Inelastic Behavior of Impulsively Loaded Beams

Methods are presented for solving design problems involving a simple beam in which (a) the applied load is impulsive and (b) the distortions are inelastic. A similarity between deflections in the simple beam and moments in an analogous beam is demonstrated, in which the latter beam, with its length corresponding to time, is loaded with the unbalanced impulse applied to the simple beam. This analogy permits a designer who is familiar with the usual concepts of static design to cope with problems involving yield and motion. A nondimensional characteristic number is proposed. This value varies directly as the product of the mass of a beam and the “braking” energy of inelastic bending distortion, and inversely as the square of the driving impulse. The number is the link between seemingly different forms of impact and impulsive loads and provides a new means of classifying all such loads on a single basis. The number facilitates the determination of the dynamic yield resistance of a beam from test data in which this resistance is often confused with inertial resistance.