Theory of Beams

The Application of the Laplace Transformation Method to Engineering Problems

2nd Edition - January 1, 1967
Author: T. Iwiński
Editor: B.G. Neal
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 8 6 0 1 - 6

Theory of Beams: The Application of the Laplace Transformation Method to Engineering Problems, Second Enlarged Edition emphasizes the method used than the broad coverage of all the… Read more

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Theory of Beams: The Application of the Laplace Transformation Method to Engineering Problems, Second Enlarged Edition emphasizes the method used than the broad coverage of all the significant cases that may be met in engineering practice. The content of this edition is mostly the topics presented in the first edition, but are roughly doubled. This edition is divided into four chapters, wherein most of the modifications made are included in the fourth chapter. The first chapter provides an introduction of the study, followed by discussions on theory of beams. Then, specific topics on the transform of the load function; beams with transverse and axial loading; beams and free beam on elastic foundations and non-homogeneous elastic foundations; and simple beam with terminal forces and couples resting on an elastic foundation are examined. This book ends with a table presenting transforms and functions. This text will be of interest to mathematicians and engineers, as well as mathematics and engineering students.

Preface to the Second Edition

Preface to the First Edition

Chapter I. Introductory Information

1. General Introduction

2. Step Functions and Multi-Step Functions

3. Some Remarks on the Laplace Transformation Method

Chapter II. Theory of Beams

1. Assumptions. Differential Equation of the Elastic Curve. Load Function

2. The Elastic Curve of Single-Span Beams

(a) Case 1. Beam Rigidly Built-in at Both Ends

(b) Case 2. Simple Beam Freely Supported at Both Ends

(c) Case 3. Cantilever Beam Propped at the Free End

(d) Case 4. Cantilever Beam Rigidly Fixed at One End

(e) Case 5. Simply Supported Beam with Overhangs

(f) Case 6. Propped Cantilever with an Overhang

(g) Case 7. Simple Beam with Terminal Forces and Couples

3. Determination of Static Quantities for a Single-Span Beam

4. Beams on Three Supports

5. The Elastic Curve of Continuous Beams

6. Theorem of Three Moments

7. Single-Span Beams on Elastic Supports

8. Continuous Beams on Elastic Supports

9. The Theorem of Five Moments

Chapter III. Theory of Beams with Variable Flexural Rigidity

1. Derivation of the Differential Equation of the Deflection Curve. Shape Function. Examples

2. Deflection Curve for Single-Span Beams

(a) Case 1. Beam Rigidly Built-in at Both Ends

(b) Case 2. Simple Beam Freely Supported at Both Ends

(c) Case 3. Cantilever Beam Propped at the Free End

(d) Case 4. Cantilever Beam

(e) Case 5. Simply Supported Beam with Overhangs

(f) Case 6. Propped Cantilever with an Overhang

(g) Case 7. Simple Beam with Terminal Couples

Chapter IV. Problems with More Complex Loading

1. The Transform of the Load Function

2. Beams with Transverse and Axial Loading

(a) Compressive Axial Forces

(b) Tensile Axial Forces

3. Beams on Elastic Foundations (Winkler's Type): General Solution

4. Free Beam on an Elastic Foundation

5. Simple Beam with Terminal Forces and Couples Resting on an Elastic Foundation

6. Beams on Non-Homogeneous Elastic Foundations Whose Elasticity Varies in a Stepwise Manner

(a) Exposition of the Problem

(b) Method of Solution

(c) Evaluation of the Shear Forces and Bending Moments at the Points of Discontinuity

(d) The Approximate Equation of Five Moments

7. On the Non-Continuous Solutions in the Theory of Structures

Chapter V. Tables of Transforms

References

Index