Tapered Cantilevers with Varying Distributed Loads

Many investigators have considered the problems of cantilever beams undergoing large deflections. Barton and Bisshopp and Drucker solved exactly a cantilever carrying a concentrated load at its free end. Hummell and Morton, Bickley, and Rhode presented an approximate treatment of a cantilever beam under uniformly distributed load. All of the above cases were for beams of constant section. Recently, Kemper solved the problems of tapered cantilevers subjected to a concentrated load at the free end by computer methods, considering both rectangular and round cross sections, and the results were checked by experimental verification. In the present note, a slender cantilever beam with a uniform taper of the rectangular cross section, carrying varying distributed loads, is considered, and the solution is obtained by the use of power series method. A general load distribution function is introduced and a set of coefficients are provide for various kinds of load distribution. Numerical results of load-deflection relationships are also presented for a cantilever with a uniformly distributed load.