A Simple Method for Elastic Analysis of Grillages

The theory of beams supported by elastic foundations has been shown to be particularly well-suited to the analysis of grillage beams [1, 2, 3[.2 This theory leads to a far more general formulation regarding the types of structures amenable to analysis than that offered by the orthotropic plate theory. As compared to the methods of finite element theory, the theory of beams supported by elastic foundations decreases the computer time by an order of magnitude, thus making the analysis particularly valuable as a design tool. This paper shows that the measurement of the grillage beam analysis based upon the elastic foundation concept can be further simplified by certain matrix transformations that uncouple the deflection equations. The problem has, in fact, been simplified to such an extent that many large grillages can be analyzed with the aid of a desk calculator. Whenever comparison with results obtained from finite element methods has been possible, it has been found that, for all practical purposes, complete correlation exists.