Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets

A new, generalized Bernoulli/Timoshenko finite beam element on a two-parameter elastic foundation is presented. The element stiffness matrix is based on the exact solution of the differential equation governing displacements, and possesses the ability for an optional consideration of shear deformations, semi-rigid connections, and rigid offsets. In addition to the proposed stiffness matrix, equivalent element nodal load vectors are developed for handling the external uniform loading and linear temperature variations. The usefulness of the new element in the analysis of reinforced concrete or steel structures is documented by three numerical examples.