Design for Thermal Stresses

Design for Thermal Stresses......Page 3
Contents......Page 7
Preface......Page 13
Nomenclature......Page 15
1.1 Definition of Thermal Stress......Page 21
1.2 Thermal–Mechanical Design......Page 23
1.3 Factor of Safety in Design......Page 24
1.4 Thermal Expansion Coefficient......Page 27
1.5 Young’s Modulus......Page 31
1.6 Poisson’s Ratio......Page 33
1.7 Other Elastic Moduli......Page 34
1.8 Thermal Diffusivity......Page 36
1.9 Thermal Shock Parameters......Page 37
1.10 Historical Note......Page 39
Problems......Page 43
References......Page 45
2.1 Stress and Strain......Page 46
2.2 Bar between Two Supports......Page 47
2.3 Bars in Parallel......Page 52
2.4 Bars with Partial Removal of Constraints......Page 55
2.5 Nonuniform Temperature Distribution......Page 63
2.6 Historical Note......Page 72
Problems......Page 73
References......Page 78
3.1 Limits on the Analysis......Page 79
3.2 Stress Relationships......Page 80
3.3 Displacement Relations......Page 84
3.4 General Thermal Bending Relations......Page 85
3.5 Shear Stresses......Page 87
3.6 Beam Bending Examples......Page 89
3.7 Thermal Bowing of Pipes......Page 117
3.8 Historical Note......Page 128
Problems......Page 130
References......Page 137
4.1 Elastic Energy Method......Page 138
4.2 Unit-Load Method......Page 143
4.3 Trusses with External Constraints......Page 149
4.4 Trusses with Internal Constraints......Page 152
4.5 The Finite Element Method......Page 162
4.6 Elastic Energy in Bending......Page 173
4.7 Pipe Thermal Expansion Loops......Page 178
4.8 Pipe Bends......Page 192
4.9 Elastic Energy in Torsion......Page 198
4.10 Historical Note......Page 205
Problems......Page 206
References......Page 215
5.1 Introduction......Page 217
5.2 Strain Relationships......Page 218
5.3 Stress Relationships......Page 223
5.4 Stress–Strain Relations......Page 226
5.5 Temperature Field Equation......Page 228
5.6 Reduction of the Governing Equations......Page 232
5.7 Historical Note......Page 235
Problems......Page 237
References......Page 240
6.1 Introduction......Page 241
6.2 Stress Resultants......Page 242
6.3 Circular Plate with a Hot Spot......Page 244
6.4 Two-Dimensional Problems......Page 259
6.5 Plate with a Circular Hole......Page 267
6.6 Historical Note......Page 276
Problems......Page 277
References......Page 282
7.1 Introduction......Page 284
7.2 Governing Relations for Bending of Rectangular Plates......Page 285
7.3 Boundary Conditions for Plate Bending......Page 293
7.4 Bending of Simply-Supported Rectangular Plates......Page 297
7.5 Rectangular Plates with Two-Dimensional Temperature Distributions......Page 303
7.6 Axisymmetric Bending of Circular Plates......Page 307
7.7 Axisymmetric Thermal Bending Examples......Page 312
7.8 Circular Plates with a Two-Dimensional Temperature Distribution......Page 325
7.9 Historical Note......Page 330
Problems......Page 332
References......Page 335
8.1 Introduction......Page 337
8.2 Cylindrical Shells with Axisymmetric Loading......Page 339
8.3 Cooldown of Ring-Stiffened Cylindrical Vessels......Page 349
8.4 Cylindrical Vessels with Axial Temperature Variation......Page 356
8.5 Short Cylinders......Page 364
8.6 Axisymmetric Loading of Spherical Shells......Page 370
8.7 Approximate Analysis of Spherical Shells under Axisymmetric Loading......Page 377
8.8 Historical Note......Page 391
Problems......Page 393
References......Page 397
9.1 Introduction......Page 398
9.2 Governing Equations for Plane Strain......Page 399
9.3 Hollow Cylinder with Steady-State Heat Transfer......Page 404
9.4 Solid Cylinder......Page 408
9.5 Thick-Walled Spherical Vessels......Page 417
9.6 Solid Spheres......Page 422
9.7 Historical Note......Page 431
Problems......Page 432
References......Page 435
10.2 Thermal Buckling of Columns......Page 436
10.3 General Formulation for Beam Columns......Page 440
10.4 Postbuckling Behavior of Columns......Page 443
10.5 Lateral Thermal Buckling of Beams......Page 446
10.6 Symmetrical Buckling of Circular Plates......Page 452
10.7 Thermal Buckling of Rectangular Plates......Page 457
10.8 Thermal Buckling of Cylindrical Shells......Page 470
10.9 Historical Note......Page 474
Problems......Page 475
References......Page 480
Appendix A Preferred Prefixes in the SI System of Units......Page 481
Appendix B Properties of Materials at 300 K......Page 482
C.1 Properties of 2024-T3 Aluminum......Page 484
C.3 Properties of 9% Nickel Steel......Page 485
C.5 Properties of Beryllium Copper......Page 486
C.7 Properties of Teflon......Page 487
References......Page 488
D.1 Introduction......Page 489
D.3 Bessel Functions of Noninteger Order......Page 490
D.4 Bessel Functions of the Second Kind......Page 492
D.5 Bessel’s Equation......Page 494
D.6 Recurrence Relationships for Jn(x) and Yn(x)......Page 495
D.7 Asymptotic Relations and Zeros for Jn(x) and Yn(x)......Page 496
D.8 Modified Bessel Functions......Page 497
D.9 Modified Bessel Equation......Page 498
D.10 Recurrence Relations for the Modified Bessel Functions......Page 499
D.11 Asymptotic Relations for In(x) and Kn(x)......Page 500
References......Page 503
E.1 Introduction......Page 505
E.2 Kelvin Functions......Page 506
E.3 Differential Equation for Kelvin Functions......Page 510
E.4 Recurrence Relationships for the Kelvin Functions......Page 511
E.5 Asymptotic Relations for the Kelvin Functions......Page 512
E.6 Zeros of the Kelvin Functions......Page 513
F.1 Determinants......Page 514
F.2 Matrices......Page 519
References......Page 524
Index......Page 525