18.4 Product liability and service provision 465 18.5 Miniaturization and multi-functionality 466 18.6 Concern for the environment and for the individua 467 18.7 Summary and conclusions 469 18.8 Further readins 469 ppendix a Useful solutions to standard problems ntroduction and synopsis 473 A1 Constitutive equations for mechanical response 474 A2 Moments of sections 476 A 3 Elastic bending of beams A 4 Failure of beams and panels A. 5 Buckling of columns, plates, and shells 482 A6 Torsion of shafts 484 A 7 Static and spinning disks A 8 Contact stresses 488 A 9 Estimates for stress concentrations A 10 Sharp cracks 49 11P1 sels A 12 Vibrating beams, tubes, and disks A 13 Creep and creep fracture 498 A 14 Flow of heat and matter 500 A 15 Solutions for diffusion equations 502 A 16 Further reading Appendix B Material indices 507 B. 1 Introduction and synopsi 508 B 2 Use of material indices 508 AppendixC Data and information for engineering materials 513 C 1 Names and applications: metals and alloys 514 C2 Names and applications: polymers and foams 515 C3 Names and applications: composites, ceramics, glasses, and natural materials 516 C 4 Melting temperature, Tm, and glass temperature, Tg 518 C5 Density, p 520 C6 Young's modulus, E C7 Yield strength, Oy, and tensile strength, ots 524 C8 Fracture toughness(plane-strain), KIc 526 C9 Thermal conductivity, A 528 C 10 Thermal expansion, a C 11 Approximate production energies and CO2 burden 532 C 12 Environmental resistance 53418.4 Product liability and service provision 465 18.5 Miniaturization and multi-functionality 466 18.6 Concern for the environment and for the individual 467 18.7 Summary and conclusions 469 18.8 Further reading 469 Appendix A Useful solutions to standard problems 471 Introduction and synopsis 473 A.1 Constitutive equations for mechanical response 474 A.2 Moments of sections 476 A.3 Elastic bending of beams 478 A.4 Failure of beams and panels 480 A.5 Buckling of columns, plates, and shells 482 A.6 Torsion of shafts 484 A.7 Static and spinning disks 486 A.8 Contact stresses 488 A.9 Estimates for stress concentrations 490 A.10 Sharp cracks 492 A.11 Pressure vessels 494 A.12 Vibrating beams, tubes, and disks 496 A.13 Creep and creep fracture 498 A.14 Flow of heat and matter 500 A.15 Solutions for diffusion equations 502 A.16 Further reading 504 Appendix B Material indices 507 B.1 Introduction and synopsis 508 B.2 Use of material indices 508 Appendix C Data and information for engineering materials 513 C.1 Names and applications: metals and alloys 514 C.2 Names and applications: polymers and foams 515 C.3 Names and applications: composites, ceramics, glasses, and natural materials 516 C.4 Melting temperature, Tm, and glass temperature, Tg 518 C.5 Density,
520 C.6 Young’s modulus, E 522 C.7 Yield strength, y, and tensile strength, ts 524 C.8 Fracture toughness (plane-strain), K1C 526 C.9 Thermal conductivity, 528 C.10 Thermal expansion,  530 C.11 Approximate production energies and CO2 burden 532 C.12 Environmental resistance 534 Contents ix