Introduction to Aircraft Structural Analysis (eBook)

Front Cover 1
Title Page 2
Copyright Page 3
Table of Contents 4
Preface 8
Part A: Fundamentals of Structural Analysis 10
Chapter 1. Basic Elasticity 12
1.1 Stress 12
1.2 Notation for Forces and Stresses 14
1.3 Equations of Equilibrium 16
1.4 Plane Stress 18
1.5 Boundary Conditions 18
1.6 Determination of Stresses on Inclined Planes 19
1.7 Principal Stresses 23
1.8 Mohr’s Circle of Stress 25
1.9 Strain 29
1.10 Compatibility Equations 33
1.11 Plane Strain 34
1.12 Determination of Strains on Inclined Planes 34
1.13 Principal Strains 36
1.14 Mohr’s Circle of Strain 37
1.15 Stress–Strain Relationships 37
1.16 Experimental Measurement of Surface Strains 46
Problems 50
Chapter 2. Two-Dimensional Problemsin Elasticity 54
2.1 Two-Dimensional Problems 54
2.2 Stress Functions 56
2.3 Inverse and Semi-Inverse Methods 57
2.4 St. Venant’s Principle 62
2.5 Displacements 63
2.6 Bending of an End-Loaded Cantilever 64
Problems 69
Chapter 3. Torsion of Solid Sections 74
3.1 Prandtl Stress Function Solution 74
3.2 St. Venant Warping Function Solution 84
3.3 The Membrane Analogy 86
3.4 Torsion of a Narrow Rectangular Strip 88
Problems 91
Chapter 4. Virtual Work and Energy Methods 94
4.1 Work 94
4.2 Principle of Virtual Work 95
4.3 Applications of the Principle of Virtual Work 108
Problems 116
Chapter 5. Energy Methods 120
5.1 Strain Energy and Complementary Energy 120
5.2 The Principle of the Stationary Value of the Total Complementary Energy 122
5.3 Application to Deflection Problems 123
5.4 Application to the Solution of Statically Indeterminate Systems 131
5.5 Unit Load Method 147
5.6 Flexibility Method 150
5.7 Total Potential Energy 156
5.8 The Principle of the Stationary Value of the Total Potential Energy 157
5.9 Principle of Superposition 160
5.10 The Reciprocal Theorem 160
5.11 Temperature Effects 165
Problems 167
Chapter 6. Matrix Methods 178
6.1 Notation 179
6.2 Stiffness Matrix for an Elastic Spring 180
6.3 Stiffness Matrix for Two Elastic Springs in Line 181
6.4 Matrix Analysis of Pin-jointed Frameworks 185
6.5 Application to Statically Indeterminate Frameworks 192
6.6 Matrix Analysis of Space Frames 192
6.7 Stiffness Matrix for a Uniform Beam 194
6.8 Finite Element Method for Continuum Structures 202
Problems 220
Chapter 7. Bending of Thin Plates 228
7.1 Pure Bending of Thin Plates 228
7.2 Plates Subjected to Bending and Twisting 232
7.3 Plates Subjected to a Distributed Transverse Load 236
7.4 Combined Bending and In-Plane Loading of a Thin Rectangular Plate 245
7.5 Bending of Thin Plates Having a Small Initial Curvature 249
7.6 Energy Method for the Bending of Thin Plates 250
Problems 259
Chapter 8. Columns 262
8.1 Euler Buckling of Columns 262
8.2 Inelastic Buckling 268
8.3 Effect of Initial Imperfections 272
8.4 Stability of Beams under Transverse and Axial Loads 275
8.5 Energy Method for the Calculation of Buckling Loads in Columns 279
8.6 Flexural–Torsional Buckling of Thin-Walled Columns 283
Problems 296
Chapter 9. Thin Plates 302
9.1 Buckling of Thin Plates 302
9.2 Inelastic Buckling of Plates 305
9.3 Experimental Determination of Critical Load for a Flat Plate 307
9.4 Local Instability 308
9.5 Instability of Stiffened Panels 309
9.6 Failure Stress in Plates and Stiffened Panels 311
9.7 Tension Field Beams 313
Problems 329
Part B: Analysis of Aircraft Structures 334
Chapter 10. Materials 336
10.1 Aluminum Alloys 336
10.2 Steel 338
10.3 Titanium 339
10.4 Plastics 340
10.5 Glass 340
10.6 Composite Materials 340
10.7 Properties of Materials 342
Problems 358
Chapter 11. Structural Components of Aircraft 360
11.1 Loads on Structural Components 360
11.2 Function of Structural Components 363
11.3 Fabrication of Structural Components 368
11.4 Connections 372
Problems 379
Chapter 12. Airworthiness 382
12.1 Factors of Safety-Flight Envelope 382
12.2 Load Factor Determination 384
Chapter 13. Airframe Loads 388
13.1 Aircraft Inertia Loads 388
13.2 Symmetric Maneuver Loads 395
13.3 Normal Accelerations Associated with Various Types of Maneuver 400
13.4 Gust Loads 402
Problems 408
Chapter 14. Fatigue 412
14.1 Safe Life and Fail-Safe Structures 412
14.2 Designing Against Fatigue 413
14.3 Fatigue Strength of Components 414
14.4 Prediction of Aircraft Fatigue Life 418
14.5 Crack Propagation 423
Problems 429
Chapter 15. Bending of Open and Closed, Thin-Walled Beams 432
15.1 Symmetrical Bending 433
15.2 Unsymmetrical Bending 442
15.3 Deflections due to Bending 450
15.4 Calculation of Section Properties 465
15.5 Applicability of Bending Theory 475
15.6 Temperature Effects 475
Problems 480
Chapter 16. Shear of Beams 488
16.1 General Stress, Strain, and Displacement Relationships for Openand Single Cell Closed Section Thin-Walled Beams 488
16.2 Shear of Open Section Beams 492
16.3 Shear of Closed Section Beams 497
Problems 505
Chapter 17. Torsion of Beams 512
17.1 Torsion of Closed Section Beams 512
17.2 Torsion of Open Section Beams 523
Problems 530
Chapter 18. Combined Open and Closed Section Beams 538
18.1 Bending 538
18.2 Shear 538
18.3 Torsion 542
Problems 543
Chapter 19. Structural Idealization 546
19.1 Principle 546
19.2 Idealization of a Panel 547
19.3 Effect of Idealization on the Analysis of Open and Closed Section Beams 550
19.4 Deflection of Open and Closed Section Beams 562
Problems 565
Chapter 20. Wing Spars and Box Beams 570
20.1 Tapered Wing Spar 570
20.2 Open and Closed Section Beams 574
20.3 Beams Having Variable Stringer Areas 580
Problems 583
Chapter 21. Fuselages 586
21.1 Bending 586
21.2 Shear 587
21.3 Torsion 590
21.4 Cutouts in Fuselages 593
Problems 594
Chapter 22. Wings 596
22.1 Three-Boom Shell 596
22.2 Bending 597
22.3 Torsion 599
22.4 Shear 603
22.5 Shear Center 608
22.6 Tapered Wings 609
22.7 Deflections 612
22.8 Cutouts in Wings 614
Problems 622
Chapter 23. Fuselage Frames and Wing Ribs 628
23.1 Principles of Stiffener/Web Construction 628
23.2 Fuselage Frames 634
23.3 Wing Ribs 635
Problems 639
Index 642