Post-buckling of a cantilever column: A more accurate linear analysis of a classical nonlinear problem

A more accurate analytical approximate expression for the slope at any point of the elastic curve of a slender cantilever column is obtained by using a heuristic but pedagogical derivation. This derivation is based on the linearization of the nonlinear differential equation that governs the post-buckling of the cantilever column. The expression proposed depends on two unknown parameters, which are obtained by comparing, term by term, the power series expansions of the approximate and exact expressions for the total length of the column. The results obtained with this new approximate expression are compared with the exact ones and with two approximations previously published in the literature. The numerical results show that the two previous approximations are not nearly as accurate as the new expression presented in this paper.