hydrostatic stress, 42 Hysteresis, 100 Indeterminacy, 155, 270, 525 Influence coefficients, 136 Initial imperfections, 517, 545 Initial perturbations, 517 Instability, 111, 113, 511 et seq. Interference, 465, 466 Invariants, 32, 34 Inverse problems, 10 Isotropic hardening, 239 Isotropy, 15, 36 Laplace transform, 366 Least squares fit, 120, 215, 561, 577 Limit analysis, 269 Limits and fits, 468 Linear elastic systems, 135 et seq. Longitudinal stress, 387 Manufacturing errors, 221, 468, 517, 520, 536, 545 Material failure, 25 et seq. Mathematical shear strain, 14 Maxwell’s reciprocal theorem, 138 et seq., 323 Melan’s theorem, 268 Metal forming, 235, 273, 283 Membrane displacement, 425 Median line, 252 Meridional stress, 386 Misalignment, 219, 517 Mode suppression, 526 Modified Mohr criterion, 61Index 617 Modulus, bulk, 485 of a foundation, 354 of rigidity, 16 shear, 16 Young’s, 15 Mohr’s circle, 28, 35 of second moments, 208 Mohr’s failure theory, 61 Multiply-connected section, 305 Neutral axis, 193, 216, 241, 489 Neutral plane, 188 Neutrally stable, 514, 515 Newton’s second law, 449, 451 Nodes, 141, 142, 563 Nodal displacements, 568, 579 Nodal forces, 570, 584 Nodal values, 563 Nominal stress, 74 Non-linearity, 118 Non-local displacement, 353, 362 Notch sensitivity, 76 Octahedral normal stress, 46 Octahedral plane, 45 Octahedral shear stress, 45, 46 Open section, 305 Orthogonality, 32, 125, 521 Parallel axis theorem, 200, 201 Particular solution, 365, 518 Periodic loading, 63 et seq., 268 Perturbations, 517 Plane sections remain plane, 186, 235, 236 Plane stress, 37, 453 Plane strain, 453, 461 Plastic hinge, 242, 269 Plastic moment, 242, 249, 251 Plates, 385 Poisson’s ratio, 15 strains, 422, 427, 453, 462 Potential energy, 110, 115 Pressure vessels, 460 plastic deformation, 468 Pressure vessel code, 439 Procedures, 8–10 Principal axes, 13, 29, 31, 209 Principal coordinates, 213 Principal second moments, 209 Principal stress, 29, 30 Process zone, 54 Product second moment (product inertia), 190, 199 Radial clearance, 466 Radial interference, 465 Radial stress, 472, 499 Rayleigh-Ritz method, 120 et seq., 540, 560, 571 Reciprocal theorem, 138 et seq., 323 Redundant reactions, 17, 155, 525 Reinforcing ringes, 436 Reliability, 68, 70 Residual stress, 263, 476 Residual curvature, 264 Rotation, 451, 456, 473, 534 S–N curve, 65 Safety factor, 47, 57, 63, 64, 78, 80, 84, 87 Saint Venant’s principle, 236 Second moments of area, 199, 599–602 Series, 124, 520, 560 eigenfunction, 520 Fourier, 124 Shakedown, 268 Shape factor, 249 Shape functions, 560, 564, 580 Shear centre, 303 et seq. for angle sections, 312 for closed sections, 323 et seq. Shear flow, 291, 294 Shear force, 287 et seq. twist due to, 324, 331 Shear modulus, 16 Shells, 385 et seq. displacements, 403 bending stresses in, 419 et seq. membrane stresses in, 386 et seq. radii, 393 self weight, 398 transitions, 430 Shrink fit, 482 Simply connected section, 305 Size effect, 68, 71 Springback, 264, 273, 283 Stability, 111, 113, 511 et seq. Statically indeterminate, 155, 270, 525 Stationary potential energy, 113 Stiff axis, 209 Stiffness, 101 of a shell, 422618 Index Stiffness matrix, 141 et seq., 559, 566 assembly, 146, 559, 569, 582 element stiffness matrix, 569 global stiffness matrix, 569 Strain, 11 circumferential, 403, 421, 422 normal, 13 shear, 14, 42 Strain energy, 43, 101 et seq., 492 in axial loading, 108 in bending, 102, 106 in a spring, 101 in torsion, 108, 319 Strain energy density, 44, 109 Strain energy release rate, 58 Stress, 11 alternating, 79 circumferential, 391, 472, 489 complementary shear, 12, 291 coordinate transformation, 26–36 deviatoric, 44 equivalent tensile, 47 hydrostatic, 42 invariants, 32, 34 longitudinal, 386 meridional, 386 nominal, 74 normal, 12 octahedral shear, 45 principal, 29, 30 radial, 472, 499 residual, 263, 476 shear, 12, 291 Stress concentration factor, 74, 603 Stress intensity factor, 51 et seq. Surface energy, 52 Surface factor, 72 Surface finish, 71 coefficient of, 16 Taylor, series, 386, 419 Thermal conductivity, 437 Thermal expansion, 16 Thermal stress, 437, 458 Thin-walled sections, 204, 287 et seq., 511 Tolerances, 468 Toroidal transition, 431 et seq. Torque wrench, 133 Torsion, 18, 108 of closed thin-walled sections, 318 design considerations, 322 multicell sections, 327 of open thin-walled sections, 328 Torsional stiffness, 319 Transformation of coordinates, 26–36, 146, 207, 393 Twist, 319, 324 Tresca’s theory, 43, 48, 469 Ultimate strength, 67, 80, 81 Unilateral support, 360 Uniqueness, 11 Unit load method, 154 Unloading, 238, 263, 476 Unsymmetrical bending, 185 et seq. plastic, 258 shear stresses, 311 Variational methods, 99 et seq. Volume change, 41, 45 von Mises theory, 43, 48 Weibull distribution, 68 Weight functions, 561 Welds, 299 Whirling of shafts, 533 Whirling speed, 534 Winkler foundation, 354 Work done, 100, 319 Work hardening, 167, 238 Yielding, 25, 39 Young’s modulus, 15
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