Large and small deflections of a cantilever beam

The classical problem of the deflection of a cantilever beam of linear elastic material, under the action of an external vertical concentrated load at the free end, is analysed. We present the differential equation governing the behaviour of this physical system and show that this equation, although straightforward in appearance, is in fact rather difficult to solve due to the presence of a non-linear term. In this sense, this system is similar to another well known physical system: the simple pendulum. An approximation of the behaviour of a cantilever beam for small deflections was obtained from the equation for large deflections, and we present various numerical results for both cases. Finally, we compare the theoretical results with the experimental results obtained in the laboratory.