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Elastic beams and frames (Second edition)

J D Renton, University of Oxford, UK

Woodhead Publishing Series in Civil and Structural Engineering No. 9

 - approaches the basic theory of elastic beams and frames from a different perspective from standard pedagogy
 - provides an introduction to more advanced ideas on the theory of structures and contains much additional material
 - includes consideration of work and energy concepts as fundamental and the equations of statistics derived from them

The book approaches the basic theory of structures from a different perspective from standard pedagogy. There is consideration of work and energy concepts as fundamental and the equations of statics derived from them. Likewise, these concepts, together with that of the characteristic response, are used in the derivation of beam theory. Plane sections remaining plane is then seen as a particular result for isotropic, homogeneous, prismatic beams. The general theory may still be used where none of these conditions holds, and can even be applied to trusses. It also corrects errors in the theory of beam shear. Special topics discussed include non-uniform torsion, the exact analysis of shear, anisotropy, advanced energy methods, optimum structures, and regular frames. Software provided in the book includes seven general purpose programs for analysis of plane, space frames with rigid or pinned joints, and uses the augmented Gaussian elimination process and dynamic storage techniques.

ISBN 1 898563 86 1
ISBN-13: 978 1 898563 86 0
March 2002
416 pages  234 x 156mm  paperback  
£80.00 / US$135.00 / €95.00

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About the author

John D Renton, University of Oxford, UK

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Contents

Introduction
 - Loads, deflexions, joints and supports
 - Small deflexion theory
 - Energy, equilibrium and stability
 - Linear response
 - Symmetry and antisymmetry

Statics
 - Distributed mass and load, force fields
 - Particular cases of equilibrium
 - Method of sections
 - Joint resolution
 - Tension coefficients
 - Static analysis of beams
 - Static determinacy
 - Displacement diagrams
 - Full determinacy analysis

Elasticity
 - Stress and equilibrium
 - Strain and compatibility
 - Linear elastic behaviour of isotropic materials
 - Strain energy of a body
 - Strain energy density
 - Saint-Venant’s principle
 - Stress transformations and principal stresses
 - Mohr’ s Circle for strain
 - Failure criteria for ductile materials
 - Cylindrical polar coordinates
 - Anisotropic e1asticit
 - Stress and strain tensors

Beams with axial stresses
 - Introduction
 - The differential equations of flexure
 - Non beams and other exceptional cases
 - Moment-area methods
 - The slope-deflexion equations
 - Strain energy of bending and axial loading
 - Anisotropic beams subject to axial stresses

Torsion of beams
Introduction
 - Isotropic Beams with Circular Sections
 - Thin Tubes and Approximate Analyses of Non-Circular Secflons
 - Saint-Venant Torsion
 - The Membrane Analogy
 - Strain Energy of Torsion
 - Non-Prismatic Bars and Other Exceptional Cases
 - Anisotropic Beams in Torsion
 - Non-Uniform Torsion of Thin-Walled Open Sections

Shear of beams
 - Introduction
 - The Engineering Theory of Shear of Thin-Walled Sections
 - Shear Strain Energy and the Shear Stiffness of Thin-Walled Sections
 - A Closer Examination of Deflexion and Support Conditions
 - The Exact Analysis of Flexural Shear
 - Non-Prismatic and Inhomogeneous Beams
 - Anisotropic Beams

Energy methods
 - Introduction
 - The Principle of Minimum Potential Energy
 - The Principle of Minimum Complementary Energy
 - Prescribed Resultants, Corresponding Deflexions and Work
 - Castigliano’s Strain Energy Theorem
 - Castigliano’s and Crotti’s Complementary Energy Theorems
 - The Rayleigh-Ritz Method
 - The Calculus of Variations

General theory of beams
 - Introduction
 - The Constant Response
 - The Linear Response
 - The Deformation Matrix
 - The Slope-Defiexion Equations for Modular Beams
 - The Characteristic Response for Circular Beams

Stability of beams
 - Introduction
 - The Classical Problems of Structural Stability
 - The Slope-Deflexion Equations for Large Axial Loads
 - Flexure and Shear
 - Flexure and Torsion
 - Lateral ‘Buckling
 - Local Buckling of Thin-Walled Sections
 - Approximate Methods
 - General Theories of Stability

Vibration of beams
 - Introduction
 - The Flexural Vibration of Beams
 - The Natural Frequencies of Simple Beams
 - The Axial Vibration of Beams
 - The Torsional Vibration of Beams
 - Flexural Vibration with Large Axial Loading
 - Response to Arbitrary Time-Dependent Loading
 - Travelling Waves in Rods and Beams
 - The Whirling of Shafts
 - Approximate Methods

Matrix analysis of structures
 - Introduction
 - Plane Pin-Jointed Frames
 - Plane Rigid-Jointed Frames
 - Three-Dimensional Frames
 - The Stability of Frames
 - The Vibration of Frames
 - Equilibrium Matrices
 - Non-Prismatic Members
 - Transfer Matrices
 - Special Applications

Computer analysis of frames
 - Introduction
 - The Nature of the Frame Stiffness Matrix
 - Data Input
 - Organisation of the Data
 - Methods of Solution
 - Data Output
 - Stability and Vibration Problems

Influence lines
 - Introduction
 - Elementary Beam Problems
 - Envelope Diagrams
 - Trusses
 - Muller Theorem

Optimum structures
 - Introduction
 - Maxwell’s Theorem
 - Michell Structures
 - Linear Programming
 - General Methods of Optimisation
 - Vibration Optimisation
 - Optimisation with Buckling Problems

Regular structures
 - Introduction
 - Mathematical Preliminaries
 - Regular Plane Trusses
 - Regular Space Trusses
 - Membranes and Cable Nets
 - Plane Grids
 - Space Grids
 - Reticulated Barrel Vaults
 - Braced Domes
 - Stability Considerations
 - Vibration Problems

Appendix 1: Common Notation

Appendix 2: How to Use the Structural Analysis Programs

Appendix 3: How to Use the Other Progams

Appendix 4: Section Properties and Related Formulae

Appendix 5: Properties of Regular Structures and Standard Solutions

Appendix 6: Tables

Appendix 7: The Characteristic Response of Cones

Appendix 8: Elements of Plate Theory

Appendix 9: Further Theoretical Considerations

References and Suggested Reading