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عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Mechanics and Strength of Materials الأحد 02 أكتوبر 2022, 7:22 pm | |
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أخواني في الله أحضرت لكم كتاب Mechanics and Strength of Materials Vitor Dias da Silva
و المحتوى كما يلي :
Contents Part I Introduction to the Mechanics of Materials I Introduction . 3 I.1 General Considerations . 3 I.2 Fundamental Definitions . 4 I.3 Subdivisions of the Mechanics of Materials 6 II The Stress Tensor . 9 II.1 Introduction 9 II.2 General Considerations . 9 II.3 Equilibrium Conditions 12 II.3.a Equilibrium in the Interior of the Body . 12 II.3.b Equilibrium at the Boundary 15 II.4 Stresses in an Inclined Facet 16 II.5 Transposition of the Reference Axes . 17 II.6 Principal Stresses and Principal Directions 19 II.6.a The Roots of the Characteristic Equation . 21 II.6.b Orthogonality of the Principal Directions 22 II.6.c Lam´e’s Ellipsoid . 22 II.7 Isotropic and Deviatoric Components of the Stress Tensor 24 II.8 Octahedral Stresses 25 II.9 Two-Dimensional Analysis of the Stress Tensor 27 II.9.a Introduction . 27 II.9.b Stresses on an Inclined Facet 28 II.9.c Principal Stresses and Directions . 29 II.9.d Mohr’s Circle 31 II.10 Three-Dimensional Mohr’s Circles . 33 II.11 Conclusions . 36 II.12 Examples and Exercises 37XII Contents III The Strain Tensor . 41 III.1 Introduction 41 III.2 General Considerations . 41 III.3 Components of the Strain Tensor 44 III.4 Pure Deformation and Rigid Body Motion 49 III.5 Equations of Compatibility . 51 III.6 Deformation in an Arbitrary Direction . 54 III.7 Volumetric Strain . 58 III.8 Two-Dimensional Analysis of the Strain Tensor . 59 III.8.a Introduction . 59 III.8.b Components of the Strain Tensor . 60 III.8.c Strain in an Arbitrary Direction . 60 III.9 Conclusions . 63 III.10 Examples and Exercises 64 IV Constitutive Law 67 IV.1 Introduction 67 IV.2 General Considerations . 67 IV.3 Ideal Rheological Behaviour – Physical Models 69 IV.4 Generalized Hooke’s Law . 75 IV.4.a Introduction . 75 IV.4.b Isotropic Materials . 75 IV.4.c Monotropic Materials . 80 IV.4.d Orthotropic Materials . 82 IV.4.e Isotropic Material with Linear Visco-Elastic Behaviour . 83 IV.5 Newtonian Liquid . 84 IV.6 Deformation Energy . 86 IV.6.a General Considerations . 86 IV.6.b Superposition of Deformation Energy in the Linear Elastic Case . 89 IV.6.c Deformation Energy in Materials with Linear Elastic Behaviour . 90 IV.7 Yielding and Rupture Laws . 92 IV.7.a General Considerations . 92 IV.7.b Yielding Criteria . 93 IV.7.b.i Theory of Maximum Normal Stress . 93 IV.7.b.ii Theory of Maximum Longitudinal Deformation 94 IV.7.b.iii Theory of Maximum Deformation Energy . 94 IV.7.b.iv Theory of Maximum Shearing Stress 95 IV.7.b.v Theory of Maximum Distortion Energy . 95 IV.7.b.vi Comparison of Yielding Criteria 96 IV.7.b.vii Conclusions About the Yielding Theories 100 IV.7.c Mohr’s Rupture Theory for Brittle Materials 101 IV.8 Concluding Remarks . 105Contents XIII IV.9 Examples and Exercises 106 Part II Strength of Materials V Fundamental Concepts of Strength of Materials . 119 V.1 Introduction 119 V.2 Ductile and Brittle Material Behaviour . 121 V.3 Stress and Strain 123 V.4 Work of Deformation. Resilience and Tenacity . 125 V.5 High-Strength Steel 127 V.6 Fatigue Failure 128 V.7 Saint-Venant’s Principle 130 V.8 Principle of Superposition 131 V.9 Structural Reliability and Safety 133 V.9.a Introduction . 133 V.9.b Uncertainties Affecting the Verification of Structural Reliability . 133 V.9.c Probabilistic Approach 134 V.9.d Semi-Probabilistic Approach . 135 V.9.e Safety Stresses . 136 V.10 Slender Members 137 V.10.a Introduction . 137 V.10.b Definition of Slender Member 138 V.10.c Conservation of Plane Sections . 138 VI Axially Loaded Members 141 VI.1 Introduction 141 VI.2 Dimensioning of Members Under Axial Loading . 142 VI.3 Axial Deformations 142 VI.4 Statically Indeterminate Structures 143 VI.4.a Introduction . 143 VI.4.b Computation of Internal Forces 144 VI.4.c Elasto-Plastic Analysis 145 VI.5 An Introduction to the Prestressing Technique 150 VI.6 Composite Members . 153 VI.6.a Introduction . 153 VI.6.b Position of the Stress Resultant 153 VI.6.c Stresses and Strains Caused by the Axial Force 154 VI.6.d Effects of Temperature Variations 155 VI.7 Non-Prismatic Members 157 VI.7.a Introduction . 157 VI.7.b Slender Members with Curved Axis 157 VI.7.c Slender Members with Variable Cross-Section 159 VI.8 Non-Constant Axial Force – Self-Weight 160XIV Contents VI.9 Stress Concentrations 161 VI.10 Examples and Exercises 163 VII Bending Moment 189 VII.1 Introduction 189 VII.2 General Considerations . 190 VII.3 Pure Plane Bending . 193 VII.4 Pure Inclined Bending . 196 VII.5 Composed Circular Bending 200 VII.5.a The Core of a Cross-Section . 202 VII.6 Deformation in the Cross-Section Plane 204 VII.7 Influence of a Non-Constant Shear Force . 209 VII.8 Non-Prismatic Members 210 VII.8.a Introduction . 210 VII.8.b Slender Members with Variable Cross-Section 210 VII.8.c Slender Members with Curved Axis 212 VII.9 Bending of Composite Members . 213 VII.9.a Linear Analysis of Symmetrical Reinforced Concrete Cross-Sections . 216 VII.10 Nonlinear bending . 219 VII.10.a Introduction . 219 VII.10.b Nonlinear Elastic Bending . 220 VII.10.c Bending in Elasto-Plastic Regime 221 VII.10.d Ultimate Bending Strength of Reinforced Concrete Members . 226 VII.11 Examples and Exercises 228 VIII Shear Force 251 VIII.1 General Considerations . 251 VIII.2 The Longitudinal Shear Force . 252 VIII.3 Shearing Stresses Caused by the Shear Force 258 VIII.3.a Rectangular Cross-Sections 258 VIII.3.b Symmetrical Cross-Sections . 259 VIII.3.c Open Thin-Walled Cross-Sections 261 VIII.3.d Closed Thin-Walled Cross-Sections . 265 VIII.3.e Composite Members 268 VIII.3.f Non-Principal Reference Axes 269 VIII.4 The Shear Centre . 270 VIII.5 Non-Prismatic Members 273 VIII.5.a Introduction . 273 VIII.5.b Slender Members with Curved Axis 273 VIII.5.c Slender Members with Variable Cross-Section 274 VIII.6 Influence of a Non-Constant Shear Force . 275 VIII.7 Stress State in Slender Members . 276 VIII.8 Examples and Exercises 278Contents XV IX Bending Deflections . 297 IX.1 Deflections Caused by the Bending Moment 297 IX.1.a Introduction . 297 IX.1.b Method of Integration of the Curvature Equation 298 IX.1.c The Conjugate Beam Method 302 IX.1.d Moment-Area Method 304 IX.2 Deflections Caused by the Shear Force . 308 IX.2.a Introduction . 308 IX.2.b Rectangular Cross-Sections 311 IX.2.c Symmetrical Cross-Sections . 312 IX.2.d Thin-Walled Cross-Sections 312 IX.3 Statically Indeterminate Frames Under Bending . 315 IX.3.a Introduction . 315 IX.3.b Equation of Two Moments 317 IX.3.c Equation of Three Moments . 317 IX.4 Elasto-Plastic Analysis Under Bending . 320 IX.5 Examples and Exercises 323 X Torsion 347 X.1 Introduction 347 X.2 Circular Cross-Sections . 347 X.2.a Torsion in the Elasto-Plastic Regime 353 X.3 Closed Thin-Walled Cross-Sections 356 X.3.a Applicability of the Bredt Formulas 361 X.4 General Case . 362 X.4.a Introduction . 362 X.4.b Hydrodynamical Analogy . 364 X.4.c Membrane Analogy . 365 X.4.d Rectangular Cross-Sections 367 X.4.e Open Thin-Walled Cross-Sections 368 X.5 Optimal Shape of Cross-Sections Under Torsion . 369 X.6 Examples and Exercises 371 XI Structural Stability 389 XI.1 Introduction 389 XI.2 Fundamental Concepts . 391 XI.2.a Computation of Critical Loads . 391 XI.2.b Post-Critical Behaviour . 393 XI.2.c Effect of Imperfections 396 XI.2.d Effect of Plastification of Deformable Elements . 399 XI.3 Instability in the Axial Compression of a Prismatic Bar . 401 XI.3.a Introduction . 401 XI.3.b Euler’s Problem 402 XI.3.c Prismatic Bars with Other Support Conditions 403XVI Contents XI.3.d Safety Evaluation of Axially Compressed Members405 XI.3.e Optimal Shape of Axially Compressed Cross-Sections . 409 XI.4 Instability Under Composed Bending 409 XI.4.a Introduction and General Considerations 409 XI.4.b Safety Evaluation 414 XI.4.c Composed Bending with a Tensile Axial Force . 416 XI.5 Examples and Exercises 416 XI.6 Stability Analysis by the Displacement Method . 439 XI.6.a Introduction . 439 XI.6.b Simple Examples . 440 XI.6.c Framed Structures Under Bending . 445 XI.6.c.i Stiffness Matrix of a Compressed Bar . 445 XI.6.c.ii Stiffness Matrix of a Tensioned Bar . 451 XI.6.c.iiiLinearization of the Stiffness Coefficients 452 XI.6.c.ivExamples of Application . 455 XII Energy Theorems 465 XII.1 General Considerations . 465 XII.2 Elastic Potential Energy in Slender Members 466 XII.3 Theorems for Structures with Linear Elastic Behaviour . 468 XII.3.a Clapeyron’s Theorem . 468 XII.3.b Castigliano’s Theorem 469 XII.3.c Menabrea’s Theorem or Minimum Energy Theorem 473 XII.3.d Betti’s Theorem . 473 XII.3.e Maxwell’s Theorem . 477 XII.4 Theorems of Virtual Displacements and Virtual Forces . 479 XII.4.a Theorem of Virtual Displacements 479 XII.4.b Theorem of Virtual Forces . 482 XII.5 Considerations About the Total Potential Energy 485 XII.5.a Definition of Total Potential Energy 485 XII.5.b Principle of Stationarity of the Potential Energy . 486 XII.5.c Stability of the Equilibrium . 486 XII.6 Elementary Analysis of Impact Loads 489 XII.7 Examples and Exercises 491 XII.8 Chapter VII 517 XII.9 Chapter IX . 518 References . 523 Index . Index action 3 action axis 192 of the bending moment 192 of the shear force 193 analogy hydrodynamical 364 membrane 364 physical 364 anticlastic 206 axial force 141 axial stiffness 143 behaviour models 67 bending 189 composed 190, 202 in elasto-plastic regime 221 inclined 197, 199 non-uniform 189 nonlinear 219 of composite members 213 plane 192 pure or circular 189 bending moment 189 bending stiffness 195 Bernoulli’s hypothesis 139 Betti’s theorem 473 boundary balance equations 16 Bredt’s formulas 376 buckling modes 442, 445, 454, 457 bulk modulus 79 Castigliano’s theorem 469 Cauchy equations 16 centroid 142 characteristic equation 19, 20 of the stress state 19 characteristic values 135 Clapeyron’s theorem 468 coefficient buckling 415 dynamic 490 homogenizing 154, 216 of thermal expansion 132 Poisson’s 76, 124 retardation 73 safety 137, 406 stiffness 452 collapse mechanism 320 compatibility of deformations 144 composite material 3 conjugate beam method 302 conservation of energy 80, 309, 359, 468 of plane sections 138 constitutive law 7 continuity conditions 299 Continuum Mechanics 4 core of a cross section 201 creep 69 creep modulus 73 critical phase 390 curvature 189 curvature equation 298 deflection curve 193 deflection plane 193 deformation 5526 Index compatible 51 elastic 68 homogeneous 43 plastic 68 pure 49 visco-elastic 71 visco-plastic 69 viscous 68 deformation energy 86, 126 degree of connection 53 degree of indeterminacy kinematic 143, 153 deviatoric tensor 26 differential equations of equilibrium 14 dimensional tolerance 134 direction cosines 16 displacement method 144 displacement-strain relations 6 distortion 46 Drucker-Prager’s criterion 104 effective length 404 elastic limit stress 129 elastic phase 93 elasto-plastic analysis 145, 223 bending 223 elasto-plastic phase 147 energy deformation 86 dissipated 88, 113, 127 elastic potential 80, 126 kinetic 511 potential 80, 390 total potential 485 equation of three moments 317 equation of two moments 317 equations of compatibility integral 54 local 54 of the strain 44 equilibrium conditions 9 Euler’s hyperbola 408 Euler’s problem 410 Eulerian formulation 300 execution imperfections 134 external forces 5 of mass 5 of surface 5 virtual 484 external friction 465 fatigue failure 128 fatigue limit stress 129 fibre 193 first area moment 192, 253 flow lines 364, 365 Fluid Mechanics 85 force method 144 force-stress relations 6 framed structures 138 generalized displacements 469 generalized forces 469 generalized Maxwell model 74 geometrical stiffness 442 hardening 122 natural hardening 128 strain hardening 127 homogenization 215, 377, 378 Hooke’s law 67, 75, 105 hyperstatic unknowns 153 hypothesis of continuity 4 imperfections (effect of) 396 inertial forces 5, 14 influence lines 475 instability 389 by divergence 433 by equilibrium bifurcation 398 in axial compression 414 in composed bending 411 interaction formula 415 internal forces 5, 6 internal friction 88, 466 intrinsic strength curve 101 invariants 19 of the strain tensor 49 of the stress tensor 20 irradiation poles 31 isotropic tensor 24 Johnson’s parabola 407 Kelvin chain 74, 83 Kelvin’s solid 71 kinematic coordinates 454 kinematic method 321 kinematic unknowns 144Index 527 Lagrangian formulation 300, 413 Lam´e’s constant 79 Lam´e’s ellipsoid 22 level curves 365 limit states 133 of serviceability 133 ultimate 133 linear visco-elasticity 74, 83 liquid 69 load collapse 321 critical 414 elasticity limit 122 Euler 413 proportionality limit 131 yielding 131 longitudinal modulus of elasticity 76, 124 longitudinal shear flow 254 longitudinal shear force 252, 310 longitudinal strain 44 M¨ uller-Breslau’s principle 476 material brittle 69, 121 composite 3 continuous 5 ductile 69, 121 elastic 87 isotropic 68 monotropic 68 orthotropic 68 material stiffness 442 mathematical models 3, 67 Maxwell’s model 73 Maxwell’s theorem 477 mean rotation 50 Mechanics of Materials 3 Menabrea’s theorem 473 method of integration of the curvature equation 298 minimum energy theorem 473 minimum loads 153 Mohr’s circle 30 Mohr’s criterion 104 Mohr’s representation 58 three-dimensional 34 moment of inertia 195, 218 moment-area method 304 multiply connected body 53 neutral axis 193 neutral equilibrium 390, 403 neutral surface 193, 206 Newtonian liquid 84 nominal values 135 normal stress 11 octahedral stress 24 partial factors 136 perfect liquid 84, 364 physical models 68, 150 plane of actions 193 plane strain 59 plane stress state 39 plastic hinge 225 plastic moment 223 plastic section modulus 224 polar decomposition theorem 50 post-critical behaviour 393 stable 395 symmetrical 395 unstable 398 pressure centre 201 prestressing technique 150 principal axis of inertia 198 principal directions of the stress state 19 principal strains 58 principal stress trajectories 276, 352 principal stresses 19 principle conservation 80, 309, 359, 468, 479 of energy 80 of M¨ uller-Breslau 476 of Saint-Venant 130 of stationarity of the 485 of superposition 76, 131 potential energy 485 probabilistic approach 134 probabilistic density curve 134 product of inertia 198, 239 proportionality limit stress 131, 407 quantiles 136 reciprocity of shearing stresses 12528 Index redistribution of internal forces 152 redistribution of stresses 161 reduced area 310 reinforced concrete 3 relaxation 69 relaxation modulus 74 resilience 126, 127 retardation time 73 rheological behaviour 3, 7 elastic 143 elasto-visco-plastic 69 rigid body motion 5 safety stresses 136 Saint-Venant’s hypothesis 252 Saint-Venant’s principle 130 secant formula 411 second-order theories 391 section modulus 195 semi-normal of the facet 10 semi-probabilistic approach 135 shape factor 223 shear centre 270, 493 shear flow 265, 358 shear force 254 shear modulus 77 shearing strain 44, 77 simplifying hypotheses 120, 134, 257, 361 simply connected body 53 slender members 138 cross-section 138, 222, 274 non-prismatic 157, 209, 273 prismatic 138 with curved axis 157, 212, 273 slenderness ratio 403 solid 69 Solid Mechanics 7, 37, 120, 121, 466 stability 389 stable equilibrium 390, 395 state of deformation 43 around a point 49 isotropic 58 state of stress 17 around a point 17 axisymmetric 24 isotropic 22 three-dimensional 92 static method 321 statically determinate structures 143 statically indeterminate structures 143, 315 statistical dispersion 134 stiffness 123 stiffness matrix 441 of a compressed bar 445 of a tensioned bar 451 strain 5 strain tensor 6, 40 Strength of Materials 120 stress 5, 10 stress concentration 161, 364 stress tensor 6, 17, 20 support conditions 303 tangent elasticity modulus 124 tangential 11 tenacity 126, 134 tensor 9 tensorial quantities 9 Tetmeyer’s line 406, 407 theorem of virtual displacements 479 theorem of virtual forces 482 theory of elasticity 119 theory of strain 6 theory of stress 6 torque 347 torsion 346 of circular cross-sections 347 of thin-walled cross-sections 356, 360 torsion centre 271, 370 torsion modulus 351 torsional moment 347 torsional stiffness 351, 359, 368, 369 transversal modulus of elasticity 77 transversal strain 75 twisting moment 347 uncertainties 133 unstable equilibrium 390, 442 virtual displacements 479 virtual stress 482 viscosity modulus 85, 86 volumetric modulus of elasticity 79 von Karman convention 36 yielding bending moment 223Index 529 yielding criteria 93, 96 Beltrami 98, 106 Rankine 106 Saint-Venant 106 Tresca 98 Von Mises 95 yielding stress 68, 92, 125 yielding surface 99, 100 yielding zone 121 Young’s modulus 124
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