Contents xi 9.12 Solution for displacements and reactions 349 Bibliography 350 Examples 350 Problems 375 10 Contact Stress,Residual Stress and Stress Concentrations 381 Summary 381 10.1 Contact stresses 382 Introduction 382 10.1.1 General case of contact between two curved surfaces 385 10.1.2 Special case 1-Contact of parallel cylinders 386 10.1.3 Combined normal and tangential loading 388 10.1.4 Special case 2-Contacting spheres 389 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 10.2 Residual stresses 394 Introduction 10.2.1 Reasons for residual stresses (a)Mechanical processes (b)Chemical treatment (c)Heat treatment 40909090800 (d)Welds (e)Castings 10.2.2 The influence of residual stress on failure 10.2.3 Measurement of residual stresses 咖 The hole-drilling technique X-ray diffraction 81 10.2.4 Summary of the principal effects of residual stress 408 10.3 Stress concentrations 408 Introduction 408 10.3.1 Evaluation of stress concentration factors 413 10.3.2 St.Venant's principle 420 10.3.3 Theoretical considerations of stress concentrations due to concentrated loads 422 (a)Concentrated load on the edge of an infinite plate 422 (b)Concentrated load on the edge of a beam in bending 423 10.3.4 Fatigue stress concentration factor 423 10.3.5 Notch sensitivity 424 10.3.6 Strain concentration-Neuber's rule 425 10.3.7 Designing to reduce stress concentrations 426 (a)Fillet radius 427 (b）Keyways or splines 427Contents xi 9.12 Solution for displacements and reactims Bibliography Examples Problems 10 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 loading 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 treatment (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 factors 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 of an infinite plate (b) Concentrated load on the edge of a beam in bending 10.3.4 Fatigue stress concentration factor 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 1 392 393 394 394 395 395 397 398 400 401 402 402 404 407 408 408 408 413 420 422 422 423 423 424 425 426 427 427