This paper deals with buckling lengths of the heavy column with various end conditions, where both top and bottom ends are either free or hinged or clamped. Based on equilibrium equations of the buckled column element, the differential equation governing the buckled mode shape is derived. For solving the buckling length, the differential equation is integrated by the direct integration method and the buckling length is calculated by the determinant search method. The buckling lengths of this study agree well with those of references. The buckling lengths with various end conditions, buckled mode shapes and buckling stresses are presented.

This paper deals with the elastica and buckling loads of the nonlinear elastic tapered cantilever columns subjected to an axial load at the free end. The column cross section is rectangular, where the width and depth vary linearly with the column axis. The column material is nonlinear elastic, which obeys the Ludwick's constitutive law. The ordinary differential equations governing the elastica of buckled column are derived and solved numerically for computing the elastica and buckling loads. Parametric studies for the annealed copper, N.P. 8 aluminum alloy and steel columns are conducted.