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 |  موضوع: كتاب Strength of Materials and Structures - An Introduction to the Mechanics of Solids and Structures الإثنين 10 أكتوبر 2022, 12:22 am | |
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Strength of Materials and Structures - An Introduction to the Mechanics of Solids and Structures
(SI units)
JOHN CASE
M . A . , F . R . A E . S . Formerly Head of the Department of Applied
Mechanics, Royal Naval Engineering College, Plymouth
A. H. CHILVER
Vice Chancellor, Cranfield Institute of Technology,
Formerly Chadwick Professor of Civil Engineering,
University College, London
و المحتوى كما يلي :
Table of Contents
Tension and compression: direct stress
Pin-jointed frames or trusses
Shearing stress
Joints and connections
Analysis of stress and strain
Thin shells under internal pressure
Bending moments and shearing forces
Geometrical properties of cross-sections
Longitudinal stresses in beams
Shearing stresses in beams
Beams of two materials
Bending stresses and direct stresses combined
Deflections of beams
Built-in and continuous beams
Plastic bending of mild-steel beams
Torsion of circular shafts and thin-walled tubes
Energy methods
Buckling of columns and beams
Lateral deflections of circular plates
Torsion of non-circular sections
Thick circular cylinders, discs and spheres
Introduction to matrix algebra
Matrix methods of structural analysis
The finite element method
Structural vibrations
Principal notation
a length
b breadth
c wave velocity, distance
d diameter
e eccentricity
h depth
j number of joints
/ length
m mass, modular ratio,
number of members
η frequency, load factor, distance
ρ pressure
q shearing force per unit length
r radius
s distance
t thickness
u displacement
I? displacement, velocity
w displacement, load intensity,
force
χ coordinate
y coordinate
ζ coordinate
α coefficient of linear expansion
y shearing strain
δ deflection
£ direct strain
η efficiency
Θ temperature, angle of twist
ν Poisson's ratio
A area
C complementary energy
D diameter
Ε Young's modulus
F shearing force
G shearing modulus
H force
/ second moment of area
J torsion constant
Κ bulk modulus
L length
M bending moment
Ρ force
Q force
R force, radius
S force
Τ torque
U strain energy
V force, volume, velocity
W work done, force
X force
Y force
Ζ section modulus
ρ density
σ direct stress
τ shearing stress
ω angular velocity
Δ deflection
Φ step-function
INDEX
Numbers refer to pages
Analysis of strain, 79
Analysis of stress, 69
Anti-clastic curvature, 169
Barrel-like failure in mild-steel, 10, 11
Beams, built-in, 248
- compound, 167
- continuous, 248
- curved, 128, 131
- deflections, 212
- with end couples, 232
- lateral buckling, 369
- longitudinal bending stresses, 149
- plane curved, 128
- principal stresses, 183
- shearing stresses, 173
- superimposed, 184
- two materials, 189
- vibrations, 373
Bending, bi-symmetric beams, 154
- combined with direct stresses, 202
- elastic, 149
- mono-symmetric beams, 156
- plasticity in mild-steel beams, 263
- rectangular beam, 149
- strain energy, 168
Bending moment, 110
- diagrams, 114
- graphical methods of analysis, 126
- influence lines, 146
- sign conventions, 113
- slowly moving loads, 134
Bending stiffness, 152
Bolted connections, 55
Breakdown of brittle materials, 98
Breaking point, 2
Brittle materials, 2
- breakdown, 98
- stress-strain curves, 6
Buckling of beams, 369
Buckling of struts, 346
- Euler load, 348
Buckling of struts, modes, 348
- pin-ended, 346
- torsional, 365
Built-in beams, 248
- fixed-end moments, 248
Butt weld, 63
Cantilevers, 110, 114
Channel-section beam, 185
Circle of second moments of area, 166
Circle of strain, 81
Circle of stress, 77
Circular ring rotating, 31
Circular ring under radial pressure, 30
Close-coiled conical spiral spring, 341
Close-coiled helical spring, 336
Cold-driven rivets, 58
Combined bending and direct stresses, 202
- core of a section, 205
Combined torsion and direct stresses, 284
Compatibility of strain, 44
Complementary energy, 322
- bending problems, 329
- initial lack of fit, 329
- statically-indeterminate frames, 326
Complementary shearing stress, 51
Composite bars, 26
- temperature stresses, 28
- tension and compression, 26
Composite beams, 189
- transformed section, 189
Compound beams, 167
- shearing stresses, 182
Compression, 4
- composite bars, 26
Compressive strain, 6
Compressive stress, 4
Concentrated loads, 111
- traversing a beam, 134, 138
Concrete, stress-strain curves, 8
Concrete beams,
- ordinary reinforced, 194
- pre-compressed eccentrically, 209
- pre-stressed, 207
Conical springs, 341
- close-coiled spiral, 341
Connections, 55
- bolted, 55
400 INDEX
- efficiency, 59
- group-riveted, 60
- welded, 63
Continuous beams, 248
- slope-deflection equations, 255
- three-moment equation, 256
Contra-flexure, points of, 124
Core of a section, 205
Couple applied to a beam, 229
Creep under sustained stress, 33
Criterion of yielding, 96
Cup-like failure in light-alloy, 10
Cup-and-cone failure in mild-steel, 10
Curvature, anti-clastic, 169
Curved beams, 131
- plane, 128
Cylindrical shells, 100
- hemispherical ends, 108
Damped vibrations of beams, 380
Deflections of beams, 212
- cantilever, 217
- due to couples, 229
- Fourier analysis, 240
- funicular analogue, 243
- moment-area analysis, 238
- propped cantilever, 220
- pure bending, 214
- shear effects, 245
- simply-supported beams, 216, 222
- step-function analysis, 225
- varying-section beams, 235
- virtual work analysis, 306
Design of pin-ended struts, 357
Direct stress, 1,4, 70
- combined with bending stresses, 202
- lateral strains, 18
Displacement diagrams, 39
Displacements of pin-jointed frames, 39, 297
Distortion strain energy, 93
Distributed loads, 111
- traversing a beam, 136
Ductile materials, 9
Eccentrically-loaded riveted joints, 61
Eccentrically-loaded strut, 350
Eccentrically pre-compressed concrete beam,
209
Economy of materials, 21
Efficiency of connections, 59
Elastic bending, 212
- section modulus, 161
- strain energy, 168
Elasticity, 2
Elastic-plastic bending, 265
Elongation at fracture, 8
Endurance limit, 34
Endurance-stress curves, 35
Endurance under repeated stresses, 34
Energy, complementary, 322
- strain, 317
Equilibrium, neutral, 348
- stable, 349
- unstable, 349
Euler formula, 348
Failure, compressed timber, 71, 72
- riveted joints, 55
Fatigue, endurance limit, 34
- repeated stresses, 34
Fillet weld, 64
Fixed-end moments, 248
Flexural stiffness, 152
Forced vibrations of beams, 378
Fracture, elongation, 8
Frames, non-linear members, 42
- redundant, 38, 302, 305, 318, 326
- simply-stiff, 38
- statically-determinate pin-jointed, 38
Free vibrations of beams, 375
Fully-plastic moment, 265
- I-section, 267
Funicular analogue, 243
Graphical methods for bending moment diagrams, 126
Group-riveted joints, 60
Helical springs, 335
- close-coiled, 336
- open-coiled, 338
Hooke's law, 2
Hydrostatic pressure, 91
I-beam, shearing stresses, 178
Impact of rods, 385
- constant stress applied at one end, 388
- particle velocity, 389
- stress waves, 385
- velocity of stress propagation, 386
- velocity of stress waves, 388
- with masses, 393
Inelastic extensions, 2
Inflection, points of, 123
Influence lines, bending moment and shearing
force, 146
401 INDEX
Initial curvature in struts, 353
Initial lack of fit, 329
Initial stresses, 24
Instability, 346
Intensity of loading of a beam, 111
Interaction curves for struts, 357
Joints, 55
- bolted, 55
- efficiency, 59
- group-riveted, 60
- riveted, 55
- single-riveted lap, 55
- tapered cover plates, 60
- under eccentric loads, 61
Lap joint, single-riveted, 55
Lateral strains, 18
Lateral buckling of beams, 369
Leaf springs, 343
Limit of proportionality, 2
Limit of endurance, 34
Load factor, 17
Longitudinal impact of rods, 385
Longitudinal stresses in beams, 149
Lower yield point, 9
Lüder's lines, 71
Maximum bending moment diagrams, 139
Maximum shearing force, 134
Maximum shearing force diagrams, 142
Maximum shearing stress, 75
Mild-steel, barrel-like failure, 10
- cup-and-cone failure, 10
- plastic bending, 263
- strain figures, 71
- stress-strain curves, 9
- yielding, 9
Mises yield criterion, 97
Modes of buckling, 348
- cruciform strut, 365
Modes of vibration of a beam, 377
Modulus, bulk, 92
- shearing, 53
- Young's, 7
Mohr's circle of strain, 81
Mohr's circle of stress, 77
Moment-areas, 238
Natural frequency of a mass on a beam, 375
Necking, 9
Neutral axis, 150
Neutral equilibrium, 348
Neutral surface, 150
Non-linear members in frames, 42
Open-coiled helical spring, 338
Open-sections, torsion, 293
Ordinary reinforced concrete, 194
Pin-jointed frames, 38
Plane curved beams, 128
Planes, principal stress, 74
Plastic bending, mild-steel beams, 263
- fully-plastic moment, 265, 267
- plastic section modulus, 268
- shape factor, 269
- strain-hardening, 263
- virtual-work solution, 311
Plastic collapse of built-in beams, 275
Plastic-elastic bending, 265
Plastic extensions, 2
Plastic hinges, 276
Plastic regions in beams, 271
Plastic section modulus, 268
Plastic straining, work done in, 24
Plastic torsion, 286
Points of contra-flexure, 124
Points of inflection, 123
Poisson's ratio, 18
- relation between £, G and v, 84
Pre-stressed concrete beams, 207
Principal axis of bending, 153
Principal planes, 74
Principal second moments of area, 163
Principal strains, 83
Principal stresses, 74, 83
- beams, 183
- twisted shafts, 283
Principle of virtual work, 296
Proof stresses, 16
Proportionality limit, 2
Propped cantilever, 220
Pure bending, 157
- rectangular beam, 149
Reciprocal properties of linear systems, 313
Redundant frames, 38, 302, 305, 318, 326
Reflections of stress waves, 390
Reinforced concrete beams, 194
Removal of stresses, 8
Repeated stresses, 34
Resilience of a spring, 334
Riveted joints, 55
- modes of failure, 55
402 INDEX
Rivets, cold-driven, 58
- hot-driven, 58
Rod struck by a mass, 393
Rosettes, strain, 86
Rotating circular ring, 31
Second moments of area, 163
- circle, 166
Section modulus, elastic, 161
- plastic, 268
Shafts, torsion of hollow, 279
- torsion of solid, 278
Shape factor, 269
Shear centre, 185
Shear deflections of beams, 245
Shearing force, 110
- diagrams, 114
- influence lines, 146
- maximum, due to moving load, 1
- sign conventions, 113
- slowly moving loads, 134
Shearing modulus, 53, 83
Shearing strain, 53
- energy, 53
Shearing stress, 48, 70
- complementary, 51
- maximum, 75
- tensile specimen, 69
Shearing stresses in beams, 173
- channel-section, 185
- compound, 182
- I-beam, 178
- narrow rectangular beam, 173
Shells, cylindrical, 100,108
- spherical, 107
Sign conventions for bending moments and
shearing forces, 113
Simply-stiff frames, 38
Simply-supported beams, 117
Single-riveted lap joint, 55
Sinking of beam supports, 253
Slope-deflection equations, 255
Slowly moving loads, 134
Spherical shells, 107
Spiral springs, 339
Springs, close-coiled conical, 341
- close-coiled helical, 336
- coiled, 334
- helical, 335
Springs, leaf, 343
- open-coiled helical, 338
- plane spiral, 339
- resilience, 334
- spiral, 339
- stiffness, 334
Stable equilibrium, 349
Statically-determinate frames, 38
Statically-determinate problems, 38
Statically-indeterminate beams, 310
Statically-indeterminate frames, 302
Statically-indeterminate problems, 38, 43
Step-functions in deflection analysis, 225
Stiffness of a spring, 334
Strain, analysis, 69, 79
- compatibility, 44
- compressive, 6
Strain energy, 317
- bending, 168
- distortional, 93
- elastic extensions, 21
- elastic torsion, 286
- shearing actions, 53
- tensile test, 21
- two-dimensional stresses, 89
- volume intensity, 24
Strain figures in mild-steel, 71
Strain-hardening, 9
- plastic bending, 263
Strain, Mohr's circle, 81
- principal, 83
- rate, 10
- rosettes, 86
- shearing, 53
- tensile, 5
- volumetric, 19, 91
Strength properties, 21
- table, 20
Stress, analysis, 69
- complementary shearing, 51
- compressive, 4
- creep due to, 33
- direct, 1, 4, 70
- effect of removal, 8
- endurance curves, 35
- factor, 17
Stress, fatigue due to repeated, 34
- initial, 24
- longitudinal in beams, 149
- maximum shearing, 75
- Mohr's circle, 77
- principal, 74, 83
- proof, 16
- propagation, 386
- shearing, 48, 70
- strain energy in a two-dimensional system, 89
403 INDEX
- thin non-circular tube, 289
- thin-walled open sections, 293
Transformed section, 189
Tresca yield criterion, 96
Tubes, torsion of non-circular, 289
- torsion of thin circular, 277
Two-dimensional stress system, 72
Ultimate stress, 9
Unstable equilibrium, 349
Upper yield point, 9
Vibrations of beams, 373
- damped, 380
- with end thrust, 382
- free, 375
- forced, 378
- natural frequency, 375
Virtual work principle, 296
Volumetric strain, 19, 91
Weight economy, 21
Weld, butt, 63
- fillet, 64
- throat, 64
Welded connections, 63
Work done in plastic straining, 24
Work done in tensile test, 21
Working stresses, 17
Yield, combined stresses, 94
- criterion, 96
- envelope, 96
- locus, 96
- mild-steel, 9
Yield point, lower, 9
- upper, 9
Yield stress, 10
- effect of strain rate, 10
Young's modulus, 7
- relation with G and v, 84
404
- three-dimensional system, 89
- temperature effects, 28
- tensile, 3
- two-dimensional system, 72
- ultimate, 9
- working, 17
- yield, 10
Stress-strain curves, brittle materials, 6
- concrete, 8
- ductile materials, 9
- mild-steel, 9
Stress-strain relations, elastic, 82
Stress waves, 385
- reflections, 390
- velocities, 388
Stretching of a steel wire, 1
Strip, torsion of, 292
Struts, buckling of pin-ended, 346
- built-in, 360
- design of pin-ended, 357
- eccentrically-loaded, 350
- initially-curved, 353
- interaction curves, 357
- laterally-loaded, 358
- torsional buckling, 365
- various end conditions, 360, 361
- various types of cross-section, 364
Superimposed beams, 184
Tapered cover plates for riveted joints, 60
Temperature stresses, 28
- composite bars, 28
- redundant frames, 305
Tensile strain, 5
Tensile stress, 3
Tensile test, strain energy, 21
- work done, 21
Tension, 1
- composite bars, 26
Thin shells, 100
Three-dimensional stress systems, 89
Three-moment equation, 256
Throat of weld, 64
Torsional buckling of struts, 365
Torsion, combined with direct stresses, 284
- constant, 292
- flat strip, 292
- hollow shaft, 279
- plastic, 286
- principal stresses, 283
- solid shaft, 278
- strain energy, 286
- thin circular tube, 277
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