Aircraft Structures for Engineering Students, Fourth Edition

1 1/2/2007 11: 48 Page iAircraft Structuresfor Engineering studentsThis page intentionally left blank 1/2/2007 11: 48 Page iiiAircraft Structuresfor Engineering studentsFourth EditionT. H. G. MegsonAMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORDPARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYOB utterworth-Heinemann is an imprint of 1/2/2007 11: 48 Page ivButterworth-Heinemann is an imprint of ElsevierLinacre House, Jordan Hill, Oxford OX2 8DP, UK30 Corporate Drive, Suite 400, Burlington, MA 01803, USAF irst Edition 2007 Copyright 2007, T. H. G. Megson, Elsevier Ltd. All rights reservedThe right of T. H. G. Megson to be identified as the author of this work has beenasserted in accordance with the Copyright, Designs and Patents Act 1988No part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means electronic, mechanical, photocopying,recording or otherwise without the prior written permission of the publisherPermissions may be sought directly from Elsevier s Science & Technology RightsDepartment in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333.

2 Email: Alternatively you can submit your request online byvisiting the Elsevier web site at , and selectingObtaining permission to use Elsevier materialNoticeNo responsibility is assumed by the publisher for any injury and/or damage to personsor property as a matter of products liability, negligence or otherwise, or from any useor operation of any methods , products, instructions or ideas contained in the materialherein. Because of rapid advances in the medical sciences, in particular, independentverification of diagnoses and drug dosages should be madeBritish Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryLibrary of Congress Cataloging-in-Publication DataA catalog record for this book is availabe from the Library of CongressISBN-13: 978-0-75066-7395 ISBN-10: 0-750-667397 For information on all Butterworth-Heinemannpublications visit our web site at by Charon Tec Ltd (A Macmillan Company), Chennai, and bound in Great 1/2/2007 11.

3 48 Page vContentsPrefacexiiiPreface to Second EditionxvPreface to Third EditionxviiPreface to Fourth EditionxixPart A Fundamentals of Structural Analysis1 Section A1 Elasticity31 Basic Notation for forces and Equations of Plane Boundary Determination of stresses on inclined Principal Mohr s circle of Compatibility Plane Determination of strains on inclined Principal Mohr s circle of Stress strain Experimental measurement of surface strains37 References42 Problems422 Two-dimensional problems in Two-dimensional Stress 1/2/2007 11: 48 Page Inverse and semi-inverse St. Venant s Bending of an end-loaded cantilever56 Reference61 Problems613 Torsion of solid Prandtl stress function St. Venant warping function The membrane Torsion of a narrow rectangular strip79 References81 Problems82 Section A2 Virtual Work.

4 energy and Matrix Methods854 Virtual work and energy Principle of virtual Applications of the principle of virtual work100 References108 Problems1085 energy Strain energy and complementary The principle of the stationary value of the totalcomplementary Application to deflection Application to the solution of statically indeterminate Unit load Flexibility Total potential The principle of the stationary value of the total potential Principle of The reciprocal Temperature effects154 References156 Further reading156 Problems1566 Matrix Stiffness matrix for an elastic Stiffness matrix for two elastic springs in Matrix analysis of pin-jointed Application to statically indeterminate Matrix analysis of space 1/2/2007 11: 48 Page Stiffness matrix for a uniform Finite element method for continuum structures191 References208 Further reading208 Problems209 Section A3 Thin Plate Theory2177 Bending of thin Pure bending of thin Plates subjected to bending and Plates subjected to a distributed transverse Combined bending and in-plane loading of a thin rectangular plate Bending of thin plates having a small initial energy method for the bending of thin plates240 References248 Problems248 Section A4 Structural Instability2538 Euler buckling of Inelastic Effect of initial Stability of beams under transverse and axial energy method for the calculation of buckling loads in Flexural torsional buckling of thin-walled columns275 References287 Problems2879 Thin Buckling of thin Inelastic buckling of Experimental determination of critical load for a flat Local

5 Instability of stiffened Failure stress in plates and stiffened Tension field beams306 References320 Problems320 Section A5 Vibration of Structures32510 Structural Oscillation of mass/spring Oscillation of Approximate methods for determining natural 1/2/2007 11: 48 Page viiiviiiContentsPart B Analysis of Aircraft Structures349 Section B1 Principles of Stressed Skin Construction35111 Aluminium Composite Properties of materials359 Problems37412 Structural components of Loads on structural Function of structural Fabrication of structural Connections388 Reference395 Problems395 Section B2 Airworthiness and Airframe Loads39713 Factors of safety-flight Load factor determination401 Reference40414 Airframe Aircraft inertia Symmetric manoeuvre Normal accelerations associated with varioustypes of Gust loads418 References424 Problems42515 Safe life and fail-safe Designing against Fatigue strength of Prediction of Aircraft fatigue Crack propagation440 References446 Further 1/2/2007 11.

6 48 Page ixContentsixSection B3 Bending, Shear and Torsion of Thin-Walled Beams44916 Bending of open and closed, thin-walled Symmetrical Unsymmetrical Deflections due to Calculation of section Applicability of bending Temperature effects491 References495 Problems49517 Shear of General stress, strain and displacement relationships foropen and single cell closed section thin-walled Shear of open section Shear of closed section beams512 Reference519 Problems52018 Torsion of Torsion of closed section Torsion of open section beams537 Problems54419 Combined open and closed section Torsion554 Problems55620 Structural Idealization of a Effect of idealization on the analysis of open andclosed section Deflection of open and closed section beams573 Problems576 Section B4 Stress Analysis of Aircraft Components58121 Wing spars and box Tapered wing Open and closed section Beams having variable stringer 1/2/2007 11.

7 48 Page xxContents22 Cut-outs in fuselages604 Problems60623 Three-boom Shear Tapered Cut-outs in wings623 Problems63124 Fuselage frames and wing Principles of stiffener/web Fuselage Wing ribs644 Problems64825 Laminated composite Elastic constants of a simple Stress strain relationships for an orthotropic ply(macro- approach) Thin-walled composite beams662 References674 Problems674 Section B5 Structural and Loading Discontinuities67726 Closed section General Shear stress distribution at a built-in end of aclosed section Thin-walled rectangular section beam subjected to Shear lag694 Reference710 Problems71027 Open section I-section beam subjected to Torsion of an arbitrary section 1/2/2007 11: 48 Page Distributed torque Extension of the theory to allow for general systems of Moment couple (bimoment)734 References737 Problems738 Section B6 Introduction to Aeroelasticity74328 Wing Types of Load distribution and Control effectiveness and Introduction to flutter 757 References765 Problems765 Appendix767 Index797 This page intentionally left blank 1/2/2007 11: 48 Page xiiiPrefaceDuring my experience of teaching Aircraft Structures I have felt the need for a textbookwritten specifically for students of aeronautical Engineering .

8 Although there have beena number of excellent books written on the subject they are now either out of date ortoo specialist in content to fulfil the requirements of an undergraduate textbook. Myaim, therefore, has been to fill this gap and provide a completely self-contained coursein Aircraft Structures which contains not only the fundamentals of elasticity and aircraftstructural analysis but also the associated topics of airworthiness and book in intended for students studying for degrees, Higher National Diplomasand Higher National Certificates in aeronautical Engineering and will be found of valueto those students in related courses who specialize in Structures . The subject matterhas been chosen to provide the student with a textbook which will take him from thebeginning of the second year of his course, when specialization usually begins, up to andincluding his final examination. I have arranged the topics so that they may be studiedto an appropriate level in, say, the second year and then resumed at a more advancedstage in the final year; for example, the instability of columns and beams may be studiedas examples of structural instability at second year level while the instability of platesand stiffened panels could be studied in the final year.

9 In addition, I have grouped somesubjects under unifying headings to emphasize their interrelationship; thus, bending,shear and torsion of open and closed tubes are treated in a single chapter to underline thefact that they are just different loading cases of basic structural components rather thanisolated topics. I realize however that the modern trend is to present methods of analysisin general terms and then consider specific applications. Nevertheless, I feel that incases such as those described above it is beneficial for the student s understanding ofthe subject to see the close relationships and similarities amongst the different portionsof I of the book, Fundamentals of elasticity , Chapters 1 6, includes sufficientelasticity theory to provide the student with the basic tools of structural analysis. Thework is standard but the presentation in some instances is original. In Chapter 4 I haveendeavoured to clarify the use of energy methods of analysis and present a consistent,but general, approach to the various types of structural problem for which energymethods are employed.

10 Thus, although a variety of methods are discussed, emphasis isplaced on the methods of complementary and potential energy . Overall, my intentionhas been to given some indication of the role and limitations of each method of 1/2/2007 11: 48 Page xivxivPrefacePart II, Analysis of Aircraft Structures , Chapters 7 11, contains the analysis of thethin-walled, cellular type of structure peculiar to Aircraft . In addition, Chapter 7 includesa discussion of structural materials, the fabrication and function of structural compo-nents and an introduction to structural idealization. Chapter 10 discusses the limitationsof the theory presented in Chapters 8 and 9 and investigates modifications necessaryto account for axial constraint effects. An introduction to computational methods ofstructural analysis is presented in Chapter 11 which also includes some elementarywork on the relatively modern finite element method for continuum , Part III, Airworthiness and Aeroelasticity , Chapters 12 and 13, are examples are used extensively in the text to illustrate the theory while numer-ous unworked problems with answers are listed at the end of each chapter; unitsare used am indebted to the Universities of London ( ) and Leeds for permission toinclude examples from their degree papers and also the Civil Engineering DepartmentoftheUniversityofLeedsforallow ingmeanyfacilitiesIrequiredduringtheprep arationof the manuscript.