Page 7 - Aircraft Stuctures for Engineering Student

vi Contents

Reference 48
Problems 48

3 Torsion of solid sections 51
3.1 Prandtl stress function solution 51
3.2 St. Venant warping function solution 59
3.3 The membrane analogy 61
3.4 Torsion of a narrow rectangular strip 63
References 65
Problems 65

4 Energy methods of structural analysis 68
4.1 Strain energy and complementary energy 68
4.2 Total potential energy 70
4.3 Principle of virtual work 71
4.4 The principle of the stationary value of the total potential energy 73
4.5 The principle of the stationary value of the total complementary
energy 76
4.6 Application to deflection problems 77
4.7 Application to the solution of statically indetenninate systems 85
4.8 Unit load method 100
4.9 Principle of superposition 103
4.10 The reciprocal theorem 103
4.11 Temperature effects 107
References 109
Further reading 110
Problems 110

5 Bending of thin plates 122
5.1 Pure bending of thin plates 122
5.2 Plates subjected to bending and twisting 125
5.3 Plates subjected to a distributed transverse load 129
5.4 Combined bending and in-plane loading of a thin rectangular plate 137
5.5 Bending of thin plates having a small initial curvature 141
5.6 Energy method for the bending of thin plates 142
Further reading 149
Problems 149
6 Structural instability 152
6.1 Euler buckling of columns 152
6.2 Inelastic buckling 156
6.3 Effect of initial imperfections 160
6.4 Stability of beams under transverse and axial loads 162
6.5 Energy method for the calculation of buckling loads in columns 165
6.6 Buckling of thin plates 169
6.7 Inelastic buckling of plates 173
6.8 Experimental determination of critical load for a flat plate 174