Megson_StructlStressAnalysis_2nd_etxtbk.pdf

Structural and Stress Analysis

Structural and Stress

Analysis

Second Edition

Dr. T.H.G. Megson

Senior Lecturer in Civil Engineering (now retired)

University of Leeds

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Elsevier Butterworth-Heinemann

Linacre House, Jordan Hill, Oxford OX2 8DP

30 Corporate Drive, Burlington, MA 01803

First published in Great Britain by Arnold 1996

Reprinted by Butterworth-Heinemann 2000

Second Edition 2005

The right of T.H.G. Megson to be identiﬁed as the author of this Work

has been asserted in accordance with the Copyright, Designs and

Patents Act 1988

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A catalogue record for this book is available from the British Library

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A catalogue record for this book is available from the Library of Congress

ISBN 0 7506 6221 2

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Preface to First Edition

The purpose of this book is to provide, in a uniﬁed form, a text covering the associated

topics of structural and stress analysis for students of civil engineering during the ﬁrst

two years of their degree course. The book is also intended for students studying for

Higher National Diplomas, Higher National Certiﬁcates and related courses in civil

engineering.

Frequently, textbooks on these topics concentrate on structural analysis or stress

analysis and often they are lectured as two separate courses. There is, however, a

degree of overlap between the two subjects and, moreover, they are closely related.

In this book, therefore, they are presented in a uniﬁed form which illustrates their

interdependence. This is particularly important at the ﬁrst-year level where there is a

tendency for students to ‘compartmentalize’ subjects so that an overall appreciation

of the subject is lost.

The subject matter presented here is conﬁned to the topics students would be

expected to study in their ﬁrst two years since third- and fourth-year courses in struc-

tural and/or stress analysis can be relatively highly specialized and are therefore best

served by specialist texts. Furthermore, the topics are arranged in a logical manner so

that one follows naturally on from another. Thus, for example, internal force systems

in statically determinate structures are determined before their associated stresses and

strains are considered, while complex stress and strain systems produced by the simul-

taneous application of different types of load follow the determination of stresses and

strains due to the loads acting separately.

Although in practice modern methods of analysis are largely computer based, the

methods presented in this book form, in many cases, the basis for the establishment

of the ﬂexibility and stiffness matrices that are used in computer-based analysis. It is

therefore advantageous for these methods to be studied since, otherwise, the student

would not obtain an appreciation of structural behaviour, an essential part of the

structural designer’s background.

In recent years some students enrolling for degree courses in civil engineering,

while being perfectly qualiﬁed from the point of view of pure mathematics, lack a

knowledge of structural mechanics, an essential basis for the study of structural and

stress analysis. Therefore a chapter devoted to those principles of statics that are a

necessary preliminary has been included.

As stated above, the topics have been arranged in a logical sequence so that they

forma coherent and progressive ‘story’. Hence, inChapter 1, structures are considered

in terms of their function, their geometries in different roles, their methods of support

and the differences between their statically determinate and indeterminate forms. Also

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Preface

considered is the role of analysis in the design process and methods of idealizing struc-

tures so that they become amenable to analysis. In Chapter 2 the necessary principles

of statics are discussed and applied directly to the calculation of support reactions.

Chapters 3–6 are concerned with the determination of internal force distributions in

statically determinate beams, trusses, cables and arches, while in Chapter 7 stress

and strain are discussed and stress–strain relationships established. The relationships

between the elastic constants are then derived and the concept of strain energy in axial

tension and compression introduced. This is then applied to the determination of the

effects of impact loads, the calculation of displacements in axially loaded members

and the deﬂection of a simple truss. Subsequently, some simple statically indetermi-

nate systems are analysed and the compatibility of displacement condition introduced.

Finally, expressions for the stresses in thin-walled pressure vessels are derived. The

properties of the different materials used in civil engineering are investigated in Chap-

ter 8 together with an introduction to the phenomena of strain-hardening, creep and

relaxation and fatigue; a table of the properties of the more common civil engineering

materials is given at the end of the chapter. Chapters 9, 10 and 11 are respectively con-

cerned with the stresses produced by the bending, shear and torsion of beams while

Chapter 12 investigates composite beams. Deﬂections due to bending and shear are

determined in Chapter 13, which also includes the application of the theory to the

analysis of some statically indeterminate beams. Having determined stress distribu-

tions produced by the separate actions of different types of load, we consider, in Chap-

ter 14, the state of stress and strain at a point in a structural member when the loads

act simultaneously. This leads directly to the experimental determination of surface

strains and stresses and the theories of elastic failure for both ductile and brittle mater-

ials. Chapter 15 contains a detailed discussion of the principle of virtual work and the

various energy methods. These are applied to the determination of the displacements

of beams and trusses and to the determination of the effects of temperature gradi-

ents in beams. Finally, the reciprocal theorems are derived and their use illustrated.

Chapter 16 is concerned solely with the analysis of statically indeterminate structures.

Initially methods for determining the degree of statical and kinematic indeterminacy

of a structure are described and then the methods presented in Chapter 15 are used

to analyse statically indeterminate beams, trusses, braced beams, portal frames and

two-pinned arches. Special methods of analysis, i.e. slope–deﬂection and moment dis-

tribution, are then applied to continuous beams and frames. The chapter is concluded

by an introduction to matrix methods. Chapter 17 covers inﬂuence lines for beams,

trusses and continuous beams while Chapter 18 investigates the stability of columns.

Numerous worked examples are presented in the text to illustrate the theory, while

a selection of unworked problems with answers is given at the end of each chapter.

T.H.G. MEGSON

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