Buckling and Stress Softening of Beam-columns Under Complex Three-dimensional Loading

This paper is concerned with buckling and stress softening of beam-columns under axial compression, biaxial bending and torsion. Members with no warping whose cross sections vary along the axis in a uniform manner with respect to the principal directions are also considered. The basic four coupled differential equations governing the behavior of three-dimensional beam columns are reformulated to include varying cross sections. A 12 × 12 stiffness matrix is assembled by solving the equations 6 times (which is sufficient to describe 3D behavior) for a sequence of appropriate discontinuities using the finite difference method. Two sets of curves are then computed. One set displays interaction diagrams that highlight the stress softening of beam stiffnesses. The other set of curves displays the buckling compressive load of a rectangular cantilevered beam under a variety of tri-directional moments (two bending moments and one twisting moment).