The large deformation, post-buckling and catastrophic stability of slender cantilever columns

Several solutions, analytical and numerical, exist for the cases of nonlinear bending of beams and post-buckling of columns. However, the solution for the general case of an arbitrarily inclined load does not seem to exist. In this paper, the governing equation of equilibrium for a cantilever of variable cross section under an arbitrarily inclined load is formulated, by using the axial and transverse displacement quantities. The solution is obtained by means of a simple numerical iterative procedure. The results for the post-buckling and non-linear bending of the structure under concentrated tip load, uniformily distributed load and linearly varying load are presented, and compared with the available results, wherever possible. Further, a type of catastrophic behaviour in post-buckling region is observed and studied using the same numerical scheme. The method is general and can be used for any load variation and for any tapered beam-column. © 1978.