An Integrated Project for Teaching the Post-Buckling of a Slender Cantilever Bar

Abstract

We describe an integrated project that includes theoretical, numerical and experimental studies designed to facilitate teaching the non-linear post-buckling of a cantilever column to undergraduate mechanical engineering students. We present the differential equation governing the behaviour of this mechanical system and show that this equation, although straightforward in appearance, is in fact rather difficult to solve owing to the presence of a non-linear term. In this sense, the system is similar to another well known physical system: the simple pendulum. This educational paper also addresses a simplified procedure for calculating the elliptical integrals that appear when the differential equation is solved. We present numerical results for various cases. Finally, we compare the theoretical results with the experimental ones obtained in the laboratory using materials which are easily and cheaply sourced.