Three-Dimensional Beam-Columns of Varying Cross Section

This paper is concerned with three-dimensional rectangular beam-columns whose height and width may vary linearly along their length. The basic four coupled differential equations governing the behavior of three-dimensional beam columns are first rederived using the method of perturbations. These equations are reformulated to include varying cross sections. Finally a 6x6 stiffness matrix (which is sufficient to describe 3-D behavior) is computed by solving the equations 6 times for a sequence of appropriate discontinuities. The finite difference method is employed for that purpose. Timoshenko's closed form solution of a tapered column is chosen for establishing confidence in the proposed formulation.