Large-Deflection Analysis of Whipping Pipes. II: Rigid, Perfectly-Plastic Beam Model with Elastic Root Spring

In a companion paper, the effects of large deflections were evaluated for plastic deformation of a cantilever beam under a transverse force pulse applied at its tip. Here, the effect of material elasticity is introduced in addition to the large deflections through a simple model. The beam is assumed to be rigid and perfectly-plastic, but instead of the usual fully clamped constraint at its root, an elastic, perfectly-plastic rotational spring is incorporated there so that the beam-spring system has a certain capacity to store elastic energy. Compared with the rigid, perfectly-plastic model, the present beam-spring model shows differences in the initial plastic hinge position and in the minimum magnitude of the force needed to produce plastic collapse. It is also shown that a range of different responses may occur as the remaining plastic hinge travels along the beam segment toward the root, rather than the unique response mode in the rigid, perfectly-plastic analysis.