Strength of Materials

Strength of Materials
N. M. Belyaev
translated from the Russian
by N. R. Mehia
Contents
Nikolai Mikhailovich Belyaev 5
Preface to the Fifteenth Russian Edition 7
PART 1. Introduction. Tension and Compression
Chapter 1. Introduction 17
§ 1. The science of strength of materials 17 !2. Classification of forces acting on elements of structures 18

3. Deformations and stresses 21
4. Scheme of a solution of the fundamental problem of strength of
   materials 23
   § 5. Types of deformations 27
   Chapter 2. Stress and Strain in Tension and Compression Within the Elastic Limit
   Selection of Cross-sectional Area 27
   § 6. Determining the stresses in planes perpendicular io tile axis
   of the bar 27
   §7. Permissible stresses. Selecting the cross-sectional area 30
   1 8. Deformations under tension and compression. Hooke’s law 32
   §9. Lateral deformation coefficient. Poisson’s ratio 36
   Chapter 3. Experimental Study of Tension and Compression In Various Materials and
   the Basis of Selecting the Permissible Stresses 40
   § 10. Tension test diagram. Mechanical properties of materials 40
   1 11. Stress-strain diagram 47
   § 12. True stress-strain diagram 48
   § 13. Stress-strain diagram for ductile and brittle materials 62
   § 14. Rupture in compression of brittle and ductile materials. Compression test diagram 64
   § 16. Comparative study of the mechanical properties of ductile and
   brittle materials 57
   § 16. Considerations in selection of safety factoi 59
   § 17. Permissible stresses under tension and compression for various
   materials 64
   PART II. Complicated Cases of Tension and
   Compression
   Chapter 4. Design of Statically Indeterminate Systems for Permissible Stresses 66
   $ 18. Statically indeterminate systems 66
   1 19. The effect of manufacturing inaccuracies on the forces acting in the
   elements of statically indeterminate structures 73
   §20. Tension and compression in bars made of heterogeneous materials 77
   §21. Stresses due to temperature change 79
   §22. Simultaneous account for various factors 82
   §23. More complicated cases of statically indeterminate structures 8510 Contents
   Chapter 5. Account for Dead Weight In Tension and Compression* Design of Flexible
   Strings 88
   § 24. Selecting the cross-sectional area with the account for the dead
   weight (in tension and compression) 86
   §25. Deformations due to dead weight 81
   §26. Flexible cables 92
   Chapter 6. Compound Stressed State. Stress and Strain 99
   § 27. Stresses along Inclined sections under axial tension or compression
   (uniaxial stress) 99
   § 28. Concept of principal stresses. Types of stresses of materials 101
   § 29. Examples oil biaxial and triaxiaf stresses. Design of a cylindrical
   reservoir 103
   §30. Stresses In a biaxial stressed state 107
   §31. Graphic determination of stresses (Mohr’s circle) 110
   §32. Determination of the. principal stresses with the help of the stress
   circle 114
   S33. Stresses in triaxia! stressed state 117 34. Deformations In the compound stress 121
5. Potential energy of elastic deformation in compound stress 124
6. Pure shear. Stresses and strains. Hooke’s law. Potential
   energy 127
   Chapter 7. Strength of Materials in Compound Stress 132
   § 37. Resistance to failure. Rupture and shear 132
   §38. Strength theories 136
   §39. Theories of brittle failure (theories of rupture) 138
   §40. Theories of ductile failure (theories of shear) 140
   §41. Reduced stresses according to different strength theories 147
   §42. Permissible stresses in pure shear 149
   PART III. Shear and Torsion
   Chapter 8. Practical Methods of Design on Shear 151
   §43. Design of riveted and bolted joints 151
   §44. Design of welded joints 158
   Chapter 9. Torsion. Strength and Rigidity of Twisted Bars 164
   !45. Torque 164 46. Calculation of torques transmitted to the shaft 167
7. Determining stresses in a round shaft under torsion 168
8. Determination of polar moments of inertia and section moduli
   of a shaft section 174
   §49. Strength condition in torsion 176
   §50. Deformations in torsion. Rigidity condition 176
   § 51. Stresses under torsion in a section inclined to the shaft axis 178
   §52. Potential energy of torsion 180
   §53. Stress and strain In dose-coiled helical springs 181
   1 54. Torsion in rods of non-circular section 187Contents II
   PART IV. Bending. Strength of Beams
   Chapter 10. Internal Forces In Bending. Shearing-force and Bendfng-momenl
   Diagrams 198
   $ 55. Fundamental concepts of deformation in bending. Construction of
   beam supports 195
   §56. Nature of stresses in a beam. Bending moment and shealine
   force 200 *
   §57. Differential relation between the intensity of a continuous load,
   shearing force and bending moment 205
   §58. Plotting bending-moment and shearing-force diagrams 207
   §59. Plotting bending-moment and shearing-force diagrams for more
   complicated loads 214
   1 60. The check of proper plotting of Qr and M-diagrams 221
   § 61. Application of the principle of superposition of forces In plotting
   shearing-force and bending-moment diagrams 223
   Chapter 1|. Determination of Normal Stresses in Bending and Strength of
   Beams 225
   §62. Experimental investigation of the working of materials in pure
   bending 225
   § 63. Determination of norma) stresses In bending. Hooke’s law and potential energy of bending 228
   § 64. Application of the results derived above in checking the strength of
   beams 235
   Chapter 12. Determination of Moments of Inertia of Plane Figures 239
   §65. Determination of moments of inertia and section moduli for simple
   sections 239
   §66. General method of calculating the moments of inertia of complex
   sections 244
   § 67. Relation between moments of inertia about two parallel axes one
   of which is the central axis 246
   §68. Relation between the moments of inertia under rotation of
   axes 247
   §69. Principal axes of inertia and principal moments of inertia 250
   §70. The maximum and minimum values oi the central moments of
   inertia 254
   § 71. Application of the formula for determining normal stresses to
   beams of non-symmetricai sections 254
   §72. Radii of inertia. Concept of the momenta! ellipse 256
   § 73. Strength check, choice of section and determination of permissible
   load in bending 258
   Chapter 13. Shearing and Principal Stresses In Beams 263
   § 74. Shearing stresses in a beam of rectangular section 263
   1 75. Shearing stresses in I-beams 270
   § 76, Shearing stresses in beams of circular and ring sections 272
   §77. Strength check for principal stresses 275
   § 78. Directions the principal stresses 280
   Chapter 14. Shear Centre. Composite Beams 283
   § 79. Shearing stresses parallel to the neutral axis.
   Concept of shear centre 233
   §80, Riveted and welded beams 28912 Contents
   PART V. Deformation of Beams due to Bending
   Chapter 15. Analytical Method of Determining Deformations 292
   § 81. Deflection and rotation oi beam sections 292
   $ 82. Differential equation of the deflected axis 294
   § 83. Integration oi the differentia) equation of the deflected axis of a
   beam fixed at one end 296
9. Integrating the differential equation of the deflected axis of a simply
   supported beam 299
   § 85. Method of equating the constants of integration oi differential
   equations when the beam has a number of differently loaded
   portions 301
   § 86. Method of initial parameters for determining displacements in
   beams 304
   ! 87, Simply supported beam unsymmettically loaded by a force 305 88. Integrating the differential equation for a hinged beam 307
10. Superposition of forces 310
11. Differential relations in bending 312
    Chapter 16. Graph-analytic Method of Calculating Displacement in Bending 3)3
    § 91. Graph-analytic method 313
    § 92. Examples of determining deformations by the graph-analytic
    method 317
    § 93. The graph-analytic method applied to curvilinear bending-moment
    diagrams 320
    Chapter 17. Non-uniform Beams 324
    § 94. Selecting the section in beams of uniform strength 324
    | 95. Practical examples of beams of uniform strength 325
    § 96. Displacements in non-uniform beams 326
    PART VI. Potential Energy. Statically Indeterminate
    Beams
    Chapter 18. Application of the Concept of Potential Energy in Determining Displacements 331
    § 97. Statement of the problem 331
    | 98. Potential energy in the simplest cases of loading 333
    § 99. Potential energy ior the case of several forces 334
    § 100. Calculating bending energy using internal forces 336
    § 101. Castigliano’s theorem 337
    $ 102. Examples of application of Castigiiano’s theorem 341
    $ 103. Method of introducing an external force 344
    § 104. Theorem of reciprocity of works 346
    § 105. The theorem of Maxwell and Mohr 347
    § 106. Vereshchagin’s method 349
    1 107. Displacements In frames 351
    1 108. Deflection of beams due to shearing force 353
    Chapter 19. Statically indeterminate Beams 356
    § 109. Fundamental concepts 356
    § 110. Removing static indeterminacy via the differential equation of the
    deflected beam axis 357Contents 13
    §111. Concepts of redundant unknown and base beam 359
    1 112. Method of comparison of displacements 360
    §113. Application of the theorems of Castigliano and Mohr and Vereshchagin’s method 362
    § 114. solution of a simple statically Indeterminate frame 364
    § 1 (5. Analysis of continuous beams 366
    1 116. The theorem of three moments 366
    1 117. An example on application erf the theorem of three moments 372
    §118. Continuous beams with cantilevers. Beams with rigidly fixed
    ends 375
    PART VII. Resistance Under Compound Loading
    Chapter 20. Unsymmetrlc Bending 378
    § 119. Fundamental concepts 378
    £ 120. Unsymmetrlc bending. Determination of stresses 379
    § 121. Determining displacements in unsymmetrlc bending 365
    Chapter 21. Combined Bending and Tension or Compression 389
    § 122. Deflection of a beam subjected to axial and lateral forces 389
    1 123. Eccentric tension or compression 392
    § 124. Core of section 396
    Chapter 22. Combined bending and torsion 401
    § 125. Determination erf twisting and bending moments 401
    § 126. Determination of stresses and strength check In combined bending
    and torsion 404
    Chapter 23. General Compound Loading 408
    § 127. Stresses in a bar section subjected to general compound
    loading 408
    § 128. Determination of normal stresses 410
12. Determination of shearing stresses 413 130. Determination of displacements 414
13. Design of a simple crank rod 417
    Chapter 24. Curved Bars 423
    § 132. General concepts 423
    § 133. Determination of bending moments and normal and shearing
    forces 424
    § 134. Determination of stresses due to normal and shearing forces 420
    § 135. Determination of stresses due to bending moment 427
    § 136. Computation of the radius of curvature of the neutral layer in a
    rectangular section 433
    § 137. Determination of the radius of curvature oi the neutral layer for
    circle and trapezoid 434
    § 138. Determining the location of neutral layer from tables 436
    § 139. Analysis of the formula for normal stresses In a curved bat 436
    § 140. Additional remarks on the formula for normal stresses 439
    § 141. An example on determining stresses in a curved bar 441
    1 142. Determination of displacements in curved bars 442
    § 143. Analysis of a circular ring 44514 Contents
    Chapter 25. Thick-walled and Thin-walled Vessels 446
    $ 144. Analysis of thick-walled cylinders 446
    1 145. Stresses in thick spherical vessels 453
    § 146. Analysis of thin-walled vessels 454
    Chapter 26. Design for Permissible toads. Design for Limiting States 467
    § 147. Design for permissible loads. Application to stattcally determinate systems 457
    § 146. Design or statically indeterminate systems under tension or
    compression by the method of permissible loads 458
    § 149. Determination of limiting lifting capacity of a twisted rod 462
    § 150. Selecting beam section Tor permissible loads 465
    1 151. Design of statically indeterminate beams for permissible loads.
    The nindamentals. Analysis of a two-span beam 468
    6 152. Analysis of a three-span beam 472
    § 153. Fundamentals of design by the method of limiting states 474
    PART VIII. Stability of Clements of Structures
    Chapter 27. Stability ot Ban Under Compression 477
    § 154. Introduction. Fundamentals of stability of shape of compressed
    bars 477
    6 155. Euler’s formula for critical force 480
    § 156. Effect of constraining the bar ends 484
    § 157. Limits of applicability of Euler’s formula. Plotting of the diagram
    of total critical stresses 488
    § 158. ‘The stability check of compressed bars 494
    § 159. Selection of the type of section and material 498
    § 160. Practical importance of stability check 502
    Chapter 28. More Complicated Questions of Stability in Elements of Structures 604
    § 161. Stability of plane surface in bending of beams 504
    § 162. Design of compressed-bent ban 512
    § 163. Effect of eccentric compressive force and initial curvature
    of bar 517
    PART IX. Dynamic Action of Forces
    Chapter 29. Effect of Forces of Inertia. Stresses due to Vibrations 521
    § 164. Introduction 521
    § 165. Determining stresses in uniformly accelerated motion of
    bodies 523
    § 166. Stresses In a rotating ring (flywheel rim) 524
    § 167. Stresses in connecting rods 525
    $ 168. Rotating disc of uniform thickness 529
    1 169. Disc o f uniform strength 533
    § 170. Effect of resonance on the magnitude of stresses 535
    § 171. Determination of stresses in elements subjected to vibration 536
    § 172. The effect of mass of the elastic system on vibrations 541
    Chapter 30. Stresses Linder Impact Loading 548
    § 173. Fundamental concepts 548
    § 174. General method of determining stresses under impact loading 549Contents 15
    § 175. Concrete cases of determining stresses and conducting strength
    checks under impact 5S4
    $ 176. Impact stresses in a non-uniform bat 559
14. Practical conclusions from tbe derived results 660 178. The effect of mass of the elastic system on impact 562
15. Impact testing for failure 565
16. Effect of various factors on the results of impact testing 568
    Chapter 31. Strength Check of Materials Under Variable Loading 571
    § 181. Basic ideas concerning the effect of variable stresses on the -strength
    of materials 571
    § 182. Cyclic stresses 573
    § 183. Strength condition under variable stresses 575
    § 184. Determination of endurance limit in a symmetrical cycle 576
    1 185. Endurance limit in an unsymmetrlcsl cycle 579
    1 186. Local stresses 682
    § 187. Effect of size of part and other factors on endurance limit 589
    § 188. Practical examples of failure undo: variable loading. Causes of
    emergence and development of fatigue cracks 593
    § 189. Selection of permissible stresses 597
    § 190. Strength check under variable stresses and compound stressed
    state 600
    § 191. Practical measures for preventing fatigue failure 602
    Chapter 32. Fundamentals of Creep Analysis 605
    § 192. Effect of high temperatures on mechanical properties oi
    metals 605
    § 193. Creep and after-effect 607
    § 194. Creep and after-effect curves 609
    § 195. Fundamentals of creep design 615
    § 196. Examples on creep design 620
    Appendix 630
    Name index 639
    Subject index 641
    x
    Belelyubskii, N. A. 283
    Beltrami, F 145
    Belyaev, N. M. 5, 6, 7, 8, 26, 106, 148,
    188, 207. 290, 479, 499, 520,
17. 565, 576
    Benardos, N. N. 158
    Bolotin, V. V. 520
    Bubnov, I. G. 353
    Castigliano. A. 340
    Clapcyron, B. P. E. 335
    Clebscb, R. F. A, 304
    Coulomb, Ch. A. 140
    Davidenkov, N. N. 148
    Druzhinln, S. I. 144
    Kachanov, L. M. 136, 620
    Kachurin. V. K. 7
    Karman, Th. 490
    Kipnis, Ya. I. 8, ICO
    Krylov, A. N. 305
    Kurkin, S. A. 163
    Kushelev, N. Yu. 8
    Lam6, G. 138, 446
    Loitsyanskii, L. G. 536
    Lurye, A. I. 536
    Malinin, N. N. 620
    Mariotte, Ed. 138
    Maxwell, J. C. 349
    Mises, R. 145
    Molir, O. 349
    MQIler<Breslau, H. F. B. 349
    Engesser, F. 490
    Euler, L. 480
    Pridman, Ya. B. 148
    Forrest, P. G. 597
    Gadoiin, A. V. 440, 446
    Galileo Galilei 18
    Goldenblat, I. 1. 520
    Golovin, Kh. S. 440
    Guest, J. J. 140
    Navier, C. M. L. 138
    Navrotskii, D. I. 160
    Nikolaev, G. A. 163
    Oding, I. A. 597
    Ovechkin, G. 163
    Pavlov, A. P. 163
    Pirlet, 349
    Poncelet, J. V. 138
    Prigorovskii, N, I. 588
    Puzyrevskii, N. P. 305
    Hencky, H. 145
    Huber, F. 145
    Rankine, W. J. M. 138
    Ivanova, V. S. 597
    Saint-Venant, B. 139, 189
    Serensen, $. V. 588, 597€40
    Shtaerman, I. Ya. 96
    Sinitskii, A. K 8
    Slavyanov, N.G. 158
    Smirnov-Alyacv, G. A. 584
    Telelbaum, I. M. 588
    Timoslienko, S. P. 5, 188, 508
    Tresca, H. 140
    Uzhik, G. V. 597
    Name Index
    Vereshchagin, A. N. 349
    Vinokurov, V. A. 163
    Vlasov, V. Z. 188
    Vol’mir, A. S. 520
    Yagn, Yu. 1. 144
    Yasinskii, F. 490
    Zhuravskii, D. I. 270Subject Index
    absolute displacement 129
    absolute elongation 33
    active force 312
    alter-effect 608
    alternating cycle 573
    amorphous material 21
    amplification factor of vibrations 539
    amplitude of vibrations 535
    angle, twisting 169
    angle of shear 129
    anisotropic material 37, 56
    axes of inertia, principal 251
    axial compression 27
    axial force 29
    axial moment of inertia 233
    axial tension 27
    axis, neutral 227
    barfs), compressibility of 559
    curved 423
    with large curvature 439
    prismatic 27
    rigidity of 34
    with small curvature 439
    beam, cantilever 213
    continuous 366
    critical section of 200
    deflection of 292
    equation of deflected axis of 293
    fictitious 314
    riveted 289
    simply supported 207
    statically determinate 199
    statically indeterminate 199, 356
    of uniform rigidity 329
    of uniform strength 324, 558
    welded 290
    beam section, angle of rotation of 293
    beam supports, reaction of 197
    bending, pure 225
    uni-platiar 256
    unsymmetric 379
    bending moment 203, 348
    diagram of 204
    biaxial stress 102
    breaking away, failure by 101
    breaking load 457
    brittle failure, theory of 138
    brittle material 41, 52
    bulk modulus 123
    butt joint 159
    cable, flexible 92
    cantilever beam 213
    capacity, lifting 471
    Castlgliano’s theorem 340
    centre, flexural 387
    characteristic cycle 574
    circle, Mohr’s 110
    moment of inertia of 240
    Ciapcyron’s theorem 335
    coefficient, damping 539
    dynamic 524
    of dynamic response 60
    of length 485
    of operating conditions 475
    of overloading 476
    for production process 593
    of reliability 475
    of stress concentration 576
    comparison of displacements 361
    complementary shearing stresses 109
    complex figure, moment of inertia of
    245
    component constant of cycle 574
    component variable of cycle 574
    composite stressed state 101
    compound loading 378642 Subject Index
    compressibility of bars 559
    compression, axial 27
    eccentric 392
    compressive stress 101
    concentrated force 19
    condition, of joint deformation 67, 80,
    360
    of strength 30
    conditional stress 41
    conical spring 186
    connecting rod 525
    conservation of energy 331
    constancy of volume 50
    constant sign cycle 573
    constant stress cycle 573
    constraint, redundant 357
    contact stress 105
    continuous beam 366
    continuous load, intensity of 206
    core of section 396
    crack, fatigue 572
    creep 607
    stable 610
    unstable 610
    creep curve 609
    creep limit 617
    critical force 478
    critical section 86
    critical stale, of material 63
    critical stress 479
    crushing of rivets 154
    crystalline lattice 21
    crystalline material 21
    curved bar 423
    cycle, alternating 573
    characteristic 574
    component constant of 574
    constant sign 573
    constant stress 573
    fluctuating 573
    mean stress of 574
    of stress variation 573
    zero base 573
    cyclic stress 573
    damage susceptibility curve 593
    damping coefficient 539
    dead weight 86
    deflection of beam 292
    deformation 21
    elastic. 21. 37
    lateral 36
    local 488
    plastic 21, 47
    total energy of 126
    design load 476
    design moment 406
    diagram, of bending moment 204
    of reduced moment 472
    of shearing forces 204
    stress-strain 47
    differentiation, successive 313
    displacement, absolute 129
    generalized 333
    distortion, potential energy of, theory
    146
    distributed force 19
    distribution, uniform 29
    doublC’Shear rivet 153
    ductile failure, theory of 140
    ductile hinge 466
    ductile material 41
    dynamic coefficient 524
    dynamic load 20
    dynamic loading 521
    dynamic response, coefficient of 60
    dynamic stress 555
    eccentric compression 392
    eccentricity 392
    eccentric tension 392
    elastic deformation 21, 37
    specific, work of 46
    elasticity, limit of 23, 43
    modulus of 34
    elementary force 23
    elongation, absolute 33
    relative 33
    relative residual 44
    endurance limit 61, 62, 575
    energy of deformation, total 126Subject Index 643
    energy theory of strength 145
    envelope 142
    equal moments, method of 471
    equation, of deflected axis 293
    of method of initial parameters 305
    of three moments 372
    equatorial moment 233
    Euler’s formula 482
    externa) force 19
    method of 344
    factor of safety 24, 30
    main 63, 64
    factor of stress concentration 583
    failure, by breaking away 101
    due to shearing 101, 133
    through rupture 132
    fatigue 60, 572
    fatigue crack 672, 594
    fatigue limit 61
    fictitious beam 314
    fillet weld, joint with 162
    fixed hinged support 197
    fixed support 198
    rigidly 198
    flexibility 483
    flexible cable 92
    flexural centre 387
    fluctuating cycle 573
    force(s), active 312
    axial 29
    concentrated 19
    critical 478
    cumulative action of 335
    distributed 19
    external 19
    method of 344
    generalized 333
    of interaction 19
    normal 29
    passive 312
    of reaction 20
    shearing 203
    superposition of 83
    volume 19
    forced vibrations 535
    formula, Saint-Venant’s 407
    frame 351
    free torsion 187
    generalized displacement 333
    generalized force 333
    generalized Hooke’s law 335
    graph-analytic method 313
    helical spring 181
    hinge, ductile 466
    hinged support, fixed 197
    movable 197
    Hooke’s law 33
    generalized 335
    hydrostatic load 455
    impact load 20
    impact test 565
    initial parameters, method of 305
    integration, successive 312
    intensity of continuous load 206
    interaction, force of 19
    I-section 285
    isotropic material 37
    joint, butt 159
    lapped 151
    riveted 159
    welded 159
    with side fillet weld 162
    joint deformation, condition of 67, 80,
    360
    lapped joint 151
    lateral deformation 36
    lattice, crystalline 21
    law, Hooke’s 33
    generalized 335
    of complementary shearing stresses 109
    conservation of energy 331
    constancy of volume 50
    of cumulative action of forces 335644 Subject Index
    lifting capacity 471
    limit, of elasticity 23, 43
    endurance 61, 62, 575
    of proportionality 41, 47
    limiting states, first group 474
    second group 474
    limiting stress circle 139
    load, breaking 457
    continuous, intensity of 206
    design 476
    dynamic 20
    hydrostatic 4%
    impact 20
    permanent 19
    repeated variable 20
    static 20
    suddenly applied 20
    temporary 19
    ultimate 457
    load area 214
    load curve 214
    local deformation 488
    local stress 58, 61, 157, 576, 582, 583
    long-term strength 618
    less of stability 483
    material, amorphous 21
    anisotropic 35. 56
    brittle 41, 52
    critical state of 63
    crystalline 21
    ductile 41
    isotropic 37
    sensitivity factor of 585
    strength of 18
    maximum rigidity, plane of 386
    maximum shearing stresses, theory of
    140
    maximum tensile stresses, theory of
    138
    Maxwell and Molir theorem 347
    mean stress of cycle 574
    method, of comparison of displacements
    361
    of equal moments 471
    of external force 344
    graph-analytic 313
    of initial parameters 305
    of superposition of forces 223
    Vereshchagin’s 349
    modulus, bulk 123
    of elasticity 34
    reduced 490
    tangential 490
    section 236
    Mohr’s circle 110
    Mohr’s strength theory 141
    moment, bending 203
    design 406
    equatorial 233
    of section, static 232
    static, about neutral axis 267
    moment of ineria, axial 233
    of circle 240
    of complex figure 245
    of parallelogram 240
    polar 173, 250
    principal 256
    multiple-shear rivet 154
    natural vibrations 535
    net area 31
    neutral axis 227
    neutral layer 227
    radius of curvature of 231
    of trapezoid 435
    normal force 29
    normal stress 100
    octahedral plane 120
    octahedral shearing stress 121
    operating conditions, coefficient of
    476
    overloading, coefficient of 47$
    parallelogram, moment of inertia of
    240
    passive force 312
    permanent load 19Subject Index 645
    permissible stress 24
    planc(s), of maximum rigidity 386
    octahedral 120
    principal 102
    plane of inertia, principal 255
    plastic deformation 21, 47
    pliability 555
    of structure, total 564
    Poisson’s ratio 37
    polar moment of inertia 173, 250
    potential energy of distortion, theory of
    146
    principal axes of inertia 251
    principal moment of inertia 256
    principal plane 102
    principal plane of inertia 255
    principal radius of inertia 256
    principal strcss(es) 102
    trajectory of 282
    shearing 120
    principle of superposition of forces 83
    prismatic bar 27
    production process, coefficient for 593
    product of inertia, of section 232, 247
    proportionality,-limit of 41, 47
    pure holding 225
    pure shear 127
    pure torsion 187
    radius of curvature of neutral layer 231
    radius of inertia 256
    principal 256
    reaction, of beam supports 197
    force of 20
    redundant 357
    reciprocity of displacements, theorem of
    347
    reciprocity of works, theorem of 347
    reduced mass 544
    reduced modulus of elasticity 490
    reduced moment, diagram of 472
    reduced stress 147
    reduction of area, permanent relative 45
    redundant constraint 359
    redundant reaction 359
    redundant unknown 359
    relative elongation 33
    relative reduction of area, permanent
    45
    relative residual elongation 44
    relative rigidity 36
    relative shear 129
    reliability, coefficient of 475
    repeated variable load 20
    reservoir, thin-walled 103
    residual elongation, relative 44
    resistance, to rupture 134
    to shear 134
    resonance 535
    rigidity, of bar 34
    maximum, plane of 386
    relative 36
    of system 550
    torsional 177
    rigidly fixed support 198
    rivel(s), crushing of 154
    double-shear 153
    multiple-shear 154
    riveted beam 289
    riveted joint 159
    rod, connecting 525
    thin-walled 194
    rupture, failure through 132
    resistance to 134
    theory of 138
    rupture strain, total true 51
    safety, factor of 24, 30
    main factor of 63, 64
    Saint-Venant’s formula 407
    scale factor 590
    section, of beam
    critical 200
    core of 396
    critical 86
    product of inertia of 232, 247
    static moment of 232
    section modulus 174 , 236
    sensitivity factor of material 585
    shear, angle of 129646 Subject Index
    pure 127
    relative 129
    resistance to 134
    theory of 140
    shear centre 387
    shear centre line 387
    shearing, failure due to 101
    modulus of elasticity for 131
    shearing force{s) 204
    diagram of 204
    shearing stress(es) 100
    complementary 109
    maximum, theory of 140
    octahedral 12!
    principal 120
    simply supported beam 207
    span 92
    specific work, of elastic deformation
    46
    total 46
    spherical tensor 117
    spring, conical 186
    helical I8t
    stability check 477
    stable creep 610
    state(s), composite stressed 101
    limiting 474
    statically determinate beam 199
    statically indeterminate beam 199, 356
    statically indeterminate problem 66
    statically indeterminate system 66
    static toad 20
    static loading 60, 521
    static moment, about neutral axis 267
    of section 232
    straight-line form, loss of stability of 483
    strength, condition of 30
    energy theory of 145
    long-term 618
    of materials 18
    tensile, ultimate 30
    theory of 136
    true ultimate 51
    ultimate 23, 43
    strength endurance 575
    in unsymmetrlc cycle 579
    strength theory, first 138
    fourth 146
    of Mohr 141
    second 139
    third 140
    stress, biaxial 102
    compressive 101
    conditional 41
    contact 105
    critical 479
    of cycle, mean 574
    cyclic 573
    dynamic 555
    local 58, 61, 157, 576, 582. 583
    maximum shearing 140
    maximum tensile 138
    normal 100
    permissible 24
    principal 102
    reduced 147
    rupture, true 51
    shearing 100
    octahedral 121
    principal 120
    tensile 100
    triaxial 103
    uniaxial 102
    variable 575
    stress circle 111
    limiiing 139
    stress concentration, coefficient of 576
    factor of 583
    stress deviator 124
    stress intensity 121
    stressed state, composite 101
    stress-strain diagram 47
    stress tensor 117
    stress variation, cycle of 573
    structure, total pliability of 564
    successive differentiation 313
    successive integration 312
    suddenly applied load 20
    superposition of forces, method of 223
    principle of 83
    support, fixed 198
    hinged, fixed 197Subject Index 647
    movable 197
    rigidly fixed 198
    system, rigidity of 550
    statically indeterminate 66
    tangential modulus of elasticity 490
    temporary load 19
    tensile strength, ultimate 30
    tensile stresses 100
    maximum, theory of 138
    tension, axial 27
    eccentric 392
    lest, impact 565
    theorem, Castigllano’s 340
    Clapeyron’s 335
    of Maxwell and Mohr 347
    of reciprocity of displacements 347
    of reciprocity of works 347
    theory’, of brittle failure 138
    of ductile failure 140
    of maximum tensile stresses 138
    of maximum shearing stresses 140
    of potential energy of distortion 146
    of rupture 138
    of shear 140
    of strength 136
    thin-walled reservoir 103
    thin-walled rod 194
    thin-walled vessel 454
    three moments, equation of 372
    torque 165
    torsion, free 187
    pure 187
    torsional rigidity 177
    total pliability of structure 564
    total specific work 46
    trajectory of principal stresses 282
    trapezoid, neutral layer of 435
    trlaxlai stress 103
    true rupture strain, total 51
    T -scction 243

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