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E NG I N E E RrN G STU DE NTS
THIRD EDITION
T.H.G. MEGSON
Aircraft Structures
for engineering students
To The Memory of My Father
Aircraft Structures
for engineering students
Third Edition
T. H. G. Megson
i
E I N E M A N N
OXFORD AMSTERDAM BOSTON LONDON NEWYORK PARIS
SANDIEGO SANFRANCISCO SINGAPORE SYDNEY TOKYO
Butterworth-Heinemann
An imprint of Elsevier Science
Linacre House, Jordan Hill, Oxford OX2 8DP
200 Wheeler Road, Burlington, MA 01803
First published by Arnold 1972
First published as paperback 1977
Second edition published by Arnold 1990
Third edition published by Arnold 1999
Reprinted by Butterworth-Heinemann 2001 (twice), 2002,2003
Copyright Q 1999, T H G Megson. All rights reserved.
The right of T H G Megson to be identified as the authors of this work
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Contents
Preface ix
Preface to Second Edition x..i.
Preface to Third Edition Xlll
Part I Elasticity 1
1 Basic elasticity 3
1.1 Stress 3
1.2 Notation for forces and stresses 5
1.3 Equations of equilibrium 7
1.4 Plane stress 8
1.5 Boundary conditions 9
1.6 Determination of stresses on inclined planes 10
1.7 Principal stresses 11
1.8 Mohr’s circle of stress 12
1.9 Strain 16
1.10 Compatibility equations 19
1.11 Plane strain 20
1.12 Determination of strains on inclined planes 21
1.13 Principal strains 23
1.14 Mohr’s circle of strain 23
1.15 Stress-strain relationships 24
1.16 Experimental measurement of surface strains 28
References 32
Problems 32
2 Two-dimensional problems in elasticity 36
2.1 Two-dimensional problems 37
2.2 Stress functions 38
2.3 Inverse and semi-inverse methods 39
2.4 St. Venant’s principle 42
2.5 Displacements 43
2.6 Bending of an end-loaded cantilever 43
vi Contents
Reference 48
Problems 48
3 Torsion of solid sections 51
3.1 Prandtl stress function solution 51
3.2 St. Venant warping function solution 59
3.3 The membrane analogy 61
3.4 Torsion of a narrow rectangular strip 63
References 65
Problems 65
4 Energy methods of structural analysis 68
4.1 Strain energy and complementary energy 68
4.2 Total potential energy 70
4.3 Principle of virtual work 71
4.4 The principle of the stationary value of the total potential energy 73
4.5 The principle of the stationary value of the total complementary
energy 76
4.6 Application to deflection problems 77
4.7 Application to the solution of statically indetenninate systems 85
4.8 Unit load method 100
4.9 Principle of superposition 103
4.10 The reciprocal theorem 103
4.11 Temperature effects 107
References 109
Further reading 110
Problems 110
5 Bending of thin plates 122
5.1 Pure bending of thin plates 122
5.2 Plates subjected to bending and twisting 125
5.3 Plates subjected to a distributed transverse load 129
5.4 Combined bending and in-plane loading of a thin rectangular plate 137
5.5 Bending of thin plates having a small initial curvature 141
5.6 Energy method for the bending of thin plates 142
Further reading 149
Problems 149
6 Structural instability 152
6.1 Euler buckling of columns 152
6.2 Inelastic buckling 156
6.3 Effect of initial imperfections 160
6.4 Stability of beams under transverse and axial loads 162
6.5 Energy method for the calculation of buckling loads in columns 165
6.6 Buckling of thin plates 169
6.7 Inelastic buckling of plates 173
6.8 Experimental determination of critical load for a flat plate 174
Contents vii
6.9 Local instability 174
6.10 Instability of stiffened panels 175
6.11 Failure stress in plates and stiffened panels i77
6.12 Flexural-torsional buckling of thin-walled columns 180
6.13 Tension field beams 188
References 197
Problems 197
Part I1 Aircraft Structures 209
7 Principles of stressed skin construction 211
7.1 Materials of aircraft construction 21 1
7.2 Loads on structural components 220
7.3 Function of structural components 223
7.4 Fabrication of structural components 225
Problems 232
8 Airworthiness and airframe loads 233
8.1 Factors of safety - flight envelope 233
8.2 Load factor determination 235
8.3 Aircraft inertia loads 238
8.4 Symmetric manoeuvre loads 244
8.5 Normal accelerations associated with various types of manoeuvre 248
8.6 Gust loads 25 1
8.7 Fatigue 257
References 27 1
Further reading 272
Problems 272
9 Bending, shear and torsion of open and closed, thin-walled beams 276
9.1 Bending of open and closed section beams 276
9.2 General stress, strain and displacement relationships for open and
single cell closed section thin-walled beams 29 1
9.3 Shear of open section beams 295
9.4 Shear of closed section beams 300
9.5 Torsion of closed section beams 307
9.6 Torsion of open section beams 316
9.7 Analysis of combined open and closed sections 322
9.8 Structural idealization 327
9.9 Effect of idealization on the analysis of open and closed
section beams 331
9.10 Deflection of open and closed section beams 342
Problems 345
10 Stress analysis of aircraft components 362
10.1 Tapered beams 3 62
10.2 Fuselages 37 4
viii Contents
10.3 Wings 380
10.4 Fuselage frames and wing ribs 406
10.5 Cut-outs in wings and fuselages 415
10.6 Laminated composite structures 425
Reference 432
Further reading 432
Problems 432
11 Structural constraint 443
11 .1 General aspects of structural constraint 443
11.2 Shear stress distribution at a built-in end of a closed section beam 445
11 .3 Thin-walled rectangular section beam subjected to torsion 449
11.4 Shear lag 455
11.5 Constraint of open section beams 465
References 485
Problems 486
12 Matrix methods of structural analysis 494
12.1 Notation 495
12.2 Stiffness matrix for an elastic spring 496
12.3 Stiffness matrix for two elastic springs in line 497
12.4 Matrix analysis of pin-jointed frameworks 500
12.5 Application to statically indeterminate frameworks 507
12.6 Matrix analysis of space frames 507
12.7 Stiffness matrix for a uniform beam 509
12.8 Finite element method for continuum structures 516
References 533
Further reading 533
Problems 533
13 Elementary aeroelasticity 540
13.1 Load distribution and divergence 54 1
13.2 Control effectiveness and reversal 546
13.3 Structural vibration 55 1
13.4 Introduction to ‘flutter’ 568
References 576
Problems 577
Index 582
Preface
During my experience of teaching aircraft structures I have felt the need for a text-
book written specifically for students of aeronautical engineering. Although there
have been a number of excellent books written on the subject they are now either
out of date or too specialist in content to fulfil the requirements of an undergraduate
textbook. My aim, therefore, has been to fill this gap and provide a completely self-
contained course in aircraft structures which contains not only the fundamentals of
elasticity and aircraft structural analysis but also the associated topics of airworthi-
ness and aeroelasticity.
The book is intended for students studying for degrees, Higher National Diplomas
and Higher National Certificates in aeronautical engineering and will be found of
value to those students in related courses who specialize in structures. The subject
matter has been chosen to provide the student with a textbook which will take him
from the beginning of the second year of his course, when specialization usually
begins, up to and including his final examination. I have arranged the topics so
that they may be studied to an appropriate level in, say, the second year and then
resumed at a more advanced stage in the final year; for example, the instability of
columns and beams may be studied as examples of structural instability at second
year level while the instability of plates and stiffened panels could be studied in the
final year. In addition, I have grouped some subjects 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 the fact that they are just
different loading cases of basic structural components rather than isolated topics. I
realize however that the modern trend is to present methods of analysis in general
terms and then consider specific applications. Nevertheless, I feel that in cases
such as those described above it is beneficial for the student’s understanding of the
subject to see the close relationships and similarities amongst the different portions
of theory.
Part I of the book, ‘Fundamentals of Elasticity’, Chapters 1-6, includes sufficient
elasticity theory to provide the student with the basic tools of structural analysis.
The work is standard but the presentation in some instances is original. In Chapter
4 I have endeavoured 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 energy methods are employed. Thus, although a variety of methods are dis-
cussed, emphasis is placed on the methods of complementary and potential energy.
