Reach of an inclined cantilever with a tip load

Abstract

We investigate the problem of determining the reach of an inclined cantilever for a given point load suspended from its tip. Two situations are considered. Firstly, we find the maximum reach of the cantilever by varying its angle of inclination. Secondly, we find the reach of the cantilever subject to the condition that its tip is at some specified height, above or below, the level of the clamped end. In the second case, the reach of the cantilever is maximised by shortening its physical length whilst keeping the physical load and physical height of load deployment constant. All of our solutions representing various reaches of an inclined cantilever for a given point load suspended from its tip are shown to be stable to the snap-back instability.