Design for Thermal Stresses

Randall F. Barron is Professor Emeritus of Mechanical Engineering at Louisiana Tech University in Ruston, Louisiana. He received his BS in mechanical engineering from Louisiana Tech University, and his MS and PhD in mechanical engineering from The Ohio State University in Columbus, Ohio. He is the author of three college-level textbooks: Cryogenic Systems, Cryogenic Heat Transfer, and Industrial Noise Control and Acoustics. Brian R. Barron is a lecturer in mathematics and statistics at Louisiana Tech University in Ruston, Louisiana. He received his BS degree in mathematics education from Louisiana Tech University, his MDiv from St. Paul School of Theology in Kansas City, Missouri, and his MS in mathematics and PhD in computational analysis and modeling from Louisiana Tech University.

Preface xi Nomenclature xiii 1 Introduction 1 1.1 Definition of Thermal Stress 1 1.2 Thermal-Mechanical Design 3 1.3 Factor of Safety in Design 4 1.4 Thermal Expansion Coefficient 7 1.5 Young's Modulus 11 1.6 Poisson's Ratio 13 1.7 Other Elastic Moduli 14 1.8 Thermal Diffusivity 16 1.9 Thermal Shock Parameters 17 1.10 Historical Note 19 Problems 23 References 25 2 Thermal Stresses in Bars 26 2.1 Stress and Strain 26 2.2 Bar between Two Supports 27 2.3 Bars in Parallel 32 2.4 Bars with Partial Removal of Constraints 35 2.5 Nonuniform Temperature Distribution 43 2.6 Historical Note 52 Problems 53 References 58 3 Thermal Bending 59 3.1 Limits on the Analysis 59 3.2 Stress Relationships 60 3.3 Displacement Relations 64 3.4 General Thermal Bending Relations 65 3.5 Shear Stresses 67 3.6 Beam Bending Examples 69 3.7 Thermal Bowing of Pipes 97 3.8 Historical Note 108 Problems 110 References 117 4 Thermal Stresses in Trusses and Frames 118 4.1 Elastic Energy Method 118 4.2 Unit-Load Method 123 4.3 Trusses with External Constraints 129 4.4 Trusses with Internal Constraints 132 4.5 The Finite Element Method 142 4.6 Elastic Energy in Bending 153 4.7 Pipe Thermal Expansion Loops 158 4.8 Pipe Bends 172 4.9 Elastic Energy in Torsion 178 4.10 Historical Note 185 Problems 186 References 195 5 Basic Equations of Thermoelasticity 197 5.1 Introduction 197 5.2 Strain Relationships 198 5.3 Stress Relationships 203 5.4 Stress-Strain Relations 206 5.5 Temperature Field Equation 208 5.6 Reduction of the Governing Equations 212 5.7 Historical Note 215 Problems 217 References 220 6 Plane Stress 221 6.1 Introduction 221 6.2 Stress Resultants 222 6.3 Circular Plate with a Hot Spot 224 6.4 Two-Dimensional Problems 239 6.5 Plate with a Circular Hole 247 6.6 Historical Note 256 Problems 257 References 262 7 Bending Thermal Stresses in Plates 264 7.1 Introduction 264 7.2 Governing Relations for Bending of Rectangular Plates 265 7.3 Boundary Conditions for Plate Bending 273 7.4 Bending of Simply-Supported Rectangular Plates 277 7.5 Rectangular Plates with Two-Dimensional Temperature Distributions 283 7.6 Axisymmetric Bending of Circular Plates 287 7.7 Axisymmetric Thermal Bending Examples 292 7.8 Circular Plates with a Two-Dimensional Temperature Distribution 305 7.9 Historical Note 310 Problems 312 References 315 8 Thermal Stresses in Shells 317 8.1 Introduction 317 8.2 Cylindrical Shells with Axisymmetric Loading 319 8.3 Cooldown of Ring-Stiffened Cylindrical Vessels 329 8.4 Cylindrical Vessels with Axial Temperature Variation 336 8.5 Short Cylinders 344 8.6 Axisymmetric Loading of Spherical Shells 350 8.7 Approximate Analysis of Spherical Shells under Axisymmetric Loading 357 8.8 Historical Note 371 Problems 373 References 377 9 Thick-Walled Cylinders and Spheres 378 9.1 Introduction 378 9.2 Governing Equations for Plane Strain 379 9.3 Hollow Cylinder with Steady-State Heat Transfer 384 9.4 Solid Cylinder 388 9.5 Thick-Walled Spherical Vessels 397 9.6 Solid Spheres 402 9.7 Historical Note 411 Problems 412 References 415 10 Thermoelastic Stability 416 10.1 Introduction 416 10.2 Thermal Buckling of Columns 416 10.3 General Formulation for Beam Columns 420 10.4 Postbuckling Behavior of Columns 423 10.5 Lateral Thermal Buckling of Beams 426 10.6 Symmetrical Buckling of Circular Plates 432 10.7 Thermal Buckling of Rectangular Plates 437 10.8 Thermal Buckling of Cylindrical Shells 450 10.9 Historical Note 454 Problems 455 References 460 Appendix A Preferred Prefixes in the SI System of Units 461 Appendix B Properties of Materials at 300 K 462 Appendix C Properties of Selected Materials as a Function of Temperature 464 C.1 Properties of 2024-T3 Aluminum 464 C.2 Properties of C1020 Carbon Steel 465 C.3 Properties of 9# Nickel Steel 465 C.4 Properties of 304 Stainless Steel 466 C.5 Properties of Beryllium Copper 466 C.6 Properties of Titanium Alloy 467 C.7 Properties of Teflon 467 References 468 Appendix D Bessel Functions 469 D.1 Introduction 469 D.2 Bessel Functions of the First Kind 470 D.3 Bessel Functions of Noninteger Order 470 D.4 Bessel Functions of the Second Kind 472 D.5 Bessel's Equation 474 D.6 Recurrence Relationships for Jn(x) and Yn(x) 475 D.7 Asymptotic Relations and Zeros for Jn(x) and Yn(x) 476 D.8 Modified Bessel Functions 477 D.9 Modified Bessel Equation 478 D.10 Recurrence Relations for the Modified Bessel Functions 479 D.11 Asymptotic Relations for In(x) and Kn(x) 480 References 483 Appendix E Kelvin Functions 485 E.1 Introduction 485 E.2 Kelvin Functions 486 E.3 Differential Equation for Kelvin Functions 490 E.4 Recurrence Relationships for the Kelvin Functions 491 E.5 Asymptotic Relations for the Kelvin Functions 492 E.6 Zeros of the Kelvin Functions 493 Appendix F Matrices and Determinants 494 F.1 Determinants 494 F.2 Matrices 499 References 504 Index 505