Stiffness of beam-columns on elastic foundation with exact shape functions

Exact shape functions from the solution of the governing differential equation are used to determine the stiffness and equivalent joint load matrices for a beam-column finite element resting on a Winkler-type elastic foundation. The degrees of freedom at the nodes are assumed to be lateral displacement and flexural rotation. The formulation is verified by analyzing a continuous beam-column, and the results are compared with an existing solution. A FORTRAN subroutine that generates the stiffness matrix and equivalent joint forces is appended. This subroutine can be easily incorporated into existing finite element or frame analysis programs.