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The cantilevered beam: an analytical solution for general deflections of linear-elastic materials

The deflections of a cantilevered beam made of a linear-elastic material under the influence of an external vertical concentrated force at the free end are analysed in detail and it is found that a factor that is always ignored in the theory commonly developed in the literature concerned permits the solution of the elastic curve to be obtained analytically. I introduce this analytical solution and show that the widely known simple solution for small deflections is a limiting case, which holds when forces applied are much smaller than the force needed for breaking the beam. A simple relation for an upper bound to this latter force is obtained which may be of practical importance for engineering. Finally, the most simple results obtained theoretically are compared with experiments in the laboratory.