Unilateral contact of a springboard and a fulcrum

Introduction. Springboards used in diving are hinged at the rear end and rest free on a movable fulcrum close at midspan. Those presently in use at international contests are extremely flexible, but also vulnerable to overloading, causing fatigue (aluminium) or internal buckling of fibers (wood). Although the demands put to the strength of a springboard are excessively high, specifications with respect to the allowable amount of torsion are neither prescribed by the F.I.N .A. (Federation International de Natation Amateur), nor given by the producers of springboards. We feel that a simple static test, in which a board is loaded by an excentric force, would be of some value to qualify the springboard. This paper has been written to evaluate the results of such a test quantitatively. Hence, in what follows, we shall analyse the deformation of the board and, specifically, we shall concentrate on the distribution of the reaction farces at the fulcrum In the presence of a possible detachment of the board from the latter. In doing so, we shall assume that the fulcrum behaves as a linear foundation of the so called Winkler type, which gives rise to a line load along the contact line between board and fulcrum. Throughout the analysis we apply linear field equations ensuing from a small displacement beam theory. However, in view of the unilateral characteristics of the contact between board and fulcrum, the problem is essentially a nonlinear one.