# Thin Shells

## 1st Edition

### Computing and Theory

**Author:**J. E. Gibson

**Editor:**B. G. Neal

**eBook ISBN:**9781483188669

**Imprint:**Pergamon

**Published Date:**1st January 1980

**Page Count:**300

## Description

Thin Shells: Computing and Theory introduces the basic concepts of elastic analysis of shells and the computer programming methods of such analyses. The book utilizes FORTRAN in presenting the programs for stress analysis in shells. The text first covers membrane and bending theories for cylindrical and spherical shells and the membrane theory for shells of arbitrary shape. Next, the book tackles the analysis of more complicated shell structures such as multi-shells. The next chapter deals with a finite element method. The 10th chapter details the correlation between theoretical stresses and actual experimental stresses, and the last chapter covers corrugated shells. The text will be of great use to students and practitioners of civil engineering.

## Table of Contents

Preface

1. General Introduction to Shell Theory

1.1 Introduction

1.2 Reference Axes for Shell Surfaces

1.3 Membrane Stress Resultants

1.4 Bending Stress Resultants

1.5 Membrane Theory for Circular Cylindrical Shell

1.6 Cylindrical Container Supported at Ends

1.7 Cylindrical Tank Filled with Liquid

1.8 Cantilever Cylindrical Shell Subjected to Gravitational Load

2. Programming in Fortran

2.1 Introduction

2.2 Operation of a Computer

2.3 Operation of Fortran

2.4 Program Code

2.5 Constants and Variables

2.6 Arrays

2.7 Arithmetic Operations

2.8 Arithmetic Statement

2.9 Standard Functions

2.10 Control Statements

2.11 "Go To" Statement

2.12 "If" Statement

2.13 "Do" Statement

2.14 Input/Output Operations

2.15 "Read" Statement

2.16 "Write" Statement

2.17 F Format

2.18 I Format

2.19 H Format

2.20 Program Structure for Stresses in Tank

2.21 Operation of Program

2.22 Modifications to Program

2.23 Modification of Input Data for Imperial and S.I. Units

3. Bending Theory of Closed Circular Cylindrical Shells under Axisymmetric Loads

3.1 Introduction

3.2 Equations of Equilibrium

3.3 Membrane Strains

3.4 Bending Strains

3.5 Combined Strain of "Z Surface"

3.6 Strain-Stress Resultant Equations

3.7 Strain-Displacement Equations

3.8 Curvature-Displacement Equations

3.9 Stress-Resultant Displacement Equations

3.10 Reduction to Compatibility Equation

3.11 Solution of Compatibility Equation

3.12 Cylindrical Tank Filled with Liquid

3.13 Cylindrical Pressure Vessel with Thick End Plates

3.14 Tank Filled with Liquid (Numerical Example)

3.15 Pressure Vessel (Numerical Example)

3.16 Program for the Analysis of Pressure Vessel

3.17 Listing of Program for Pressure Vessel

3.18 Output for Pressure Vessel

3.19 Program for Analysis of Stresses in Tank

3.20 Listing for Program for Stresses in Tank

3.21 Output for Stresses in Tank

4. Bending Theory of Open Circular Cylindrical Shells

4.1 Introduction

4.2 Equations of Equilibrium

4.3 Strain Displacement of Equations of the Middle Surface

4.4 Curvature Displacement Equations of Middle Surface

4.5 Strain-Stress Resultant Equations

4.6 Equation of Compatibility

4.7 Solution of Equation for Simply Supported Open Cylindrical Shell

4.8 Solution for Symmetrical Loading (Complementary Function)

4.9 Complementary Functions in Tabular Form

4.10 Particular Integral for Uniform Load

4.11 Boundary Conditions at a Free Edge

4.12 Numerical Example

4.13 Program for Open Cylindrical Shell (Schorer)

4.14 Output for Schorer Program

5. Membrane Theory for Shells Of Revolution

5.1 Introduction

5.2 Equations of Equilibrium

5.3 Membrane Theory for Shells of Revolution under Axisymmetric Load

5.4 Simply Supported Spherical Dome under Axisymmetric Load

5.5 Spherical Storage Tank

5.6 Conical Shell

5.7 Numerical Example

5.8 Program for Stresses in Astrodome

5.9 Listing of Program

5.10 Output

6. Bending Theory of Shells of Revolution under Axisymmetric

6.1 Introduction

6.2 Equations of Equilibrium

6.3 Strain Displacement Equations of Middle Surface

6.4 Curvature Displacement Equations of the Middle Surface

6.5 Stress Resultant-Displacement Equations

6.6 Spherical Shells under Axisymmetric Load

6.7 Simplified Theory of Spherical Shells under Axisymmetric Load

6.8 Spherical Dome with Rigidly Fixed Edge

6.9 Spherical Dome with Simply Supported Edge

6.10 Comparison of Exact and Approximate Theories

6.11 Numerical Example

6.12 Program for Stresses in Spherical Shell with Fixed Edges

6.13 Listing of Program

6.14 Output from Program

6.15 Program for Stresses in Spherical Shell with Simply Supported Edges

6.16 Listing of Program

6.17 Output from Program

7. Membrane Theory for Shells of General Shape

7.1 Introduction

7.2 Geometry of Surface of General Shape

7.3 Membrane Equations of Equilibrium

7.4 Transformation of Equations of Equilibrium

7.5 Solution of Transformed Equations of Equilibrium

7.6 Hyperbolic Paraboloid

7.6.1 Uniform Vertical Load

7.6.2 Uniform Gravitational Load on Hyperbolic Paraboloid

7.7 Parabolic Conoid

7.7.1 Membrane Analysis of Parabolic Conoid under Uniform Gravitational Load

7.7.2 Boundary Conditions

7.7.3 Method of Solution

7.8 Program For Membrane Stresses in Parabolic Conoid

7.9 Listing of Program

7.10 Output From Program

8. Analysis of Multi-Shell Structures for Bending and Membrane Stresses by Computer Programs

8.1 Introduction

8.2 Boundary Conditions for Open Multi-Cylindrical Shells Without Edge Beams

8.3 Solution of Boundary Conditions

8.4 General Purpose Multi-Open-Shell Program

8.5 Examples for General "Feather Edge" Multi-Shell Program

8.5.1 Partially Loaded Cylindrical Shell

8.6 Degenerate Theory for Plate Structures

8.7 Folded-Plate Roof under Wind Loading by "Degenerate Theory"

8.8 Convergency Of "Degenerate Theory" For Folded-Plate Structures

8.9 Multi-Cylindrical Shell with Edge Beams

8.10 Stringer Bridge of Three Lanes by Degenerate Theory

8.11 Closed Multi-Cylindrical Cantilever Shells

8.12 Construction of Program

8.13 Wind Stresses in Multi-Plate Core Structure

8.14 Wind Stresses in Multi-Circular and Plate External Core Structure

8.15 Wind Stresses in Core for Tall Office-Block Building

9. Finite Element Analysis of Closed Circular Shells

9.1 Introduction

9.2 Nodal Force Displacement Equation

9.3 Axisymmetric Cylindrical Segment Element

9.4 Strain-Displacement Relationships

9.5 Stress-Strain Matrix

9.6 Application of Virtual Work to the Derivation of the Stiffness Matrix

9.7 Derivation of the Stiffness Matrix for Cylindrical Finite Element

9.8 Complete Stiffness Matrix

9.9 Overall Stiffness Matrix

9.10 Output Of Stress Resultants

9.11 Finite Element Program for the Analysis of Cylindrical Pressure Vessel with Thick End Plates

9.12 Output from Program

10. Experimental Investigation of Shells

10.1 Introduction

10.2 Investigation of Single Open Cylindrical Shell

10.3 Experimental Investigation of Large-Scale Cylindrical Shell with Small Edge Beams

10.4 Investigation of Small-Scale Multi-Cylindrical Shell

10.5 Investigation of Folded-Plate Structure

10.6 Investigation of Closed Cylindrical Tank Hinged at the Base and Subjected to Hydrostatic Pressure

10.7 An Investigation of the Stresses and Deflexions in a Box Bridge

10.8 Conclusions

11. Corrugated Shells

11.1 Introduction

11.2 Plane Corrugated Shell

11.3 Corrugated Folded Plate

11.4 Corrugated Cylindrical Shell

11.5 An Experimental and Theoretical Investigation of Shells Formed from Standard Corrugated Sheeting

References

Index

## Details

- No. of pages:
- 300

- Language:
- English

- Copyright:
- © Pergamon 1980

- Published:
- 1st January 1980

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483188669