Effect of Shear in Transverse Impact on Beams

Abstract

In this paper the problem of transverse impact on a uniform beam is considered theoretically. Two examples which can be taken as representing a wide range of impacts which occur in practice are referred to particularly: (1) the beam struck transversely by a uniform square-ended rod travelling perpendicularly to it; (2) the same problem for the striker having a spherical end.In these examples it is shown that the ability of the beam to deflect in shear as well as in bending plays a dominant part in what takes place, and that, as far as the force between striker and beam is concerned, the length of the beam is usually without importance, as there is not time during the impact for an elastic wave to travel to the ends of the beam and return.It is shown that in regard to example (2) the theory presented is in good agreement with Arnold's experimental results obtained some years previously, and curves are given from which the maximum force between beam and striker can be obtained in terms of three parameters, representing respectively the velocity, the mass, and the radius of the striker, each dependent on the ratio of shear stiffness to bending stiffness for the beam.