Plastic deformation of beams under time-dependent transverse impact

The permanent deformation of a rigid perfectly-plastic beam subjected to a time-dependent line load is calculated. The beam has finite length, and the load is applied transversely in the middle of the span. At the initial time, the load is zero; thereafter, it increases linearly, reaches a maximum value, and then decreases linearly to zero. For sufficiently large values of the applied load, there is a plastic hinge moving along the beam. The system of nonlinear ordinary differential equations that governs the motion of the hinge is solved numerically. After the plastic deformation has taken place, the beam appears as a bent curve that translates in the direction of the applied load. Formulas for the permanent deformation of the beam are obtained, and curves are presented to illustrate the results