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Cover
Title Page
Series Preface
Acknowledgment
1 Membrane Theory of Shells of Revolution
1. 1.1 Introduction
2. 1.2 Basic Equations of Equilibrium
3. 1.3 Spherical and Ellipsoidal Shells Subjected to Axisymmetric Loads
4. 1.4 Conical Shells
5. 1.5 Cylindrical Shells
6. 1.6 Cylindrical Shells with Elliptical Cross Section
7. 1.7 Design of Shells of Revolution
8. Problems
2 Various Applications of the Membrane Theory
1. 2.1 Analysis of Multicomponent Structures
2. 2.2 Pressure–Area Method of Analysis
3. 2.3 Deflection Due to Axisymmetric Loads
4. Problems
3 Analysis of Cylindrical Shells
1. 3.1 Elastic Analysis of Thick‐Wall Cylinders
2. 3.2 Thick Cylinders with Off‐center Bore
3. 3.3 Stress Categories and Equivalent Stress Limits for Design and Operating Conditions
4. 3.4 Plastic Analysis of Thick Wall Cylinders
5. 3.5 Creep Analysis of Thick‐Wall Cylinders
6. 3.6 Shell Equations in the ASME Code
7. 3.7 Bending of Thin‐Wall Cylinders Due to Axisymmetric Loads
8. 3.8 Thermal Stress
9. 3.9 Discontinuity Stresses
10. Problems
4 Buckling of Cylindrical Shells
1. 4.1 Introduction
2. 4.2 Basic Equations
3. 4.3 Lateral Pressure
4. 4.4 Lateral and End Pressure
5. 4.5 Axial Compression
6. 4.6 Design Equations
7. Problems
5 Stress in Shells of Revolution Due to Axisymmetric Loads
1. 5.1 Elastic Stress in Thick‐Wall Spherical Sections Due to Pressure
2. 5.2 Spherical Shells in the ASME Code
3. 5.3 Stress in Ellipsoidal Shells Due to Pressure Using Elastic Analysis
4. 5.4 Ellipsoidal (Dished) Heads in the ASME Code
5. 5.5 Stress in Thick‐Wall Spherical Sections Due to Pressure Using Plastic Analysis
6. 5.6 Stress in Thick‐Wall Spherical Sections Due to Pressure Using Creep Analysis
7. 5.7 Bending of Shells of Revolution Due to Axisymmetric Loads
8. 5.8 Spherical Shells
9. 5.9 Conical Shells
10. Problems
6 Buckling of Shells of Revolution
1. 6.1 Elastic Buckling of Spherical Shells
2. 6.2 ASME Procedure for External Pressure
3. 6.3 Buckling of Stiffened Spherical Shells
4. 6.4 Ellipsoidal Shells
5. 6.5 Buckling of Conical Shells
6. 6.6 Various Shapes
7. Problems
7 Bending of Rectangular Plates
1. 7.1 Introduction
2. 7.2 Strain–Deflection Equations
3. 7.3 Stress–Deflection Expressions
4. 7.4 Force–Stress Expressions
5. 7.5 Governing Differential Equations
6. 7.6 Boundary Conditions
7. 7.7 Double Series Solution of Simply Supported Plates
8. 7.8 Single Series Solution of Simply Supported Plates
9. 7.9 Rectangular Plates with Fixed Edges
10. 7.10 Plate Equations in the ASME Code
11. Problems
8 Bending of Circular Plates
1. 8.1 Plates Subjected to Uniform Loads in the θ‐Direction
2. 8.2 Circular Plates in the ASME Code
3. 8.3 Plates on an Elastic Foundation
4. 8.4 Plates with Variable Boundary Conditions
5. 8.5 Design of Circular Plates
6. Problems
9 Approximate Analysis of Plates
1. 9.1 Introduction
2. 9.2 Yield Line Theory
3. 9.3 Further Application of the Yield Line Theory
4. 9.4 Design Concepts
5. Problems
10 Buckling of Plates
1. 10.1 Circular Plates
2. 10.2 Rectangular Plates
3. 10.3 Rectangular Plates with Various Boundary Conditions
4. 10.4 Finite Difference Equations for Buckling
5. 10.5 Other Aspects of Buckling
6. 10.6 Application of Buckling Expressions to Design Problems
7. Problems
11 Finite Element Analysis
1. 11.1 Definitions
2. 11.2 One‐Dimensional Elements
3. 11.3 Linear Triangular Elements
4. 11.4 Axisymmetric Triangular Linear Elements
5. 11.5 Higher‐Order Elements
6. 11.6 Nonlinear Analysis
Appendix A: Fourier Series
1. A.1 General Equations
2. A.2 Interval Change
3. A.3 Half‐Range Expansions
4. A.4 Double Fourier Series
Appendix B: Bessel Functions
1. B.1 General Equations
2. B.2 Some Bessel Identities
3. B.3 Simplified Bessel Functions
Appendix C: Conversion Factors
References
Answers to Selected Problems
Index
End User License Agreement

List of Tables

Chapter 03
1. Table 3.1 Values of functions A_βx, B_βx, C_βx, and D_βx
2. Table 3.2 Coefficients of thermal expansion (multiplied by 10⁶), inch/inch/°F
3. Table 3.3 Mean temperature
4. Table 3.4 Various discontinuity functions
Chapter 05
1. Table 5.1 Horizontal edge load on a spherical shell
2. Table 5.2 Edge loads in open spherical shells
3. Table 5.3 Edge loads in conical shells (Jawad and Farr 1989)
4. Table 5.4 Edge loads in open conical shells
Chapter 07
1. Table 7.1 Moduli of elasticity and Poisson’s ratio
2. Table 7.2 Maximum stress and deflection coefficients in a simply supported plate (μ = 0.3)
3. Table 7.3 Maximum stress and deflection coefficients in a fixed plate (μ = 0.3)
Chapter 08
1. Table 8.1 Circular plates of uniform thickness
Chapter 09
1. Table 9.1 Plastic bending moments in various plates
Chapter 10
1. Table 10.1 Critical buckling coefficient, k, of an annular plate with a free inside edge
Chapter 11
1. Table 11.1 Total stiffness and force matrices
2. Table 11.2 Total stiffness matrix (multiplied by 10⁴)
Appendix B
1. Table B.1 Values of J_o, J₁, Y_o, and Y₁

List of Illustrations

Chapter 01
1. Figure 1.1 Pressure vessels.
2. Figure 1.2 Surface of revolution
3. Figure 1.3 Shell geometry
4. Figure 1.4 Membrane forces and applied loads
5. Figure 1.5 Components of N_θ: (a) circumferential cross section and (b) longitudinal cross section
6. Figure 1.6 Components of N_θϕ: (a) side view and (b) three‐dimensional view
7. Figure 1.7 Components of N_ϕ
8. Figure 1.8 Membrane forces in a head due to deadweight: (a) dead load and (b) force patterns
9. Figure 1.9 Edge loads in a spherical head: (a) edge load and (b) forces due to edge load
10. Figure 1.10 Spherical tank: (a) spherical tank, (b) support at 110°, (c) support at 130°, and (d) forces at support junction
11. Figure 1.11 Ellipsoidal head under internal pressure
12. Figure 1.12 2 : 1 elliptical head: (a) exact configuration and (b) approximate configuration
13. Figure 1.13 Elliptical head with a/b = 2.96 ratio
14. Figure 1.14 Conical shell
15. Figure 1.15 Conical bottom head
16. Figure 1.16 Cylindrical shell: (a) circumferential force and (b) longitudinal force
17. Figure 1.17 Elliptical shell
18. Problem 1.2 Snow load on a spherical roof
19. Problem 1.3 Underwater spherical shell
20. Problem 1.4 Roof of a silo
21. Problem 1.8 Holding tank
22. Problem 1.9 Nozzle load in a conical shell: (a) axial force, (b) components of axial force, and (c) dimension origin
Chapter 02
1. Figure 2.1 Elevated water tank.
2. Figure 2.2 Storage tank
3. Figure 2.3 Free‐body diagram of storage tank: (a) roof‐to‐shell junction and (b) cone‐to‐shell junction
4. Figure 2.4 Roof‐to‐large cylinder and large cylinder‐to‐cone junctions: (a) roof‐to‐shell stiffener and (b) cone‐to‐shell stiffener
5. Figure 2.5 Cone–cylinder junction: (a) forces at small end of cone and (b) forces in small cylinder
6. Figure 2.6 Cone‐to‐small cylinder junction
7. Figure 2.7 Kettle boiler
8. Figure 2.8 Double‐cone vessel (Nooter Corp, Saint Louis, MO)
9. Figure 2.9 Various components
10. Figure 2.10 Pressure–area interaction: (a) cylindrical shell and (b) spherical shell
11. Figure 2.11 Nozzle junctions: (a) nozzle‐to‐shell junction and (b) nozzle‐to‐head junction
12. Figure 2.12 Nozzle reinforcement
13. Figure 2.13 Various shell junctions: (a) head‐to‐shell junction, (b) flue‐to‐shell junction, and (c) knuckle‐to‐shell junction
14. Figure 2.14 Cylindrical‐to‐spherical transition area
15. Figure 2.15 Spherical vessel
16. Figure 2.16 Flue transition between conical and cylindrical sections
17. Figure 2.17 Fitting reinforcement.
18. Figure 2.18 Conduit reinforcement.
19. Figure 2.19 Deflection of shell
20. Figure 2.20 Radius increment due to deflection
21. Figure 2.21 Flat bottom tank
22. Problem 2.1 Steel tower
23. Problem 2.2 Elevated water tower
24. Problem 2.3 Bellows expansion joint
25. Problem 2.4 Nozzle in a shell
26. Problem 2.5 Portion of a pressure vessel
27. Problem 2.6 Cross section of a pipe elbow
Chapter 03
1. Figure 3.1 Thick wall vessel during fabrication.
2. Figure 3.2 Thick‐walled cylinder: (a) cross section and (b) infinitesimal section
3. Figure 3.3 Circumferential stress distribution
4. Figure 3.4 Cylinder with eccentric bore
5. Figure 3.5 Stress categories and limits.
6. Figure 3.6 Decomposition of stresses in a cylindrical shell
7. Figure 3.7 Circumferential stress distribution using elastic Eq. (3.20).
8. Figure 3.8 Elastic–plastic regions in a cylinder due to internal pressure.
9. Figure 3.9 Circumferential stress distribution using elastic Eq. (3.20) and Plastic Eq. (3.40)
10. Figure 3.10 Isochronous stress–strain curves (ASME)
11. Figure 3.11 Circumferential stress distribution using elastic Eq. (3.20), plastic Eq. (3.40), and creep Eq. (3.53)
12. Figure 3.12 Infinitesimal section of a cylinder shell
13. Figure 3.13 Circumferential deflection
14. Figure 3.14 Shear and moment applied at the edge of cylinder
15. Figure 3.15 Long cylinder with edge moment M_o: (a) edge moment and (b) moment distribution along the length
16. Figure 3.16 Long cylinder with a concentrated radial load Q_o: (a) radial load on a cylinder and (b) free‐body diagram
17. Figure 3.17 Long cylinder with fixed edges: (a) cylindrical shell fixed at ends and (b) discontinuity forces
18. Figure 3.18 Pressure vessel with stiffening ring: (a) cylindrical shell, (b) discontinuity forces, and (c) free‐body diagram
19. Figure 3.19 Temperature distribution along a cylinder: (a) cylindrical shell with axial temperature distribution and (b) discontinuity forces
20. Figure 3.20 Circumferential and radial stress in a cylinder: (a) thick cylinder and (b) infinitesimal section
21. Figure 3.21 Thermal stress distribution in a wall of a cylinder
22. Figure 3.22 Temperature distribution in a thin‐wall vessel
23. Figure 3.23 Temperature distribution in a thick‐wall vessel
24. Figure 3.24 Stress–strain diagram
25. Problem 3.4 Cylindrical shell partially filled with fluid
26. Problem 3.5 Multiple radial loads on a cylinder
27. Problem 3.6 Distributed radial load on a cylinder
28. Problem 3.7 Storage tank
Chapter 04
1. Figure 4.1 Compressive forces in cylindrical shells: (a) inside cylinder under lateral external pressure; (b) cylinder under external lateral and end pressure; and (c) cylinder under axial compressive force
2. Figure 4.2 Infinitesimal element of a cylindrical shell: (a) forces and (b) deflection
3. Figure 4.3 Deflected section
4. Figure 4.4 Coordinate system in a cylindrical shell
5. Figure 4.5 Buckling modes of a cylindrical shell: (a) n = 2, (b) n = 4, (c) n = 3, (d) edges simply supported symmetrical about , and (e) edges fixed symmetrical about
6. Figure 4.6 Buckling coefficient K for cylinders with pressure on sides only, edges simply supported; μ = 0.30.
7. Figure 4.7 Jacketed cylindrical shell
8. Figure 4.8 Buckling coefficient K for cylinders with pressure on sides only, edges fixed; μ = 0.30.
9. Figure 4.9 Buckling coefficient K′ for cylinders with pressure on sides and ends, edges simply supported; μ = 0.30.
10. Figure 4.10 Buckling coefficient K′ for cylinders with pressure on sides and ends, edges fixed; μ = 0.30.
11. Figure 4.11 Gasoline tank
12. Figure 4.12 Comparison of Eq. (4.56) with test data.
13. Figure 4.13 Support cylinder
14. Figure 4.14 Geometric chart.
15. Figure 4.15 External pressure chart for carbon and low alloy steels.
16. Figure 4.16 Cylindrical shells with various end attachments
17. Figure 4.17 Storage vessel
18. Figure 4.18 Reactor vessel: (a) vertical vessel and (b) wind load
19. Figure 4.19 Allowable compressive stress in flat bottom tanks.
20. Figure 4.20 Low‐carbon steel stack
21. Figure 4.21 Flat bottom tank
22. Problem 4.1 Partially jacketed shell
23. Problem 4.2 Jacketed pressure vessel
24. Problem 4.5 Support cylinder for a spherical fuel vessel
25. Problem 4.6 Stand pipe
26. Problem 4.7 Process reactor
27. Problem 4.11 Steel stack
Chapter 05
1. Figure 5.1 Design chart for ellipsoidal heads.
2. Figure 5.2 Bending and shear forces on an infinitesimal element
3. Figure 5.3 Components of M_θ: (a) three‐dimensional view and (b) side view
4. Figure 5.4 Deflection of a shell segment
5. Figure 5.5 Rotation of a shell segment: (a) rotation of element and (b) deflection of element
6. Figure 5.6 Rotation of a shell element in the θ‐direction
7. Figure 5.7 Designation of angles in a spherical shell
8. Figure 5.8 Displacement of spherical shell
9. Figure 5.9 Horizontal edge load
10. Figure 5.10 Hemispherical‐to‐cylindrical shell junction: (a) head‐to‐shell junction and (b) discontinuity forces
11. Figure 5.11 Conical shell
12. Figure 5.12 Cone with fixed edge: (a) conical shell, (b) deflection of cone, and (c) discontinuity forces
13. Problem 5.5 Cylindrical to conical shell junction
Chapter 06
1. Figure 6.1 Buckled shape of a spherical segment
2. Figure 6.2 A plot of Eq. (6.12)
3. Figure 6.3 Stiffened spherical shell: (a) plan view and (b) cross section
4. Figure 6.4 Conical section
5. Figure 6.5 Plot of Eq. (6.25).
6. Figure 6.6 Steel conical section
Chapter 07
1. Figure 7.1 Boiler casing.
2. Figure 7.2 Duct structure.
3. Figure 7.3 Bending of a rectangular plate
4. Figure 7.4 Shear deformation of a rectangular plate: (a) shear of an infinitesimal element and (b) deflection of element
5. Figure 7.5 Stress components
6. Figure 7.6 Moments in a plate: (a) plate segment and (b) forces on plate segment
7. Figure 7.7 Lateral loads on a rectangular plate
8. Figure 7.8 Forces and moments in a rectangular plate
9. Figure 7.9 Plate with various boundary conditions
10. Figure 7.10 Edge shear
11. Figure 7.11 Plate with edge beam support
12. Figure 7.12 Edge shear moments
13. Figure 7.13 Uniformly loaded plate
14. Figure 7.14 Uniformly loaded simply supported plate
15. Figure 7.15 Coefficient K for beams and for the equation S = d²KP/t² for uniformly loaded rectangular plates with D/d = 2.0
Chapter 08
1. Figure 8.1 Lateral bending of a circular plate
2. Figure 8.2 Forces and moments in a circular plate symmetrically loaded in the θ‐direction: (a) infinitesimal element and (b) components of M_t
3. Figure 8.3 Uniformly loaded plate
4. Figure 8.4 Plot of M_r and M_t of a uniformly loaded plate
5. Figure 8.5 Plate loaded at its inner edge
6. Figure 8.6 Plate loaded at distance b from the centerline: (a) plate with a line load and (b) free‐body diagram
7. Figure 8.7 Heat exchanger
8. Figure 8.8 Plate on elastic foundation
9. Figure 8.9 Plate on elastic foundation with edge load
10. Figure 8.10 Uplift force in a flat bottom tank: (a) flat bottom tank with internal pressure and (b) uplift of the base plate
11. Figure 8.11 Uplift force Q
12. Figure 8.12 An API flat bottom tank
13. Problem 8.1 Double wall storage tank
14. Problem 8.2 Baffles in a cylindrical vessel
15. Problem 8.3 Aluminum pan
16. Problem 8.5 Plate with a rigid central attachment
17. Problem 8.6 Plate with a central hole
18. Problem 8.7 Plate with inner and outer moments
19. Problem 8.10 Forces on a flat bottom tank
20. Problem 8.11 Cylinder shell with partition plate
21. Problem 8.12 Conical shell attached to a circular plate
Chapter 09
1. Figure 9.1 Elastic and plastic stress distribution: (a) Elastic‐perfectly‐plastic stress‐strain diagram; (b) elastic stress distribution; and (c) plastic stress distribution
2. Figure 9.2 Beam with fixed ends: (a) fixed‐ends beam, (b) moment distribution, and (c) plastic deflection
3. Figure 9.3 Yield lines for various plates
4. Figure 9.4 Yield lines in a simply supported plate: (a) plastic yield lines and (b) plastic deflection
5. Figure 9.5 Vector representation of plastic moments: (a) plastic yield lines, (b) bending moments on a plate segment, (c) vector representation of the bending moments, (d) components of bending moments, and (e) deflected shape
6. Figure 9.6 Square plate fixed along the edges: (a) plastic yield lines and (b) deflected shape
7. Figure 9.7 Simply supported rectangular plate: (a) rectangular plate, (b) plastic yield lines, and (c) designate of plate segments
8. Figure 9.8 Plate with a free edge: (a) triangular plate and (b) plastic yield lines
9. Figure 9.9 Square plate with one side free: (a) square plate, (b) first assumed pattern of plastic yield lines, and (c) second assumed pattern of plastic yield lines
10. Figure 9.10 Yield lines in a circular plate
11. Figure 9.11 Yield lines in a square plate: (a) first assumed pattern of plastic yield lines in a simply supported plate; (b) second assumed pattern of plastic yield lines in a simply supported plate; (c) first assumed pattern of plastic yield lines in a fixed plate, and (d) second assumed pattern of plastic yield lines in a fixed plate
12. Figure 9.12 Fanlike yield lines in long narrow plates
13. Problem 9.1 Hexagonal plate
14. Problem 9.2 Trapezoidal plate
15. Problem 9.3 Triangular plate
16. Problem 9.4 Rectangular plate with various boundary conditions
17. Problem 9.6 Circular plate fixed at edge
18. Problem 9.7 Triangular plate
19. Problem 9.8 Plate supported by a column at one corner
Chapter 10
1. Figure 10.1 In‐plane load in a circular plate
2. Figure 10.2 In‐plane loads in a rectangular plate: (a) infinitesimal element and (b) membrane force N_x
3. Figure 10.3 In‐plane shear loads
4. Figure 10.4 Deflection of a unit segment
5. Figure 10.5 Rectangular plate subjected to force N_x
6. Figure 10.6 Plot of Eq. (4) in Example 10.2
7. Figure 10.7 Stress versus deflection of a rectangular plate
8. Figure 10.8 Stress distribution across plate: (a) rectangular plate, (b) elastic stress distribution, and (c) plastic stress distribution
9. Figure 10.9 Rectangular plate with two sides simply supported
10. Figure 10.10 Finite difference layout of a square plate: (a) simply supported plate, (b) deflection of middle surface, and (c) finite difference layout
11. Figure 10.11 Continuous plate
12. Figure 10.12 Plot of Eq. (10.42)
13. Figure 10.13 Elastic–plastic buckling
14. Figure 10.14 Various structural members: (a) structural angle, (b) double structural angles, (c) structural T, (d) box section, and (e) perforated plate
Chapter 11
1. Figure 11.1 Nozzle‐to‐head attachment
2. Figure 11.2 One‐, two‐, and three‐dimensional elements: (a) rod element, (b) triangular element, and (c) solid element
3. Figure 11.3 Conical shell
4. Figure 11.4 Element orientation
5. Figure 11.5 Stiffened triangular plate: (a) triangular plate with edge stiffeners and (b) nodal point designations
6. Figure 11.6 Triangular element
7. Figure 11.7 Various elements
8. Figure 11.8 Triangular element
9. Figure 11.9 Stress distribution in the x‐ and y‐directions for the element shown in Figure 11.8. (a) Stress in the x‐direction and (b) stress in the y‐direction. .
Appendix A
1. Figure A.1 Periodic functions
2. Figure A.2 Periodic rectangular function
3. Figure A.3 Periodic cosine function
4. Figure A.4 Periodic symmetric function. (a) Odd step function, (b) odd continuous function, and (c) even step function
5. Figure A.5 Function y = x − x²
6. Figure A.6 Rectangular plate
Appendix B
1. Figure B.1 A plot of various Bessel functions: (a) J_o and J₁ functions and (b) Y_o and Y₁ functions
2. Figure B.2 A plot of modified Bessel functions (Wylie 1972)
3. Figure B.3 Plot of the Z functions (Hetenyi 1964)

This edition first published 2018
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Library of Congress Cataloging‐in‐Publication Data

Names: Jawad, Maan H., author.
Title: Stress in ASME pressure vessels, boilers and nuclear components / by Maan H. Jawad.
Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2018. | Series: Wiley-ASME Press series | Includes bibliographical references and index. |
Identifiers: LCCN 2017018768 (print) | LCCN 2017036797 (ebook) | ISBN 9781119259268 (pdf) | ISBN 9781119259275 (epub) | ISBN 9781119259282 (cloth)
Subjects: LCSH: Shells (Engineering) | Plates (Engineering) | Strains and stresses.
Classification: LCC TA660.S5 (ebook) | LCC TA660.S5 J39 2017 (print) | DDC 624.1/776–dc23
LC record available at https://lccn.loc.gov/2017018768

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Wiley‐ASME Press Series List

STRESS IN ASME PRESSURE VESSELS, BOILERS, AND NUCLEAR COMPONENTS

Series Preface

Acknowledgment