Volume 2 The Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials.pdf

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MECHANICS OF
MATERIALS 2
An introduction to the Mechanics of Elastic and
Plastic Deformation of Solids and Structural Materials
THIRD EDITION
E. J. HEARN
PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE
University of Warwick
United Kingdom
la==--
EINEMANN
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Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
-& A member of the Reed Elsevier plc group
OXFORD AUCKLAND BOSTON
MELBOURNE NEW DELHI
First published 1977
Reprinted with corrections 1980, 1981, 1982
Second edition 1985
Reprinted with corrections 1989
Reprinted 1992, 1995, 1996
Third edition 1997
Reprinted 1 ?99
0 E.J. Hem 1977, 1985, 1997
All rights reserved. No part of this publication
may be reproduced in any materiai form (including
photocopying or storing in any medium by electronic
means and whether or not transiently or incidentally to
some other use of this publication) without the written
permission of the copyright holder except in accordance
with the provisions of the Copyright, Designs and
Patents Act 1988 or under the terms of a licence issued
by the Copyright Licensing Agency Ltd, 90 Tottenham
Court Road, London, England WlP 9HE.
Applications for the copyright holder’s written
permission to reproduce any part of this publication
should be addressed to the publishers
British Library Cataloguing in Publication Data
Hem, E. J. (Edwin John)
Mechanics of materials. - 3rd ed.
1.
materials
1. Strength of materials 2. Strains and stress
3. Deformations (Mechanics) 4. Elasticity
I. Title
620.1 12
ISBN 0 7506 3266 6
Library of Congress Cataloguing in Publication Data
Heam, E. J. (Edwin John)
Mechanics of materials 1: an introduction to the mechanics of elastic and plastic deformation of
solids and structural materialsE. J. Heam. - 3rd ed.
p. cm.
Includes bibliographical references and index.
ISBN 0 7506 3266 6
1. Strength of materials.
I. Title
TA405.H3
620.1’123-dc21
96-49967
CIP
Typeset by Laser Words, Madras, lndia
Rinted and bound in Great Britain
An introduction to the mechanics of elastic and plastic deformation of solids and structural
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CONTENTS
Introduction
xv
Notation
xvii
1 Unsymmetrical Bending
1
Summary
Introduction
I .1
1.2
1.3
1.4
1.5
Product second moment of area
Principal second moments of area
Mohr’s circle of second moments of area
Land’s circle of second moments of area
Rotation of axes: determination of moments of area in terms of the
principal values
The ellipse of second moments of area
8
9
11
11
11
13
15
16
24
I .6
1.7 Momenta1 ellipse
1.8 Stress determination
1.9 Alternative procedurefor stress determination
1.10 Alternative procedure using the momenta1 ellipse
1.11 Dejections
Examples
Problems
2 Struts
28
Summary
Introduction
2.1 Euler’s theory
2.2 Equivalent strut length
2.3
2.4 Euler “validity limit”
2.5 Rankine or Rankine-Gordon formula
2.6 Perry- Robertson formula
2.7
2.8 Struts with initial curvature
2.9 Struts with eccentric load
2.10 Laterally loaded struts
2.1 1
Comparison of Euler theory with experimental results
28
30
31
35
36
37
38
39
41
41
42
46
48
British Standard procedure (BS 449)
Alternative procedurefor any strut-loading condition
V
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vi
Contents
2.12 Struts with unsymmetrical cross-section
Examples
Problems
49
50
56
3 Strains Beyond the Elastic Limit
61
Summary
Introduction
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.1 1
3.12
3.13
3.14
3.15
Plastic bending of rectangular-sectioned beams
Shape factor - symmetrical sections
Application to I-section beams
Partially plastic bending of unsymmetrical sections
Shape factor - unsymmetrical sections
Dejections of partially plastic beams
Length of yielded area in beams
Collapse loads - plastic limit design
Residual stresses after yielding: elastic-perfectly plastic material
Torsion of shafts beyond the elastic limit - plastic torsion
Angles of twist of shafts strained beyond the elastic limit
Plastic torsion of hollow tubes
Plastic torsion of case-hardened shafts
Residual stresses after yield in torsion
Plastic bending and torsion of strain-hardening materials
(a)Inelastic bending
(b)Inelastic torsion
Residual stresses - strain-hardening materials
Influence of residual stresses on bending and torsional strengths
Plastic yielding in the eccentric loadirzg of rectangular sections
Plastic yielding and residual stresses under axial loading with stress
concentrations
Plastic yielding of axially symmetric components
(a)Thick cylinders - collapse pressure
(b)Thick cylinders - “auto-frettage ’’
(c)Rotating discs
Examples
Problems
61
62
64
65
67
67
69
69
69
71
73
75
77
77
79
79
80
80
83
84
84
85
3.16
3.17
3.18
3.19
86
87
87
89
94
96
109
3.20
4 Rings, Discs and Cylinders Subjected to Rotation
and Thermal Gradients
117
Summary
4.1
4.2 Rotating solid disc
4.3
4.4
4.5
Thin rotating ring or cylinder
117
118
119
122
124
125
Rotating disc with a central hole
Rotating thick cylinders or solid shafs
Rotating disc of uniform strength
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