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 xiii1 Introduction 11.1 Definition of Thermal Stress 11.2 Thermal–Mechanical Design 31.3 Factor of Safety in Design 41.4 Thermal Expansion Coefficient 71.5 Young’s Modulus 111.6 Poisson’s Ratio 131.7 Other Elastic Moduli 141.8 Thermal Diffusivity 161.9 Thermal Shock Parameters 171.10 Historical Note 19Problems 23References 252 Thermal Stresses in Bars 262.1 Stress and Strain 262.2 Bar between Two Supports 272.3 Bars in Parallel 322.4 Bars with Partial Removal of Constraints 352.5 Nonuniform Temperature Distribution 432.6 Historical Note 52Problems 53References 583 Thermal Bending 593.1 Limits on the Analysis 593.2 Stress Relationships 603.3 Displacement Relations 643.4 General Thermal Bending Relations 653.5 Shear Stresses 673.6 Beam Bending Examples 693.7 Thermal Bowing of Pipes 973.8 Historical Note 108Problems 110References 1174 Thermal Stresses in Trusses and Frames 1184.1 Elastic Energy Method 1184.2 Unit-Load Method 1234.3 Trusses with External Constraints 1294.4 Trusses with Internal Constraints 1324.5 The Finite Element Method 1424.6 Elastic Energy in Bending 1534.7 Pipe Thermal Expansion Loops 1584.8 Pipe Bends 1724.9 Elastic Energy in Torsion 1784.10 Historical Note 185Problems 186References 1955 Basic Equations of Thermoelasticity 1975.1 Introduction 1975.2 Strain Relationships 1985.3 Stress Relationships 2035.4 Stress–Strain Relations 2065.5 Temperature Field Equation 2085.6 Reduction of the Governing Equations 2125.7 Historical Note 215Problems 217References 2206 Plane Stress 2216.1 Introduction 2216.2 Stress Resultants 2226.3 Circular Plate with a Hot Spot 2246.4 Two-Dimensional Problems 2396.5 Plate with a Circular Hole 2476.6 Historical Note 256Problems 257References 2627 Bending Thermal Stresses in Plates 2647.1 Introduction 2647.2 Governing Relations for Bending of Rectangular Plates 2657.3 Boundary Conditions for Plate Bending 2737.4 Bending of Simply-Supported Rectangular Plates 2777.5 Rectangular Plates with Two-Dimensional Temperature Distributions 2837.6 Axisymmetric Bending of Circular Plates 2877.7 Axisymmetric Thermal Bending Examples 2927.8 Circular Plates with a Two-Dimensional Temperature Distribution 3057.9 Historical Note 310Problems 312References 3158 Thermal Stresses in Shells 3178.1 Introduction 3178.2 Cylindrical Shells with Axisymmetric Loading 3198.3 Cooldown of Ring-Stiffened Cylindrical Vessels 3298.4 Cylindrical Vessels with Axial Temperature Variation 3368.5 Short Cylinders 3448.6 Axisymmetric Loading of Spherical Shells 3508.7 Approximate Analysis of Spherical Shells under Axisymmetric Loading 3578.8 Historical Note 371Problems 373References 3779 Thick-Walled Cylinders and Spheres 3789.1 Introduction 3789.2 Governing Equations for Plane Strain 3799.3 Hollow Cylinder with Steady-State Heat Transfer 3849.4 Solid Cylinder 3889.5 Thick-Walled Spherical Vessels 3979.6 Solid Spheres 4029.7 Historical Note 411Problems 412References 41510 Thermoelastic Stability 41610.1 Introduction 41610.2 Thermal Buckling of Columns 41610.3 General Formulation for Beam Columns 42010.4 Postbuckling Behavior of Columns 42310.5 Lateral Thermal Buckling of Beams 42610.6 Symmetrical Buckling of Circular Plates 43210.7 Thermal Buckling of Rectangular Plates 43710.8 Thermal Buckling of Cylindrical Shells 45010.9 Historical Note 454Problems 455References 460Appendix A Preferred Prefixes in the SI System of Units 461Appendix B Properties of Materials at 300 K 462Appendix C Properties of Selected Materials as a Function of Temperature 464C.1 Properties of 2024-T3 Aluminum 464C.2 Properties of C1020 Carbon Steel 465C.3 Properties of 9% Nickel Steel 465C.4 Properties of 304 Stainless Steel 466C.5 Properties of Beryllium Copper 466C.6 Properties of Titanium Alloy 467C.7 Properties of Teflon 467References 468Appendix D Bessel Functions 469D.1 Introduction 469D.2 Bessel Functions of the First Kind 470D.3 Bessel Functions of Noninteger Order 470D.4 Bessel Functions of the Second Kind 472D.5 Bessel’s Equation 474D.6 Recurrence Relationships for Jn(x) and Yn(x) 475D.7 Asymptotic Relations and Zeros for Jn(x) and Yn(x) 476D.8 Modified Bessel Functions 477D.9 Modified Bessel Equation 478D.10 Recurrence Relations for the Modified Bessel Functions 479D.11 Asymptotic Relations for In(x) and Kn(x) 480References 483Appendix E Kelvin Functions 485E.1 Introduction 485E.2 Kelvin Functions 486E.3 Differential Equation for Kelvin Functions 490E.4 Recurrence Relationships for the Kelvin Functions 491E.5 Asymptotic Relations for the Kelvin Functions 492E.6 Zeros of the Kelvin Functions 493Appendix F Matrices and Determinants 494F.1 Determinants 494F.2 Matrices 499References 504Index 505