Shell Structures: Theory and Application

✍ Scribed by Mitchell Gohnert

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 355
• Category: Library

✦ Synopsis

This text provides a complete and thorough derivation of the mathematical theory of shell structures. Many books on shells only give the key equations or snippets of theory, skipping all of the mathematical steps required to solve for the key equations. This is understandable, because of the mathematical complexity of shell structures. Thus, the reader must just accept the design equations blindly, without achieving a complete understanding of shell theory. This book, therefore, fills this gap by providing a complete picture of shell theory. Class tested over three university post-graduate courses and one public course on shell structures, the book is mathematically intensive, but it written in an accessible style ideal for students of engineering mechanics in civil and mechanical engineers concentrations, as well as practicing structural engineers looking for a reference on shells.

✦ Table of Contents

Foreword
Contents
Chapter 1: Introduction
References
Chapter 2: Construction Materials and Stress Flow
2.1 Introduction
2.2 The Basic Characteristics of Stresses and Strains
2.3 Economy of Stresses
2.4 The Flawed Nature of Construction Materials
2.5 The Flow of Stress in Flat and Curved Walls
2.6 The Flow of Stress around Openings
2.7 Exercises
References
Chapter 3: Cylindrical Shells
3.1 Introduction
3.2 The Membrane Theory of Cylindrical Shells
3.2.1 Circumferential (Hoop) Equilibrium
3.2.2 Vertical Equilibrium
3.2.3 Radial Equilibrium
3.2.4 General Membrane Stress Equations
3.2.5 Membrane Stress Equations for Various Loadings on the Shell
3.3 Displacement Theory for Membrane Stresses
3.3.1 Strains, Displacements, and Stresses
3.3.2 Displacements in the Shell Due to Various Loads
3.4 Boundary Effects
3.4.1 Circumferential Equilibrium
3.4.2 Vertical Equilibrium
3.4.3 Radial Equilibrium
3.4.4 Moment Equilibrium Equation About the Horizontal Direction
3.4.5 Moment Equilibrium Equation About the Vertical Direction
3.4.6 Equilibrium Equation Summary for Symmetrical Loading
3.4.7 Stress Equations for the Boundary Effects
3.5 Displacement Theory for the Boundary Effects
3.6 Compatibility Equations
3.7 Steps in Solving the Deformations and Stresses in the Shell
3.8 Worked Example
3.9 Exercises
References
Chapter 4: Circular Domes
4.1 Introduction
4.2 The Membrane Theory of the Circular Dome
4.2.1 Equilibrium in the Hoop Direction (θ-Direction)
4.2.2 Equilibrium in the Meridian Direction (훟-Direction)
4.2.3 Equilibrium in the Radial Direction (z-Direction)
4.2.4 Summary of Equilibrium Equations and Simplifications
4.2.5 Uniform Vertical Loading
4.2.6 Horizontal Vertical Loading
4.2.7 Uniform Pressure
4.2.8 Circular Openings at the Apex of the Shell
4.3 Displacement Theory
4.3.1 Circumferential, or Hoop Strain
4.3.2 Meridional, or Vertical Strains
4.3.3 General Equations for Deflections and Slopes
4.3.4 Deformations for the Case of Uniformly Distributed Load (Gravity Load)
4.3.5 Deformations for the Case of a Horizontal Uniformly Distributed Load
4.3.6 Deformations for the Case of a Uniform Pressure
4.4 Boundary Effects
4.4.1 Equilibrium in the Hoop Direction (θ-Direction)
4.4.2 Equilibrium in the Meridian Direction (훟-Direction)
4.4.3 Stresses That Contribute to the Equilibrium Equation in the z-Direction
4.4.4 Equilibrium of Moments About the Hoop Direction
4.4.5 Equilibrium of Moments About the Meridian Direction
4.4.6 Simplifying the General Equilibrium Equations
4.5 Displacement Theory of the Boundary Effects
4.6 Compatibility Equations
4.7 Steps in Solving the Deformations and Stresses in the Shell
4.8 Worked Example
4.9 Exercises
References
Chapter 5: Derivatives of Dome Theory: The Conoidal, Elliptical, and Conical Domes and the Hyperbolic Shell
5.1 Introduction
5.2 Conical Shells
5.2.1 Conical Water Reservoir
5.2.1.1 Equilibrium in the Hoop Direction
5.2.1.2 Equilibrium in the y-Direction (Fig. 5.5)
5.2.1.3 Equilibrium in the z-Direction
5.2.1.4 General Equations for Membrane Stresses
5.2.1.5 Membrane Stresses for Self-Weight (Gravity) Load
5.2.1.6 Membrane Stresses for Water Load
5.2.1.7 Membrane Stresses for Wind Load
5.2.2 Conical Dome
5.3 Elliptical Dome
5.3.1 Total Load R
5.3.2 Membrane Stresses
5.4 Conoidal Dome
5.5 Hyperbolic Shell
5.5.1 Equilibrium in the Circumferential, or Hoop Direction
5.5.2 Equilibrium in the Vertical, or y-Direction
5.5.3 Equilibrium in the Radial, or z-Direction
5.5.4 Defining the Principle Radii r1 and r2
5.5.5 Membrane Stresses Due to Gravity Load
5.6 Example Solutions and a Comparison of the Circular, Conoidal, Elliptical, and Conical Domes
5.7 Exercises
References
Chapter 6: The Circular Barrel Vault
6.1 Introduction
6.2 Membrane Theory of the Barrel Vault
6.2.1 External Loading on the Shell
6.2.2 Membrane Stresses for the Case of Gravity Loading
6.3 Deformation Theory
6.3.1 Strains in the x-Direction
6.3.2 Strains in the 훟-Direction, Due to an Extension v
6.3.3 Strains in the 훟-Direction, Due to a Change in Radius
6.3.4 Total Strain in the 훟-Direction
6.3.5 Shearing Strain
6.3.6 Membrane Stresses
6.3.7 Horizontal and Vertical Deformations
6.4 Shallow Shell Theory to Solve for the Boundary Effects
6.4.1 Stresses from Boundary Effects
6.4.2 The Complementary Solution
6.4.3 The Particular Solution
6.4.4 The General Solution for Deformations
6.4.5 Moments, Shears, and Stresses Due to Boundary Effects
6.5 Edge Beams
6.5.1 Stress Equations
6.5.2 Compatibility Equations
6.5.2.1 Vertical Compatibility
6.5.2.2 Horizontal Compatibility
6.5.3 Components of the Compatibility Equations
6.6 Steps in Solving the Deformations and Stresses in the Shell
6.6.1 Barrel Shells with Free Edges
6.6.2 Barrel Shells with Edge Beams
6.7 Worked Examples
6.7.1 Simply Supported Barrel Vault with Free Edges
6.7.2 Simply Supported Barrel Vault with Edge Beams
6.8 Exercises
References
Chapter 7: Catenary Arches and Domes
7.1 Introduction
7.2 The Catenary Arch
7.3 The Funicular Arch
7.3.1 Derivation of the Funicular Arch Theory, Using an Iterative Approach
7.4 Membrane Theory of Catenary Domes
7.4.1 Catenary Relationships
7.4.2 Arch Length of the Catenary Curve
7.4.3 Membrane Stress Equations
7.4.4 Membrane Stress Equation for a Dome with an Oculus
7.5 Worked Examples
7.5.1 Arch Subjected to a Uniform Gravity Load
7.5.2 Arch Subjected to a Uniform Gravity Load and a Point Load
7.5.3 Membrane Solution of a Catenary Dome Subjected to Gravity Load
7.6 Exercises
References
Appendixes
Appendix A
Appendix B
Index