Impact Deflection Analysis of Concrete Beams

Abstract

An analytical solution is presented for the instantaneous deflection of pin‐ended beams under mid‐span impact of below‐yield intensity. Hertz's contact law and vibration theory are incorporated, leading to an integral equation for the force history. The beam displacement and velocity at the end of impact are used as initial conditions for the free vibration that ensues. The maximum deflection that may occur during the forced or free vibration stage is obtained automatically on a computer. To account for cracking of reinforced and prestressed concrete beams, Branson's effective moment of inertia,