An introduction to aircraft structural analysis / T.H.G. Megson.

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
PART A FUNDAMENTALS OF STRUCTURAL ANALYSIS
CHAPTER 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 ........................................................................................... 9
1.5 Boundary Conditions ................................................................................ 9
1.6 Determination of Stresses on Inclined Planes .................................................... 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 Inclined Planes...................................................... 25
1.13 Principal Strains ...................................................................................... 27
1.14 Mohr’s Circle of Strain .............................................................................. 28
1.15 Stress–Strain Relationships ......................................................................... 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. VenantWarping Function Solution ............................................................ 75
3.3 The Membrane Analogy ............................................................................ 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 of VirtualWork ........................................................................... 86
4.3 Applications of the Principle of VirtualWork .................................................... 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
iv Contents
5.3 Application to Deflection Problems ............................................................... 114
5.4 Application to the Solution of Statically Indeterminate Systems............................... 122
5.5 Unit Load Method ................................................................................... 138
5.6 Flexibility Method ................................................................................... 141
5.7 Total Potential Energy ............................................................................... 147
5.8 The Principle of the Stationary Value of the Total Potential Energy ........................... 148
5.9 Principle of Superposition .......................................................................... 151
5.10 The Reciprocal Theorem............................................................................ 151
5.11 Temperature Effects ................................................................................. 156
Problems .............................................................................................. 158
CHAPTER 6 Matrix Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.1 Notation ............................................................................................... 170
6.2 Stiffness Matrix for an Elastic Spring ............................................................. 171
6.3 Stiffness Matrix for Two Elastic Springs in Line................................................. 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 Pure Bending of Thin Plates ........................................................................ 219
7.2 Plates Subjected to Bending and Twisting ........................................................ 223
7.3 Plates Subjected to a Distributed Transverse Load............................................... 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 Energy Method for the Bending of Thin Plates .................................................. 241
Problems .............................................................................................. 250
CHAPTER 8 Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
8.1 Euler Buckling of Columns ......................................................................... 253
8.2 Inelastic Buckling .................................................................................... 259
8.3 Effect of Initial Imperfections ...................................................................... 263
8.4 Stability of Beams under Transverse and Axial Loads .......................................... 266
8.5 Energy Method for the Calculation of Buckling Loads in Columns ........................... 270
8.6 Flexural–Torsional Buckling of Thin-Walled Columns ......................................... 274
Problems .............................................................................................. 287
CHAPTER 9 Thin Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
9.1 Buckling of Thin Plates ............................................................................. 293
9.2 Inelastic Buckling 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
Contents v
PART B ANALYSIS OF AIRCRAFT STRUCTURES
CHAPTER 10 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
10.1 Aluminum Alloys .................................................................................... 327
10.2 Steel ................................................................................................... 329
10.3 Titanium............................................................................................... 330
10.4 Plastics ................................................................................................ 331
10.5 Glass ................................................................................................... 331
10.6 Composite Materials................................................................................. 331
10.7 Properties of Materials .............................................................................. 333
Problems .............................................................................................. 349
CHAPTER 11 Structural Components of Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
11.1 Loads on Structural Components .................................................................. 351
11.2 Function of Structural Components................................................................ 354
11.3 Fabrication of Structural Components ............................................................. 359
11.4 Connections........................................................................................... 363
Problems .............................................................................................. 370
CHAPTER 12 Airworthiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
12.1 Factors of Safety-Flight Envelope ................................................................. 373
12.2 Load Factor Determination ......................................................................... 375
CHAPTER 13 Airframe Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
13.1 Aircraft Inertia Loads................................................................................ 379
13.2 Symmetric Maneuver Loads ........................................................................ 386
13.3 Normal Accelerations Associated with Various Types of Maneuver .......................... 391
13.4 Gust Loads ............................................................................................ 393
Problems .............................................................................................. 399
CHAPTER 14 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
14.1 Safe Life and Fail-Safe Structures ................................................................. 403
14.2 Designing Against Fatigue .......................................................................... 404
14.3 Fatigue Strength of Components ................................................................... 405
14.4 Prediction of Aircraft Fatigue Life................................................................. 409
14.5 Crack Propagation ................................................................................... 414
Problems .............................................................................................. 420
CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
15.1 Symmetrical Bending................................................................................ 424
15.2 Unsymmetrical Bending ............................................................................ 433
15.3 Deflections due to Bending ......................................................................... 441
15.4 Calculation of Section Properties .................................................................. 456
15.5 Applicability of Bending Theory................................................................... 466
15.6 Temperature Effects ................................................................................. 466
Problems .............................................................................................. 471
CHAPTER 16 Shear of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
16.1 General Stress, Strain, and Displacement Relationships for Open
and Single Cell Closed Section Thin-Walled Beams ............................................ 479
16.2 Shear of Open Section Beams ...................................................................... 483
vi Contents
16.3 Shear of Closed Section Beams .................................................................... 488
Problems .............................................................................................. 496
CHAPTER 17 Torsion of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
17.1 Torsion of Closed Section Beams .................................................................. 503
17.2 Torsion of Open Section Beams.................................................................... 514
Problems .............................................................................................. 521
CHAPTER 18 Combined Open and Closed Section Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
18.1 Bending ............................................................................................... 529
18.2 Shear................................................................................................... 529
18.3 Torsion ................................................................................................ 533
Problems .............................................................................................. 534
CHAPTER 19 Structural Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
19.1 Principle............................................................................................... 537
19.2 Idealization of a Panel ............................................................................... 538
19.3 Effect of Idealization on the Analysis of Open and Closed Section Beams................... 541
19.4 Deflection of Open and Closed Section Beams .................................................. 553
Problems .............................................................................................. 556
CHAPTER 20 Wing Spars and Box Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
20.1 TaperedWing Spar................................................................................... 561
20.2 Open and Closed Section Beams................................................................... 565
20.3 Beams Having Variable Stringer Areas............................................................ 571
Problems .............................................................................................. 574
CHAPTER 21 Fuselages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
21.1 Bending ............................................................................................... 577
21.2 Shear................................................................................................... 578
21.3 Torsion ................................................................................................ 581
21.4 Cutouts in Fuselages ................................................................................. 584
Problems .............................................................................................. 585
CHAPTER 22 Wings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
22.1 Three-Boom Shell ................................................................................... 587
22.2 Bending ............................................................................................... 588
22.3 Torsion ................................................................................................ 590
22.4 Shear................................................................................................... 594
22.5 Shear Center .......................................................................................... 599
22.6 TaperedWings........................................................................................ 600
22.7 Deflections ............................................................................................ 603
22.8 Cutouts inWings ..................................................................................... 605
Problems .............................................................................................. 613
CHAPTER 23 Fuselage Frames and Wing Ribs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619
23.1 Principles of Stiffener/Web Construction ......................................................... 619
23.2 Fuselage Frames ..................................................................................... 625
23.3 Wing Ribs ............................................................................................. 626
Problems .............................................................................................. 630
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

Includes bibliographical references and index.