Strength of Materials and Structures – An Introduction to the Mechanics of Solids and Structures

Strength of Materials and Structures – An Introduction to the Mechanics of Solids and Structures
اسم المؤلف
John Case, A. H. Chilver
التاريخ
10 أكتوبر 2022
المشاهدات
295
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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
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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