Mechanics of Aircraft Structures, 2nd Edition

Preface xiii

Preface to the First Edition xv

1 Characteristics of Aircraft Structures and Materials 1

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 Elasticity 19

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 Torsion 63

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 Shear 115

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 Sections 149

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 Materials 183

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 Buckling 225

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 Laminates 271

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

Index 295