Abstract

The ‘exact’ stiffness matrix of a beam element resting on a linear one-parameter medium with a variable subgrade modulus is derived and utilized for an iterative analysis of beams resting on nonlinear media. Owing to the nature of the series solution approach adopted in developing the stiffness matrix and fixed-end actions vector of the new element, the nonlinear behaviour of soil can be represented by any continuous pressure-deflection model and the span load by any continuous function. Numerical comparisons with existing closed form and approximate solutions of special cases verify the accuracy and efficiency of the proposed element and analysis procedure. The worked examples demonstrate the effects of incorporating the soil nonlinearity on the behaviour of both the substructure and the superstructure.

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