Dynamic behaviour of a rigid, perfectly plastic free-free beam subjected to step-loading at any cross-section along its span

The initial, small deflection response of a free-free beam subjected to a concentrated step-load at any cross-section along its span is examined. The material of the beam is assumed to be rigid, perfectly-plastic. Solutions are obtained for various combinations of the magnitude and location of the load and the partitioning of the initial energy dissipation rates are discussed for some typical situations. It is concluded that (i) when the load is applied at the cross-section 0.6595L (L = half of span of the beam) away from the mid-span, the beam is most difficult to deform plastically, it exhibits its "hardest" behaviour; (ii) when the load is applied at the free end, the beam is most liable to deform plastically, it displays its "softest" behaviour; (iii) no less than 2/3 of the input energy is transferred into kinetic energy of rigid-body motions. This implies that the plastically dissipated energy is always less than 1/3 of the input energy.