Linear Stability Analysis of Beam-Columns

A finite element formulation is presented for the stability analysis of beam columns and its application is demonstrated as a practical tool for direct use by researchers and designers. A systematic procedure, based on a displacement formulation, is developed to evaluate the geometric stiffness matrices for beam columns for large axial, lateral and torsional displacements. The finite element solutions are compared to analytical solutions for a variety of problems, e.g., columns under distributed axial loads, tapered columns, columns imbedded in an elastic medium, pretwisted columns, lateral-torsional buckling of beam columns, and space frames. In all cases, a good convergence is observed and satisfactory accuracy is obtained by using few elements. The required computational effort is found to be minimal.