Beam‐Column Element on Weak Winkler Foundation

The analysis of beam‐column systems resting on a Winkler foundation is simplified using modern numerical techniques. Recently, finite elements based on the solution of the governing differential equation have been derived for efficient and accurate analysis of such systems. However, the existing elements cannot be applied to beams under high axial loads and resting on a weak foundation. To overcome this limitation, in this paper the shape functions, stiffness matrix, and nodal load vector of a new element are explicitly obtained using the solution of the governing differential equation. Also, for the determination of the displacements and internal forces anywhere along a beam, the complete solution of the differential equation corresponding to some common types of loading is provided. The explicit form of the various expressions provided lends them to easy implementation in existing frame analysis or finite element programs.