Introduction to Aircraft Structural Analysis

726 Pages·2013·10.59 MB·English

by  T.H.G. Megson

Introduction to Aircraft
Structural Analysis
Second Edition
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Introduction to Aircraft
Structural Analysis
Second Edition
T. H. G. Megson
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Contents
Preface..................................................................................................................................................xi
PART A FUNDAMENTALS OF STRUCTURAL ANALYSIS
Section A1 Elasticity...........................................................................3
CHAPTER 1 Basic elasticity...............................................................................................5
1.1 Stress...........................................................................................................................5
1.2 Notation for forces and stresses.................................................................................7
1.3 Equations of equilibrium............................................................................................9
1.4 Plane stress...............................................................................................................11
1.5 Boundary conditions.................................................................................................11
1.6 Determination of stresses on inclined planes..........................................................12
1.7 Principal stresses......................................................................................................15
1.8 Mohr’s circle of stress.............................................................................................17
1.9 Strain.........................................................................................................................22
1.10 Compatibility equations...........................................................................................25
1.11 Plane strain...............................................................................................................26
1.12 Determination of strains on inclined planes............................................................27
1.13 Principal strains........................................................................................................29
1.14 Mohr’s circle of strain.............................................................................................30
1.15 Stress–strain relationships........................................................................................30
1.16 Experimental measurement of surface strains.........................................................37
References.................................................................................................................43
Problems...................................................................................................................43
CHAPTER 2 Two-dimensional problems in elasticity.........................................................47
2.1 Two-dimensional problems......................................................................................47
2.2 Stress functions.........................................................................................................49
2.3 Inverse and semi-inverse methods...........................................................................50
2.4 St. Venant’s principle...............................................................................................56
2.5 Displacements...........................................................................................................57
2.6 Bending of an end-loaded cantilever.......................................................................58
Reference..................................................................................................................63
Problems...................................................................................................................63
CHAPTER 3 Torsion of solid sections...............................................................................69
3.1 Prandtl stress function solution................................................................................69
3.2 St. Venant warping function solution......................................................................81
v
vi Contents
3.3 The membrane analogy............................................................................................82
3.4 Torsion of a narrow rectangular strip......................................................................84
References.................................................................................................................86
Problems...................................................................................................................87
Section A2 Virtual work, energy, and matrix methods .........................89
CHAPTER 4 Virtual work and energy methods..................................................................91
4.1 Work.........................................................................................................................91
4.2 Principle of virtual work..........................................................................................92
4.3 Applications of the principle of virtual work.......................................................106
Reference................................................................................................................117
Problems.................................................................................................................118
CHAPTER 5 Energy methods..........................................................................................123
5.1 Strain energy and complementary energy.............................................................123
5.2 Principle of the stationary value of the total complementary
energy.....................................................................................................................125
5.3 Application to deflection problems.......................................................................126
5.4 Application to the solution of statically indeterminate systems...........................135
5.5 Unit load method....................................................................................................152
5.6 Flexibility method..................................................................................................155
5.7 Total potential energy............................................................................................160
5.8 Principle of the stationary value of the total potential energy.............................161
5.9 Principle of superposition......................................................................................164
5.10 Reciprocal theorem................................................................................................164
5.11 Temperature effects................................................................................................168
References...............................................................................................................171
Problems.................................................................................................................171
CHAPTER 6 Matrix methods...........................................................................................183
6.1 Notation..................................................................................................................184
6.2 Stiffness matrix for an elastic spring.....................................................................185
6.3 Stiffness matrix for two elastic springs in line.....................................................186
6.4 Matrix analysis of pin-jointed frameworks...........................................................189
6.5 Application to statically indeterminate frameworks.............................................196
6.6 Matrix analysis of space frames............................................................................196
6.7 Stiffness matrix for a uniform beam.....................................................................198
6.8 Finite element method for continuum structures..................................................205
References...............................................................................................................223
Further reading.......................................................................................................223
Problems.................................................................................................................223
Contents vii
Section A3 Thin plate theory............................................................231
CHAPTER 7 Bending of thin plates.................................................................................233
7.1 Pure bending of thin plates....................................................................................233
7.2 Plates subjected to bending and twisting..............................................................236
7.3 Plates subjected to a distributed transverse load..................................................240
7.4 Combined bending and in-plane loading of a thin rectangular plate...................250
7.5 Bending of thin plates having a small initial curvature.......................................254
7.6 Energy method for the bending of thin plates......................................................255
Further reading.......................................................................................................263
Problems.................................................................................................................263
Section A4 Structural instability.......................................................267
CHAPTER 8 Columns.....................................................................................................269
8.1 Euler buckling of columns.....................................................................................269
8.2 Inelastic buckling...................................................................................................275
8.3 Effect of initial imperfections................................................................................279
8.4 Stability of beams under transverse and axial loads............................................282
8.5 Energy method for the calculation of buckling loads in columns.......................286
8.6 Flexural–torsional buckling of thin-walled columns............................................289
References...............................................................................................................301
Problems.................................................................................................................302
CHAPTER 9 Thin plates.................................................................................................311
9.1 Buckling of thin plates...........................................................................................311
9.2 Inelastic buckling of plates....................................................................................314
9.3 Experimental determination of the critical load for a flat plate..........................316
9.4 Local instability......................................................................................................316
9.5 Instability of stiffened panels................................................................................317
9.6 Failure stress in plates and stiffened panels..........................................................319
9.7 Tension field beams...............................................................................................322
References...............................................................................................................338
Problems.................................................................................................................338
PART B ANALYSIS OF AIRCRAFT STRUCTURES
Section B1 Principles of stressed skin
construction......................................................................................345
CHAPTER 10 Materials...................................................................................................347
10.1 Aluminum alloys....................................................................................................347
viii Contents
10.2 Steel........................................................................................................................349
10.3 Titanium..................................................................................................................350
10.4 Plastics....................................................................................................................351
10.5 Glass.......................................................................................................................351
10.6 Composite materials...............................................................................................351
10.7 Properties of materials...........................................................................................353
Problems.................................................................................................................368
CHAPTER 11 Structural components of aircraft................................................................371
11.1 Loads on structural components............................................................................371
11.2 Function of structural components........................................................................373
11.3 Fabrication of structural components....................................................................378
11.4 Connections............................................................................................................383
Reference................................................................................................................389
Problems.................................................................................................................389
Section B2 Airworthiness and airframe loads....................................393
CHAPTER 12 Airworthiness.............................................................................................395
12.1 Factors of the safety-flight envelope.....................................................................395
12.2 Load factor determination......................................................................................397
Reference................................................................................................................400
Problems.................................................................................................................400
CHAPTER 13 Airframe loads............................................................................................401
13.1 Aircraft inertia loads..............................................................................................401
13.2 Symmetric maneuver loads....................................................................................407
13.3 Normal accelerations associated with various types
of maneuver............................................................................................................412
13.4 Gust loads...............................................................................................................416
References...............................................................................................................424
Problems.................................................................................................................424
CHAPTER 14 Fatigue.......................................................................................................431
14.1 Safe life and fail-safe structures............................................................................431
14.2 Designing against fatigue.......................................................................................432
14.3 Fatigue strength of components.............................................................................433
14.4 Prediction of aircraft fatigue life...........................................................................439
14.5 Crack propagation..................................................................................................445
References...............................................................................................................452
Further reading.......................................................................................................452
Problems.................................................................................................................452