CONTENTS vii 5.3 Buckling of Rectangular Sandwich Plates 185 5.3.1 Long Plates 185 5.3.2 Simply Supported Plates-Orthotropic and Symmetrical Layup 187 5.3.3 Face Wrinkling 190 5.4 Free Vibration of Rectangular Sandwich Plates 196 5.4.1 Long Plates 196 5.4.2 Simply Supported Plates-Orthotropic and Symmetrical Layup 199 6 Beams 203 6.1 Governing Equations 203 6.1.1 Boundary Conditions 205 6.1.2 Stiffness Matrix 205 6.1.3 Compliance Matrix 209 6.1.4 Replacement Stiffnesses 210 6.2 Rectangular,Solid Beams Subjected to Axial Load and Bending 210 6.2.1 Displacements-Symmetrical Layup 211 6.2.2 Displacements-Unsymmetrical Layup 213 6.2.3 Stresses and Strains 214 6.3 Thin-Walled,Open-Section Orthotropic or Symmetrical Cross-Section Beams Subjected to Axial Load and Bending 217 6.3.1 Displacements of T-Beams 217 6.3.2 Displacements of L-Beams 221 6.3.3 Displacements of Arbitrary Cross-Section Beams 226 6.3.4 Stresses and Strains 233 6.4 Thin-Walled,Closed-Section Orthotropic Beams Subjected to Axial Load and Bending 243 6.5 Torsion of Thin-Walled Beams 248 6.5.1 Thin Rectangular Cross Section 248 6.5.2 Open-Section Orthotropic Beams 250 6.5.3 Closed-Section Orthotropic Beams-Single Cell 252 6.5.4 Closed-Section Orthotropic Beams-Multicell 260 6.5.5 Restrained Warping-Open-Section Orthotropic Beams 261 6.5.6 Restrained Warping-Closed-Section Orthotropic Beams 264 6.6 Thin-Walled Beams with Arbitrary Layup Subjected to Axial Load,Bending,and Torsion 265 6.6.1 Displacements of Open-and Closed-Section Beams 267 6.6.2 Stresses and Strains in Open-and Closed-Section Beams 268 6.6.3 Centroid 271 6.6.4 Restrained Warping 271 6.7 Transversely Loaded Thin-Walled Beams 274 6.7.1 Beams with Orthotropic Layup or with Symmetrical Cross Section 276 6.7.2 Beams with Arbitrary Layup 280 6.7.3 Shear Center 283 6.8 Stiffened Thin-Walled Beams 288CONTENTS vii 5.3 Buckling of Rectangular Sandwich Plates 185 5.3.1 Long Plates 185 5.3.2 Simply Supported Plates – Orthotropic and Symmetrical Layup 187 5.3.3 Face Wrinkling 190 5.4 Free Vibration of Rectangular Sandwich Plates 196 5.4.1 Long Plates 196 5.4.2 Simply Supported Plates – Orthotropic and Symmetrical Layup 199 6 Beams 203 6.1 Governing Equations 203 6.1.1 Boundary Conditions 205 6.1.2 Stiffness Matrix 205 6.1.3 Compliance Matrix 209 6.1.4 Replacement Stiffnesses 210 6.2 Rectangular, Solid Beams Subjected to Axial Load and Bending 210 6.2.1 Displacements – Symmetrical Layup 211 6.2.2 Displacements – Unsymmetrical Layup 213 6.2.3 Stresses and Strains 214 6.3 Thin-Walled, Open-Section Orthotropic or Symmetrical Cross-Section Beams Subjected to Axial Load and Bending 217 6.3.1 Displacements of T-Beams 217 6.3.2 Displacements of L-Beams 221 6.3.3 Displacements of Arbitrary Cross-Section Beams 226 6.3.4 Stresses and Strains 233 6.4 Thin-Walled, Closed-Section Orthotropic Beams Subjected to Axial Load and Bending 243 6.5 Torsion of Thin-Walled Beams 248 6.5.1 Thin Rectangular Cross Section 248 6.5.2 Open-Section Orthotropic Beams 250 6.5.3 Closed-Section Orthotropic Beams – Single Cell 252 6.5.4 Closed-Section Orthotropic Beams – Multicell 260 6.5.5 Restrained Warping – Open-Section Orthotropic Beams 261 6.5.6 Restrained Warping – Closed-Section Orthotropic Beams 264 6.6 Thin-Walled Beams with Arbitrary Layup Subjected to Axial Load, Bending, and Torsion 265 6.6.1 Displacements of Open- and Closed-Section Beams 267 6.6.2 Stresses and Strains in Open- and Closed-Section Beams 268 6.6.3 Centroid 271 6.6.4 Restrained Warping 271 6.7 Transversely Loaded Thin-Walled Beams 274 6.7.1 Beams with Orthotropic Layup or with Symmetrical Cross Section 276 6.7.2 Beams with Arbitrary Layup 280 6.7.3 Shear Center 283 6.8 Stiffened Thin-Walled Beams 288