Analysis of plates on elastic foundations



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Texas Tech University


Concrete slabs (plates) supported directly by the soil continuum is a very common construction form. The behavior of the slab when it carries external loads is influenced by the soil, and the behavior of the soil is, in turn, influenced by the action of the slab under load. Developing a realistic mathematical model for this complex soil-structure interaction problem is essential in order to provide safe and economical designs. In the past, many researchers have worked on this problem, which is referred to as "beams and plates on elastic foundations." In many practical design problems of this type, the soil continuum is layered and may be resting over rigid rock or a relatively stronger soil

Most of die previous work began with the well known Winkler model, which was originally developed for the analysis of railroad tracks. The use of the Winkler model involves one major problem and one significant behavioral inconsistency. The problem involves the necessity for determining the modulus of subgrade reaction, "k," and the behavioral inconsistency is that an analysis of plates carrying a uniformly distributed load will produce a rigid body displacement.

Vlasov and Leont'ev (1966), recognizing die difficulty in determining values of "k" for soils, as well as the behavioral inconsistency, postulated a two-parameter model Vlasov's model provided for die effect of die neglected shear strain energy in the soil and die subsequent shear forces on die plate edges as a result of the soil displacement Recent work by Vallabhan and Das (1987, 1988, 1989) strengthened die Vlasov postulation for beams on elastic foundations but stopped short of developing computational techniques for plates.

This research develops a three-parameter mathematical model for die analysis of plates on elastic foundations. The involved equations are explained in a step-by-step manner. The procedures developed are then used in a computer program to perform the analysis. The necessity of determining die value of "k" and die soil shear parameter, "t," is avoided through the computation of a third parameter, “y," which provides a deformation profile for the soil continuum.