An Introduction to Aircraft Structural Analysis - Megson T.H.G.pdf

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An Introduction to Aircraft
Structural Analysis
T. H. G. Megson
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Butterworth-Heinemann is an imprint of Elsevier
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Butterworth-Heinemann is an imprint of Elsevier
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Copyright © 2010, T. H. G. Megson. Published by Elsevier Ltd. All rights reserved.
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
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Notices
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Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information,
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging-in-Publication Data
Megson, T.H.G. (Thomas Henry Gordon)
An introduction to aircraft structural analysis / T.H.G. Megson.
p. cm.
Rev. ed. of: Aircraft structures for engineering students / T.H.G. Megson. 4th ed. 2007.
Includes bibliographical references and index.
ISBN 978-1-85617-932-4 (alk. paper)
1. Airframes. 2. Structural analysis (Engineering) I. Title.
TL671.6.M36 2010
629.134’31–dc22
2009050354
For information on all Butterworth-Heinemann publications
visit our Web site at www.elsevierdirect.com
Printed in the United States of America
1011121314 10987654321
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Contents
Preface ............................................................................................. vii
PART A FUNDAMENTALS OF STRUCTURAL ANALYSIS
CHAPTER 1 Basic Elasticity ........................................................................... 3
1.1 Stress .................................................................................................. 3
1.2 Notation for Forces andStresses ................................................................... 5
1.3 Equations of Equilibrium ........................................................................... 7
1.4 Plane Stress ........................................................................................... 9
1.5 Boundary Conditions ................................................................................ 9
1.6 Determination of Stresses on InclinedPlanes .................................................... 10
1.7 Principal Stresses .................................................................................... 14
1.8 Mohr’s Circle of Stress .............................................................................. 16
1.9 Strain .................................................................................................. 20
1.10 Compatibility Equations ............................................................................ 24
1.11 Plane Strain ........................................................................................... 25
1.12 Determination of Strains on InclinedPlanes...................................................... 25
1.13 Principal Strains...................................................................................... 27
1.14 Mohr’s Circle of Strain .............................................................................. 28
1.15 Stress–StrainRelationships ......................................................................... 28
1.16 Experimental Measurement of Surface Strains ................................................... 37
Problems .............................................................................................. 41
CHAPTER 2
Two-Dimensional Problems in Elasticity .............................................. 45
2.1
Two-Dimensional Problems ........................................................................ 45
2.2
Stress Functions...................................................................................... 47
2.3
Inverse and Semi-Inverse Methods ................................................................ 48
2.4
St. Venant’s Principle................................................................................ 53
2.5
Displacements ........................................................................................ 54
2.6
Bending of an End-Loaded Cantilever ............................................................ 55
Problems .............................................................................................. 60
CHAPTER 3
Torsion of Solid Sections ............................................................... 65
3.1
Prandtl Stress Function Solution ................................................................... 65
3.2
St. VenantWarpingFunctionSolution ............................................................ 75
3.3
TheMembraneAnalogy ............................................................................ 77
3.4
Torsion of a Narrow Rectangular Strip ............................................................ 79
Problems .............................................................................................. 82
CHAPTER 4 Virtual Work and Energy Methods ..................................................... 85
4.1 Work................................................................................................... 85
4.2 Principle ofVirtualWork ........................................................................... 86
4.3 Applications of the Principle ofVirtualWork .................................................... 99
Problems .............................................................................................. 107
CHAPTER 5
Energy Methods .......................................................................... 111
5.1
Strain Energy and Complementary Energy ....................................................... 111
5.2
The Principle of the Stationary Value of the Total Complementary Energy .................. 113
iii
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iv
Contents
5.3 Application to Deflection Problems ............................................................... 114
5.4 Application to the Solution of Statically Indeterminate Systems............................... 122
5.5 Unit LoadMethod ................................................................................... 138
5.6 FlexibilityMethod ................................................................................... 141
5.7 Total Potential Energy............................................................................... 147
5.8 The Principle of the StationaryValue of theTotal Potential Energy........................... 148
5.9 Principle of Superposition .......................................................................... 151
5.10 TheReciprocal Theorem............................................................................ 151
5.11 TemperatureEffects ................................................................................. 156
Problems .............................................................................................. 158
CHAPTER 6 Matrix Methods ........................................................................... 169
6.1 Notation ............................................................................................... 170
6.2 StiffnessMatrix for anElastic Spring ............................................................. 171
6.3 StiffnessMatrix for TwoElastic Springs inLine................................................. 172
6.4 Matrix Analysis of Pin-jointed Frameworks ...................................................... 176
6.5 Application to Statically Indeterminate Frameworks ............................................ 183
6.6 Matrix Analysis of Space Frames .................................................................. 183
6.7
Stiffness Matrix for a Uniform Beam.............................................................. 185
6.8
Finite Element Method for Continuum Structures ............................................... 193
Problems .............................................................................................. 211
CHAPTER 7
Bending of Thin Plates .................................................................. 219
7.1
PureBending of ThinPlates........................................................................ 219
7.2
Plates Subjected toBending andTwisting ........................................................ 223
7.3
Plates Subjected to aDistributedTransverseLoad............................................... 227
7.4
Combined Bending and In-Plane Loading of a Thin Rectangular Plate ....................... 236
7.5
Bending of Thin Plates Having a Small Initial Curvature ....................................... 240
7.6
EnergyMethod for theBending of ThinPlates .................................................. 241
Problems .............................................................................................. 250
CHAPTER 8
Columns ................................................................................... 253
8.1
Euler Buckling of Columns......................................................................... 253
8.2
InelasticBuckling.................................................................................... 259
8.3
Effect of Initial Imperfections ...................................................................... 263
8.4
Stability of Beams under Transverse and Axial Loads .......................................... 266
8.5
EnergyMethod for theCalculation of BucklingLoads inColumns ........................... 270
8.6
Flexural–Torsional Buckling of Thin-Walled Columns ......................................... 274
Problems .............................................................................................. 287
CHAPTER 9
Thin Plates ................................................................................ 293
9.1
Buckling of ThinPlates ............................................................................. 293
9.2
InelasticBuckling of Plates......................................................................... 296
9.3
Experimental Determination of Critical Load for a Flat Plate.................................. 298
9.4
Local Instability ...................................................................................... 299
9.5
Instability of Stiffened Panels ...................................................................... 300
9.6
Failure Stress in Plates and Stiffened Panels...................................................... 302
9.7
Tension Field Beams ................................................................................ 304
Problems .............................................................................................. 320
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