# Stress in ASME Pressure Vessels, Boilers, and Nuclear Components

Wiley-ASME Press Series

1. Edition December 2017

352 Pages, Hardcover*Wiley & Sons Ltd*

**978-1-119-25928-2**

An illustrative guide to the analysis needed to achieve a safe design in ASME Pressure Vessels, Boilers, and Nuclear Components

Stress in ASME Pressure Vessels, Boilers, and Nuclear Components offers a revised and updatededition of the text, Design of Plate and Shell Structures. This important resource offers engineers and students a text that covers the complexities involved in stress loads and design of plates and shell components in compliance with pressure vessel, boiler, and nuclear standards. The author covers the basic theories and includes a wealth of illustrative examples for the design of components that address the internal and external loads as well as other loads such as wind and dead loads.

The text keeps the various derivations relatively simple and the resulting equations are revised to a level so that they can be applied directly to real-world design problems. The many examples clearly show the level of analysis needed to achieve a safe design based on a given required degree of accuracy. Written to be both authoritative and accessible, this important updated book:

* Offers an increased focus on mechanical engineering and contains more specific and practical code-related guidelines

* Includes problems and solutions for course and professional training use

* Examines the basic aspects of relevant theories and gives examples for the design of components

* Contains various derivations that are kept relatively simple so that they can be applied directly to design problems

Written for professional mechanical engineers and students, this text offers a resource to the theories and applications that are needed to achieve an understanding of stress loads and design of plates and shell components in compliance with pressure vessel, boiler, and nuclear standards.

Acknowledgment xi

1 Membrane Theory of Shells of Revolution 1

1.1 Introduction 1

1.2 Basic Equations of Equilibrium 1

1.3 Spherical and Ellipsoidal Shells Subjected to Axisymmetric Loads 6

1.4 Conical Shells 18

1.5 Cylindrical Shells 20

1.6 Cylindrical Shells with Elliptical Cross Section 22

1.7 Design of Shells of Revolution 23

Problems 23

2 Various Applications of the Membrane Theory 27

2.1 Analysis of Multicomponent Structures 27

2.2 Pressure-Area Method of Analysis 35

2.3 Deflection Due to Axisymmetric Loads 42

Problems 47

3 Analysis of Cylindrical Shells 51

3.1 Elastic Analysis of Thick-Wall Cylinders 51

3.2 Thick Cylinders with Off-center Bore 56

3.3 Stress Categories and Equivalent Stress Limits for Design and

Operating Conditions 57

3.4 Plastic Analysis of Thick Wall Cylinders 63

3.5 Creep Analysis of Thick-Wall Cylinders 65

3.6 Shell Equations in the ASME Code 69

3.7 Bending of Thin-Wall Cylinders Due to Axisymmetric Loads 71

3.8 Thermal Stress 89

3.9 Discontinuity Stresses 98

Problems 100

4 Buckling of Cylindrical Shells 103

4.1 Introduction 103

4.2 Basic Equations 103

4.3 Lateral Pressure 108

4.4 Lateral and End Pressure 114

4.5 Axial Compression 117

4.6 Design Equations 120

Problems 136

5 Stress in Shells of Revolution Due to Axisymmetric Loads 141

5.1 Elastic Stress in Thick-Wall Spherical Sections Due to Pressure 141

5.2 Spherical Shells in the ASME Code 142

5.3 Stress in Ellipsoidal Shells Due to Pressure Using Elastic Analysis 145

5.4 Ellipsoidal (Dished) Heads in the ASME Code 146

5.5 Stress in Thick-Wall Spherical Sections Due to Pressure Using Plastic Analysis 150

5.6 Stress in Thick-Wall Spherical Sections Due to Pressure Using Creep Analysis 150

5.7 Bending of Shells of Revolution Due to Axisymmetric Loads 151

5.8 Spherical Shells 156

5.9 Conical Shells 165

Problems 174

6 Buckling of Shells of Revolution 175

6.1 Elastic Buckling of Spherical Shells 175

6.2 ASME Procedure for External Pressure 179

6.3 Buckling of Stiffened Spherical Shells 180

6.4 Ellipsoidal Shells 181

6.5 Buckling of Conical Shells 181

6.6 Various Shapes 184

Problems 184

7 Bending of Rectangular Plates 187

7.1 Introduction 187

7.2 Strain-Deflection Equations 189

7.3 Stress-Deflection Expressions 194

7.4 Force-Stress Expressions 196

7.5 Governing Differential Equations 197

7.6 Boundary Conditions 200

7.7 Double Series Solution of Simply Supported Plates 204

7.8 Single Series Solution of Simply Supported Plates 206

7.9 Rectangular Plates with Fixed Edges 211

7.10 Plate Equations in the ASME Code 212

Problems 213

8 Bending of Circular Plates 215

8.1 Plates Subjected to Uniform Loads in the theta-Direction 215

8.2 Circular Plates in the ASME Code 225

8.3 Plates on an Elastic Foundation 227

8.4 Plates with Variable Boundary Conditions 231

8.5 Design of Circular Plates 234

Problems 235

9 Approximate Analysis of Plates 239

9.1 Introduction 239

9.2 Yield Line Theory 239

9.3 Further Application of the Yield Line Theory 247

9.4 Design Concepts 253

Problems 255

10 Buckling of Plates 259

10.1 Circular Plates 259

10.2 Rectangular Plates 263

10.3 Rectangular Plates with Various Boundary Conditions 271

10.4 Finite Difference Equations for Buckling 275

10.5 Other Aspects of Buckling 277

10.6 Application of Buckling Expressions to Design Problems 279

Problems 282

11 Finite Element Analysis 283

11.1 Definitions 283

11.2 One-Dimensional Elements 287

11.3 Linear Triangular Elements 295

11.4 Axisymmetric Triangular Linear Elements 302

11.5 Higher-Order Elements 305

11.6 Nonlinear Analysis 307

Appendix A: Fourier Series 309

A.1 General Equations 309

A.2 Interval Change 313

A.3 Half-Range Expansions 314

A.4 Double Fourier Series 316

Appendix B: Bessel Functions 319

B.1 General Equations 319

B.2 Some Bessel Identities 323

B.3 Simplified Bessel Functions 325

Appendix C: Conversion Factors 327

References 329

Answers to Selected Problems 333

Index 335