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PART A FUNDAMENTALS OF STRUCTURAL ANALYSIS3

Section A1 Elasticity3

CHAPTER 1 Basic elasticity5

1.1 Stress5

1.2 Notation for forces and stresses7

1.3 Equations of equilibrium9

1.4 Plane stress11

1.5 Boundary conditions11

1.6 Determination of stresses on inclined planes12

1.7 Principal stresses15

1.8 Mohr’s circle of stress17

1.9 Strain22

1.10 Compatibility equations25

1.11 Plane strain26

1.12 Determination of strains on inclined planes27

1.13 Principal strains29

1.14 Mohr’s circle of strain30

1.15 Stress-strain relationships30

1.16 Experimental measurement of surface strains37

Reference43

Problems43

CHAPTER 2 Two-dimensional problems in elasticity47

2.1 Two-dimensional problems47

2.2 Stress functions49

2.3 Inverse and semi-inverse methods50

2.4 St.Venant’s principle56

2.5 Displacements57

2.6 Bending of an end-loaded cantilever58

Reference63

Problems63

CHAPTER 3 Torsion of solid sections69

3.1 Prandtl stress function solution69

3.2 St.Venant warping function solution81

3.3 The membrane analogy82

3.4 Torsion of a narrow rectangular strip84

References86

Problems87

Section A2 Virtual work，energy，and matrix methods89

CHAPTER 4 Virtual work and energy methods91

4.1 Work91

4.2 Principle of virtual work92

4.3 Applications of the principle of virtual work106

Reference117

Problems118

CHAPTER 5 Energy methods123

5.1 Strain energy and complementary energy123

5.2 Principle of the stationary value of the total complementary energy125

5.3 Application to deflection problems126

5.4 Application to the solution of statically indeterminate systems135

5.5 Unit load method152

5.6 Flexibility method155

5.7 Total potential energy160

5.8 Principle of the stationary value of the total potential energy161

5.9 Principle of superposition164

5.10 Reciprocal theorem164

5.11 Temperature effects168

References171

Further reading171

Problems171

CHAPTER 6 Matrix methods183

6.1 Notation184

6.2 Stiffness matrix for an elastic spring185

6.3 Stiffness matrix for two elastic springs in line186

6.4 Matrix analysis of pin-jointed frameworks189

6.5 Application to statically indeterminate frameworks196

6.6 Matrix analysis of space frames196

6.7 Stiffness matrix for a uniform beam198

6.8 Finite element method for continuum structures205

References223

Further reading223

Problems223

Section A3 Thin plate theory231

CHAPTER 7 Bending of thin plates233

7.1 Pure bending of thin plates233

7.2 Plates subjected to bending and twisting236

7.3 Plates subjected to a distributed transverse load240

7.4 Combined bending and in-plane loading of a thin rectangular plate250

7.5 Bending of thin plates having a small initial curvature254

7.6 Energy method for the bending of thin plates255

Further reading263

Problems263

Section A4 Structural instability267

CHAPTER 8 Columns269

8.1 Euler buckling of columns269

8.2 Inelastic buckling275

8.3 Effect of initial imperfections280

8.4 Stability of beams under transverse and axial loads283

8.5 Energy method for the calculation of buckling loads in columns286

8.6 Flexural-torsional buckling of thin-walled columns290

References302

Problems302

CHAPTER 9 Thin plates311

9.1 Buckling of thin plates311

9.2 Inelastic buckling of plates314

9.3 Experimental determination of the critical load for a flat plate316

9.4 Local instability316

9.5 Instability of stiffened panels317

9.6 Failure stress in plates and stiffened panels319

9.7 Tension field beams323

References339

Problems340

Section A5 Vibration of structures345

CHAPTER 10 Structural vibration347

10.1 Oscillation of mass-spring systems347

10.2 Oscillation of beams356

10.3 Approximate methods for determining natural frequencies361

Problems364

PART B ANALYSIS OF AIRCRAFT STRUCTURES371

Section B1 Principles of stressed skin construction371

CHAPTER 11 Materials373

11.1 Aluminum alloys373

11.2 Steel375

11.3 Titanium376

11.4 Plastics377

11.5 Glass377

11.6 Composite materials377

11.7 Properties of materials379

Problems394

CHAPTER 12 Structural components of aircraft397

12.1 Loads on structural components397

12.2 Function of structural components399

12.3 Fabrication of structural components404

12.4 Connections409

Reference415

Problems415

Section B2 Airworthiness and airframe loads419

CHAPTER 13 Airworthiness421

13.1 Factors of safety-flight envelope421

13.2 Load factor determination423

Reference426

Problems426

CHAPTER 14 Airframe loads427

14.1 Aircraft inertia loads427

14.2 Symmetric maneuver loads433

14.3 Normal accelerations associated with various types of maneuver438

14.4 Gust loads442

References450

Problems450

CHAPTER 15 Fatigue457

15.1 Safe life and fail-safe structures457

15.2 Designing against fatigue458

15.3 Fatigue strength of components459

15.4 Prediction of aircraft fatigue life465

15.5 Crack propagation471

References478

Further reading478

Problems478

Section B3 Bending，shear and torsion of thin-walled beams481

CHAPTER 16 Bending of open and closed，thin-walled beams483

16.1 Symmetrical bending484

16.2 Unsymmetrical bending492

16.3 Deflections due to bending499

16.4 Calculation of section properties514

16.5 Applicability of bending theory523

16.6 Temperature effects523

Reference527

Problems527

CHAPTER 17 Shear of beams537

17.1 General stress，strain，and displacement relationships for open and single-cell closed section thin-walled beams537

17.2 Shear of open section beams541

17.3 Shear of closed section beams550

Reference559

Problems559

CHAPTER 18 Torsion of beams569

18.1 Torsion of closed section beams569

18.2 Torsion of open section beams579

Problems585

CHAPTER 19 Combined open and closed section beams593

19.1 Bending593

19.2 Shear595

19.3 Torsion598

Problems603

CHAPTER 20 Structural idealization605

20.1 Principle605

20.2 Idealization of a panel606

20.3 Effect of idealization on the analysis of open and closed section beams608

20.4 Deflection of open and closed section beams620

Problems623

Section B4 Stress analysis of aircraft components629

CHAPTER 21 Wing spars and box beams631

21.1 Tapered wing spar631

21.2 Open and closed section beams635

21.3 Beams having variable stringer areas640

Problems645

CHAPTER 22 Fuselages649

22.1 Bending649

22.2 Shear651

22.3 Torsion653

22.4 Cut-outs in fuselages655

Problems660

CHAPTER 23 Wings663

23.1 Three-boom shell663

23.2 Bending664

23.3 Torsion665

23.4 Shear670

23.5 Shear center677

23.6 Tapered wings677

23.7 Deflections680

23.8 Cut-outs in wings681

Problems689

CHAPTER 24 Fuselage frames and wing ribs697

24.1 Principles of stiffener/web construction697

24.2 Fuselage frames702

24.3 Wing ribs703

Problems707

CHAPTER 25 Laminated composite structures709

25.1 Elastic constants of a simple lamina709

25.2 Stress-strain relationships for an orthotropic ply （macro approach）715

25.3 Laminates724

25.4 Thin-walled composite beams740

References753

Problems753

Section B5 Structural and loading discontinuities761

CHAPTER 26 Closed section beams763

26.1 General aspects763

26.2 Shear stress distribution at a built-in end of a closed section beam764

26.3 Thin-walled rectangular section beam subjected to torsion770

26.4 Shear lag778

Reference795

Problems795

CHAPTER 27 Open section beams805

27.1 I-section beam subjected to torsion805

27.2 Torsion of an arbitrary section beam807

27.3 Distributed torque loading817

27.4 Extension of the theory to allow for general systems of loading819

27.5 Moment couple （bimoment）822

References825

Problems825

Section B6 Introduction to aeroelasticity831

CHAPTER 28 Wing problems833

28.1 Types of problem833

28.2 Load distribution and divergence834

28.3 Control effectiveness and reversal840

28.4 Introduction to “flutter”846

References853

Problems853

Appendix：Design of a rear fuselage857

Index885