An approximate analysis of a family of double layer grids.

This thesis examines approximate methods of analysis based upon the replacement of planar "trussed members" by analogous prismatic I-beams in double layer diagonal grids. The geometrical properties of the analogous I-beams are, in each case, derived from those of the planar trussed members. The results of an approximate analysis, in which the analogous I-beams are considered to have both flexural and shear rigidity, but no torsional rigidity, are compared with those of an analysis in which the planar trussed members are considered to be constructed from an assembly of members, having axial rigidity only. In all, 216 grid structures are investigated and a detailed inspection of the principal forces and displacements is made, with a view to establishing the validity of the approximate analysis. It is shown that the approximate analysis in most cases is reasonably accurate and that consideration of shear rigidity consistently leads to an improvement in the results. Chapter I defines the nature of the problems and purpose of the investigation. Chapter II contains a detailed description of both the rigorous and approximate analyses and also gives the bounds of the shear coefficient ko for the family of double layer grids examined. Chapters III and IV describe the extent of the analytical investigation, together with a brief description of the computer programme. The conclusions are contained in Chapter V; results not essential to discursive matter are relegated to the Appendix