Static and Dynamic Analyses of Beam-Columns on Winkler Foundation

Abstract

A finite element model is developed for static, free and forced vibration analyses of a compressed beam resting on a Winkler-type elastic foundation and subjected to transverse loads. The homogeneous solution of the governing differential equation of static equilibrium is used as shape functions when deriving the load vector, the stiffness and mass matrices. For the static case, a procedure is outlined for improving the internal distributions of deflections, rotations, bending moments and shear forces of the structure. In this procedure, exact results are obtained for concentrated, uniform and ramp distributed loads with a minimum number of elements. When considering free vibrations, natural frequencies converge rapidly with increasing numbers of elements, and are shown to agree with results obtained by other analytical methods. The effects of the axial load and elastic foundation on the natural frequencies are also illustrated. For forced vibrations, the Newmark β Method is employed for obtaining the time history response of a beam-column on an elastic foundation subjected to lateral time-dependent excitations and constant axial load.