Response of Beams to Shock Loading: Inelastic Range

Four classical support conditions are investigated for beams with distributed loading, which has a temporal form of rectangular pulse. First, a simple calculation is presented, using algebraic equations of momentum and energy conservation to derive approximate deflection results. Then, exact relationships, derived from work by others and describing a total of five regimes of motion, are quoted and discussed. These relations were developed using a popular, rigid-plastic material model. On the other hand, there is an elastic–perfectly plastic material model, which represents a more realistic description of material properties. When solutions are obtained by means of a numerical simulation, employing the better material model, it is found that the simpler solutions developed here provide more accurate results of final deflections.