The Effect of Principal Bending Curvature on the Lateral Buckling of Uniform Slender Beams

Abstract

The general lateral buckling equation is developed for a uniform, slender, simply supported beam fixed in torsion and with a load applied at the shear center of the midspan cross section. In this general equation, the effect of principal bending curvature (i.e., beam deflection prior to buckling) is completely accounted for. Therefore, a distinction is made between beams fixed in torsion about the deformed or undeformed elastic axis, and distinct boundary conditions are derived for each case. The equations for each of the two support conditions are then specialized to include only the first-order effect of principal bending curvature and these equations are compared with similar equations for cantilever beams and beams in pure bending. Finally, simplified buckling load formulas are derived and compared with numerical solutions of the general equations for each of the lateral buckling configurations. The comparison shows that the approximate formulas provide good estimates for the buckling load and that the classical buckling load formulas that neglect principal bending curvature are not always conservative for infinitely slender beams.