Impulsive loading of ideal fibre-reinforced rigid-plastic beams—II Beam with end supports

The theory outlined in Part I is applied to the problem of a beam, supported at both ends, struck transversely at any point by a mass which subsequently adheres to the beam. For sufficiently long beams, the resulting moving discontinuities in slope and velocity do not propagate to the ends of the beam, and for this case the solution is obtained for the non-linear strain-hardening law used in Part I. A simpler approximate solution is derived for the case of low impact velocity and/or slight strain hardening. For shorter beams, the propagating discontinuities may undergo one or more successive reflections at the end points and at the point of initial impact. The deformation after such reflections is analysed, for linear strain-hardening, in the final two sections. Some particularly simple results are found in the case of central impact.