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أخواني في الله أحضرت لكم كتاب Strength of Materials N. M. Belyaev translated from the Russian by N. R. Mehia
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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 35. Potential energy of elastic deformation in compound stress 124 36. 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 47. Determining stresses in a round shaft under torsion 168 48. 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 84. 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 89. Superposition of forces 310 90. 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 1129. Determination of shearing stresses 413 130. Determination of displacements 414 131. 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 1177. Practical conclusions from tbe derived results 660 178. The effect of mass of the elastic system on impact 562 179. Impact testing for failure 565 180. 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, 562. 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 MQIlerEngesser, 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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