Elastostatic interaction analysis of frames resting on homogeneous elastic half-space

The structural response of a building to applied loads depends on the behaviour of the soil supporting the structure. Structures may undergo various support deflections dependant on their support conditions. Such deflections are associated with soil deformation: the short-term deflections are known as the elastic component and, the long-term deflections are known as the permanent plastic component. Differential support displacements cause structural interaction between supports. To analyse such interaction, there are different approaches; it can be analytical or numerical, static or dynamic and deterministic or probabilistic, with the rigour in the analysis being commensurate to the degree of displacement likely to be experienced. Mathematical rigour, however, may or may not be justified if inadequate knowledge of parameters exists. In the context of the natural variability of constituent parameters, a closer examination of the soil parameters associated with this interaction, particularly for plane frame structures, is warranted. The behaviour of soil media at a structure's supports during structural analysis has been the focus of much investigation and research over the last century. Efforts have been made to describe such interaction and many computer packages have been developed to incorporate different soil models with the structural studies. Unfortunately the models are usually too complex or require too much input data for easy use by professional engineers. This study focuses on the interaction context through a linear elastostatic and deterministic analysis of plane frame structures with different soil idealisations. The study concentrates on the behaviour of a space frame structure that is constructed by a number of typical plane frames in a parallel series subjected to individual loads. A homogeneous elastic half space is utilised for the soil support. A displacement-type analytical-numerical technique of elastic solution is used to evaluate support interaction. In this approach, the behaviour of soil is modelled by means of homogenous, elastic half-space, whilst in the analysis of the structure, a Direct Stiffness Method is applied. The Boussinesq and Cerruti force-displacement solutions are used for isotropic behaviour, whilst the Gerrard-Wardle and Gerrard-Harrison models are used for cross-anisotropic behaviour. The flexibility matrix of the elastic half-space, related to the interaction forces is developed. The author has prepared an integrated software program to perform the analysis on a desktop PC. The interaction results of the support were analysed for sensitivity to the soil parameters. A number of typical soil parameters were considered for Winkler, isotropic and cross-anisotropic soil models in the structural analysis. Analysis outputs were shown in graphs and tables and were used to investigate for sensitivity of interaction to different soil parameters. Finally, the conclusion of the research work is drawn and the recommendation for further research study is suggested.