Finite Element Solutions of Deep Beams

Abstract

The finite element solutions of deep beams are presented. Two types of deep beam elements are introduced. The first element simulates the exact analytical solution of the deep beam of rectangular cross section. The element stiffness matrix is developed by solving the plane stress elasticity equations with the selection of the proper boundary conditions. The second element simulates the approximate solution of the deep beam of arbitrary cross section as it assumes a cubic normal strain distribution along the beam cross section. The element stiffness matrix is derived by applying the principle of virtual displacements of the system. The two elements are found to yield similar results for beam aspect ratios which are greater than 1.0. The deep beam element solutions were compared to the conventional engineering theory of beam solutions for simple (cantilever) structures and complex (turbine generator pedestal) structures; the results of the two methods of solution were found to differ significantly.