FINITE BEAMS ON INFINITE 2-PARAMETER ELASTIC FOUNDATIONS

A simple procedure is presented for solving the problem of a beam supported on an infinite two-parameter foundation and subjected to arbitrary external loads. It is shown that the problem can be analyzed by replacing the exterior region by a concentrated spring at each end of the beam, whose stiffness is given by the square root of the product of the elastic constants of the two-parameter model, and by solving the resulting finite beam-foundation problem by existing finite element techniques. Numerical results indicate that the foundation material outside the beam can affect the response of the beam itself. The extent of this interaction depends, in general, on the beam geometry, on the relative values of the beam and foundations stiffness parameters, and on the applied loads. The procedure can be extended to the analysis of plane frames supported on homogeneous and inhomogeneous two-parameter foundations.