Inelastic Spatial Stability of Restrained Beam-Columns

A numerical method for computing the deflections and rotations up to the point of instability of elastically restrained inelastic beam columns is described. The cross section considered is open, thin-walled, and arbitrary in shape. The external forces, applied at ends of the beam column, could include a normal force, two bending moments, two shear forces, or a torsional moment or a combination of these. The restraints are represented by elastic rotational or directional springs, or both, at each end of the beam column. The material considered is ideally elastic-plastic and residual stresses are included in the analysis. The equilibrium equations are written with respect to an arbitrary system of orthogonal coordinate axes. The influence of the shift in the shear center and the shift and rotation of the principal axes of partially plastified sections are thus taken care of automatically in the analysis. The resulting fourth-order nonlinear differential equations are solved using finite differences and the tangent stiffness method.