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1、MECHANICS OF MATERIALS 2 An introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials THIRD EDITION E. J. HEARN PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE University of Warwick United Kingdom la=- EINEMANN CONTENTS Introduction xv Notation xvii 1 Un
2、symmetrical Bending 1 Summary Introduction I .1 1.2 1.3 1.4 1.5 I .6 1.7 Momenta1 ellipse 1.8 Stress determination 1.9 Alternative procedure for stress determination 1.10 Alternative procedure using the momenta1 ellipse 1.1 1 Dejections Examples Problems Product second moment of area Principal secon
3、d moments of area Mohrs circle of second moments of area Lands circle of second moments of area Rotation of axes: determination of moments o f area in terms of the principal values The ellipse of second moments o f area 2 Struts Summary Introduction 2.1 Eulers theory 2.2 Equivalent strut length 2.3
4、2.4 Euler “validity limit” 2.5 Rankine or Rankine-Gordon formula 2.6 Perry- Robertson formula 2.7 2.8 Struts with initial curvature 2.9 Struts with eccentric load 2.10 Laterally loaded struts 2.1 1 Comparison of Euler theory with experimental results British Standard procedure (BS 449) Alternative p
5、rocedure for any strut-loading condition 8 9 11 11 11 13 15 16 24 28 28 30 31 35 36 37 38 39 41 41 42 46 48 V vi Contents 2.1 2 Struts with unsymmetrical cross-section Examples Problems 3 Strains Beyond the Elastic Limit Summary Introduction 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.1 1 3.12 3.13 3
6、.14 3.15 3.16 3.17 3.18 3.19 3.20 Plastic bending o f rectangular-sectioned beams Shape factor - symmetrical sections Application to I-section beams Partially plastic bending o f unsymmetrical sections Shape factor - unsymmetrical sections Dejections o f partially plastic beams Length o f yielded ar
7、ea in beams Collapse loads - plastic limit design Residual stresses after yielding: elastic-perfectly plastic material Torsion of shafts beyond the elastic limit - plastic torsion Angles of twist of shafts strained beyond the elastic limit Plastic torsion o f hollow tubes Plastic torsion of case-har
8、dened shafts Residual stresses after yield in torsion Plastic bending and torsion of strain-hardening materials (a) Inelastic bending (b) Inelastic torsion Residual stresses - strain-hardening materials Influence o f residual stresses on bending and torsional strengths Plastic yielding in the eccent
9、ric loadirzg o f rectangular sections Plastic yielding and residual stresses under axial loading with stress concentrations Plastic yielding o f axially symmetric components (a) Thick cylinders - collapse pressure (b) Thick cylinders - “auto-frettage (c) Rotating discs Examples Problems 4 Rings, Dis
10、cs and Cylinders Subjected to Rotation and Thermal Gradients Summary 4.1 4.2 Rotating solid disc 4.3 4.4 4.5 Thin rotating ring or cylinder Rotating disc with a central hole Rotating thick cylinders or solid shafs Rotating disc o f uniform strength 49 50 56 61 61 62 64 65 67 67 69 69 69 71 73 75 77
11、77 79 79 80 80 83 84 84 85 86 87 87 89 94 96 109 117 117 118 119 122 124 125 Contents 4.6 Combined rotational and thermal stresses in uniform discs and thick cylinders Examples Problems 5 Torsion of Non-Circular and Thin- Walled Sections Summary 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.1 1 Rectang
12、ular sections Narrow rectangular sections Thin-walled open sections Thin-walled split tube Other solid (non-tubular) shafts Thin-walled closed tubes of non-circular section (Bredt-Batho theory) Use o f “equivalent J” for torsion of non-circular sections Thin-walled cellular sections Torsion of thin-
13、walled stifSened sections Membrane analogy EfSect of warping of open sections Examples Problems 6 Experimental Stress Analysis Introduction 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.1 1 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19 6.20 6.21 Brittle lacquers Strain gauges Unbalanced bridge circuit Null b
14、alance or balanced bridge circuit Gauge construction Gauge selection Temperature compensation Installation procedure Basic measurement systems D.C. and A.C. systems Other types of strain gauge Photoelasticity Plane-polarised light - basic polariscope arrangements Temporary birefringence Production o
15、 f fringe patterns Interpretation o f fringe patterns Calibration Fractional fringe order determination - compensation techniques Isoclinics-circular polarisation Stress separation procedures Three-dimensional photoelasticity vii 126 129 136 141 141 142 143 143 145 145 147 149 150 151 152 153 154 16
16、0 166 166 167 171 173 173 173 175 175 176 177 179 180 181 182 183 184 185 186 187 188 190 1 90 . VI11 Contents 6.22 Rejective coating technique 6.23 Other methods o f strain measurement Bibliography 7 Circular Plates and Diaphragms Summary A. CIRCULAR PLATES 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10
17、7.1 1 7.12 7.13 7.14 Stresses Bending moments General equation for slope and dejection General case o f a circular plate or diaphragm subjected to combined uniformly distributed load q (pressure) and central concentrated load F Uniformly loaded circular plate with edges clamped Uniformly loaded circ
18、ular plate with edges freely supported Circular plate with central concentrated load F and edges clamped Circular plate with central concentrated load F and edges freely supported Circular plate subjected to a load F distributed round a circle Application to the loading of annular rings Summary o f
19、end conditions Stress distributions in circular plates and diaphragms subjected to lateral pressures Discussion of results - limitations of theory Other loading cases of practical importance B. BENDING OF RECTANGULAR PLATES 7.15 7.16 Rectangular plates with simply supported edges carrying uniformly
20、distributed loads Rectangular plates with clamped edges carrying uniformly distributed loads Examples Problems 8 Introduction to Advanced Elasticity Theory 8.1 Types o f stress 8.2 8.3 8.4 The Cartesian stress components: notation and sign convention 8.2.1 Sign conventions The state o f stress at a
21、point Direct, shear and resultant stresses on an oblique plane 8.4.1 8.4.2 Line o f action o f resultant stress Line o f action of normal stress 190 192 192 193 193 195 195 197 198 199 200 202 203 205 206 208 208 209 21 1 212 213 213 214 215 218 220 220 220 22 1 22 1 224 226 227 Contents ix 8.5 8.6
22、8.7 8.8 8.9 8.10 8.1 1 8.12 8.13 8.14 8.15 8.16 8.17 8.18 8.19 8.20 8.21 8.22 8.23 8.24 8.25 8.26 8.27 8.4.3 8.4.4 Principal stresses and strains in three dimensions - Mohr s circle representation Graphical determination of the direction of the shear stress r, on an inclined plane in a three-dimensi
23、onal principal stress system The combined Mohr diagram for three-dimensional stress and strain systems Application of the combined circle to two-dimensional stress systems Graphical construction for the state of stress at a point Construction for the state of strain on a general strain plane State o
24、f stress-tensor notation The stress equations of equilibrium Principal stresses in a three-dimensional Cartesian stress system 8.13.1 Solution of cubic equations Stress invariants - Eigen values and Eigen vectors Stress invariants Reduced stresses Strain invariants Alternative procedure for determin
25、ation of principal stresses 8.1 8.1 Evaluation of direction cosines for principal stresses Octahedral planes and stresses Deviatoric stresses Deviatoric strains Plane stress and plane strain 8.22.1 Plane stress 8.22.2 Plane strain The stress-strain relations The strain-displacement relationships The
26、 strain equations of transformation Compatibility The stress function concept 8.27.1 Forms of Airy stress function in Cartesian coordinates 8.27.2 Case 1 - Bending of a simply supported beam by a uniformly 8.27.3 The use of polar coordinates in two dimensions 8.27.4 Forms of stress function in polar
27、 coordinates 8.27.5 Case 2 - hi-symmetric case: solid shaft and thick cylinder radially loaded with uniform pressure 8.27.6 Case 3 - The pure bending of a rectangular section curved beam 8.27.7 Case 4 - Asymmetric case n = 1. Shear loading of a circular arc cantilever beam 8.27.8 Case 5 - The asymme
28、tric cases n , 2 -stress concentration at a circular hole in a tension$eld Line of action of shear stress Shear stress in any other direction on the plane distributed loading 227 227 228 229 230 232 234 235 235 236 242 242 243 244 246 247 247 248 249 25 1 25 3 254 255 255 256 257 259 26 1 263 265 26
29、7 27 1 272 273 273 274 276 X Contents 8.27.9 Other useful solutions o f the biharmonic equation Examples Problems 9 Introduction to the Finite Element Method 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.1 1 Introduction Basis of the finite element method Applicability of the finite element method Form
30、ulation of the Jinite element method General procedure o f the Jinite element method 9.4.1 Identification o f the appropriateness of analysis by the jinite element method 9.4.2 Identification of the type o f analysis 9.4.3 Idealisation 9.4.4 Discretisation of the solution region 9.4.5 Creation of th
31、e material model 9.4.6 Node and element ordering 9.4.7 Application of boundary conditions 9.4.8 Creation of a data file 9.4.9 Computer, processing, steps 9.4.10 Interpretation and validation of results 9.4.1 1 Modification and re-run Fundamental arguments 9.5.1 Equilibrium 9.5.2 Compatibility 9.5.3
32、Stress-strain law 9.5.4 Forceldisplacement relation The principle of virtual work A rod element 9.7.1 Formulation of a rod element using fundamental equations 9.7.2 Formulation of a rod element using the principle o f virtual work equation A simple beam element 9.8.1 Formulation of a simple beam ele
33、ment using fundamental equations 93.2 Formulation of a simple beam element using the principle of virtual work equation A simple triangular plane membrane element 9.9.1 Formulation of a simple triangular plane membrane element using the principle of virtual work equation Formation of assembled stcfi
34、ess matrix by use of a dof. correspondence table Amlieation of boundarv conditions and uartitioninn r , “ 279 283 290 300 300 300 302 303 303 303 305 305 305 312 312 316 317 318 318 319 319 319 321 322 322 323 324 324 32% 334 3 34 339 343 344 347 349 Contents xi 9.12 Solution for displacements and r
35、eactims Bibliography Examples Problems 1 0 Contact Stress, Residual Stress and Stress Concentrations Summary 10.1 Contact stresses Introduction 10.1.1 General case of contact between two curved surfaces 10.1.2 Special case I - Contact of parallel cylinders 10.1.3 Combined normal and tangential loadi
36、ng 10.1.4 Special case 2 - Contacting spheres 10.1.5 Design considerations 10.1.6 Contact loading of gear teeth 10.1.7 Contact stresses in spur and helical gearing 10.1.8 Bearing failures Introduction 10.2.1 Reasom for residual stresses (a) Mechanical processes (b) Chemical treatment (c) Heat treatm
37、ent (d) Welds (e) Castings 10.2 Residual stresses 10.2.2 The injuence of residual stress on failure 10.2.3 Measurement of residual stresses The hole-drilling technique X-ray difiaction 10.2.4 Summary of the principal effects of residual stress Introduction 10.3.1 Evaluation of stress concentration f
38、actors 10.3.2 St. Venant s principle 10.3.3 Theoretical considerations of stress concentrations due to 10.3 Stress concentrations concentrated loads (a) Concentrated load on the edge o f an infinite plate (b) Concentrated load on the edge of a beam in bending 10.3.4 Fatigue stress concentration fact
39、or 10.3.5 Notch sensitivity 10.3.6 Strain concentration - Neuber s rule 10.3.7 Designing to reduce stress concentrations (a) Fillet radius (b) Keyways or splines 349 350 350 375 381 38 1 382 382 385 386 388 389 390 39 1 392 393 394 394 395 395 397 398 400 401 402 402 404 407 408 408 408 413 420 422
40、422 423 423 424 425 426 427 427 xii Contents (e) Grooves and notches (d) Gear teeth (e) Holes cf) Oil holes (g) Screw threads (h) Press or shrink Jit members 10.3.8 Use of stress concentration factors with yield criteria 10.3.9 Design procedure References Examples Problems 11 Fatigue, Creep and Frac
41、ture Summary 11.1 Fatigue Introduction 11.1.1 The SIN curve 1 1.1.2 PISIN curves 1 1.1.3 Effect o f mean stress 1 1.1.4 Effect o f stress concentration 11.1.5 Cumulative damage 1 1.1.6 Cyclic stress-strain 1 1.1.7 Combating fatigue 1 1.1.8 Slip bands and fatigue Introduction 1 1.2.1 The creep test 1
42、 1.2.2 Presentation of creep data 11.2.3 The stress-rupture test 11.2.4 Parameter methods 1 1.2.5 Stress relaxation 1 1.2.6 Creep-resistant alloys 1 1.3 Fracture mechanics Introduction 1 1.3.1 Energy variation in cracked bodies (a) Constant displacement (b) Constant loading (a) Grifith s criterion f
43、or fiacture (b) Stress intensity factor 11.2 Creep 1 1.3.2 Linear elastic fracture mechanics (L.E.F.M.) 1 1.3.3 Elastic-plastic fracture mechanics (E.P.F.M.) 1 1.3.4 Fracture toughness 1 1.3.5 Plane strain and plane stress fracture modes 1 1.3.6 General yielding fracture mechanics 1 1.3.7 Fatigue cr
44、ack growth 1 1.3.8 Crack tip plasticity under fatigue loading 429 430 43 1 43 1 43 1 433 434 434 435 437 442 443 443 446 446 446 449 45 1 453 454 455 458 460 462 462 462 465 466 467 470 47 1 472 472 473 474 474 475 475 477 48 1 483 484 484 486 488 . Contents Xlll 11.3.9 Measurement of fatigue crack
45、growth References Examples Problems 489 490 49 1 503 12 Miscellaneous topics 509 12.1 Bending of beams with initial curvature 12.2 Bending of wide beams 12.3 General expression for stresses in thin-walled pressure or selj-weight 12.4 Bending stresses at discontinuities in thin shells 1 2.5 Viscoelas
46、ticity References Examples Problems 509 515 517 518 521 527 527 527 shells subjected to Appendix 1. npical mechanical and physical properties for engineering metals Appendix 2. Typical mechanical properties of non-metals Appendix 3. Other properties of non-metals 534 535 536 Index 537 INTRODUCTION T
47、his text is a revised and extended third edition of the highly successful text initially published in 1977 intended to cover the material normally contained in degree and honours degree courses in mechanics of materials and in courses leading to exemption from the academic requirements of the Engine
48、ering Council. It should also serve as a valuable refer- ence medium for industry and for post-graduate courses. Published in two volumes, the text should also prove valuable for students studying mechanical science, stress analysis, solid mechanics or similar modules on Higher Certificate, Higher D
49、iploma or equivalent courses in the UK or overseas and for appropriate NVQ* programmes. The study of mechanics of materials is the study of the behaviour of solid bodies under load. The way in which they react to applied forces, the deflections resulting and the stresses and strains set up within the bodies, are all considered in an attempt to provide sufficient knowledge to enable any component to be designed such that it will not fail within its service life. Typical components considered in detail in the first volume, Mechanics of Materials I , include beams, shafts, cylind