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1 Characteristics of Aircraft Structures and Materials1

1.1 Introduction 1

1.2 Basic Structural Elements in Aircraft Structure 2

1.2.1 Axial Member 2

1.2.2 Shear Panel 4

1.2.3 Bending Member （Beam） 5

1.2.4 Torsion Member 7

1.3 Wing and Fuselage 8

1.3.1 Load Transfer 9

1.3.2 Wing Structure 10

1.3.3 Fuselage 11

1.4 Aircraft Materials 12

Problems 17

2 Introduction to Elasticity19

2.1 Concept of Displacement 19

2.2 Strain 21

2.3 Stress 25

2.4 Equations of Equilibrium in a Nonuniform Stress Field 28

2.5 Principal Stress 31

2.6 Shear Stress 34

2.7 Revisit of Transformation of Stress 36

2.8 Linear Stress-Strain Relations 38

2.8.1 Strains Induced by Normal Stress 39

2.8.2 Strains Induced by Shear Stress 42

2.8.3 Three-Dimensional Stress-Strain Relations 43

2.9 Elastic Strain Energy 47

2.10 Plane Elasticity 49

2.10.1 Stress-Strain Relations for Plane Isotropic Solids 50

2.10.2 Stress-Strain Relations for Orthotropic Solids in Plane Stress 53

2.10.3 Governing Equations 54

2.10.4 Solution by Airy Stress Function for Plane Isotropic Solids 56

Problems 57

3 Torsion63

3.1 Saint-Venant’s Principle 63

3.2 Torsion of Uniform Bars 67

3.3 Bars with Circular Cross-Sections 74

3.4 Bars with Narrow Rectangular Cross-Sections 77

3.5 Closed Single-Cell Thin-Walled Sections 81

3.6 Multicell Thin-Walled Sections 91

3.7 Warping in Open Thin-Walled Sections 96

3.8 Warping in Closed Thin-Walled Sections 101

3.9 Effect of End Constraints 103

Problems 110

4 Bending and Flexural Shear115

4.1 Derivation of the Simple （Bernoulli-Euler） Beam Equation 115

4.2 Bidirectional Bending 120

4.3 Transverse Shear Stress due to Transverse Force in Symmetric Sections 128

4.3.1 Narrow Rectangular Cross-Section 128

4.3.2 General Symmetric Sections 130

4.3.3 Thin-Walled Sections 132

4.3.4 Shear Deformation in Thin-Walled Sections 133

4.4 Timoshenko Beam Theory 136

4.5 Shear Lag 140

Problems 144

5 Flexural Shear Flow in Thin-Walled Sections149

5.1 Flexural Shear Flow in Open Thin-Walled Sections 149

5.1.1 Symmetric Thin-Walled Sections 150

5.1.2 Unsymmetric Thin-Walled Sections 155

5.1.3 Multiple Shear Flow Junctions 157

5.1.4 Selection of Shear Flow Contour 158

5.2 Shear Center in Open Sections 159

5.3 Closed Thin-Walled Sections and Combined Flexural and Torsional Shear Flow 165

5.3.1 Shear Center 167

5.3.2 Statically Determinate Shear Flow 171

5.4 Closed Multicell Sections 173

Problems 177

6 Failure Criteria for Isotropic Materials183

6.1 Strength Criteria for Brittle Materials 183

6.1.1 Maximum Principal Stress Criterion 184

6.1.2 Coulomb-Mohr Criterion 184

6.2 Yield Criteria for Ductile Materials 186

6.2.1 Maximum Shear Stress Criterion （Tresca Yield Criterion） in Plane Stress 187

6.2.2 Maximum Distortion Energy Criterion （von Mises Yield Criterion） 188

6.3 Fracture Mechanics 193

6.3.1 Stress Concentration 193

6.3.2 Concept of Cracks and Strain Energy Release Rate 194

6.3.3 Fracture Criterion 196

6.4 Stress Intensity Factor 201

6.4.1 Symmetric Loading （Mode I Fracture） 201

6.4.2 Antisymmetric Loading （Mode Ⅱ Fracture） 204

6.4.3 Relation between K and G 206

6.4.4 Mixed Mode Fracture 210

6.5 Effect of Crack Tip Plasticity 211

6.6 Fatigue Failure 214

6.6.1 Constant Stress Amplitude 215

6.6.2 S-N Curves 215

6.6.3 Variable Amplitude Loading 216

6.7 Fatigue Crack Growth 217

Problems 219

7 Elastic Buckling225

7.1 Eccentrically Loaded Beam-Column 225

7.2 Elastic Buckling of Straight Bars 227

7.2.1 Pinned-Pinned Bar 228

7.2.2 Clamped-Free Bar 231

7.2.3 Clamped-Pinned Bar 232

7.2.4 Clamped-Clamped Bar 234

7.2.5 Effective Length of Buckling 235

7.3 Initial Imperfection 236

7.4 Postbuckling Behavior 238

7.5 Bar of Unsymmetric Section 244

7.6 Torsional-Flexural Buckling of Thin-Walled Bars 246

7.6.1 Nonuniform Torsion 246

7.6.2 Torsional Buckling of Doubly Symmetric Section 248

7.6.3 Torsional-Flexural Buckling 251

7.7 Elastic Buckling of Flat Plates 256

7.7.1 Governing Equation for Flat Plates 256

7.7.2 Cylindrical Bending 258

7.7.3 Buckling of Rectangular Plates 259

7.7.4 Buckling under Shearing Stresses 263

7.8 Local Buckling of Open Sections 264

Problems 266

8 Analysis of Composite Laminates271

8.1 Plane Stress Equations for Composite Lamina 271

8.2 Off-Axis Loading 277

8.3 Notation for Stacking Sequence in Laminates 280

8.4 Symmetric Laminate under In-Plane Loading 282

8.5 Effective Moduli for Symmetric Laminates 285

8.6 Laminar Stresses 288

8.7 [±45°] Laminate 290

Problems 292

Index295