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 |  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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