Beam Response to Longitudinal Impact by a Pole

Abstract

The linear response of a flexible longitudinal pole hitting a column or beam is investigated. Based on Timoshenko beam theory, an efficient analytical solution method using mode superposition for the coupled beam-pole system is presented. Any physical set of boundary conditions can be accommodated, such as a free pole impacting a column with arbitrary boundary conditions or a free-free beam hitting a pole that is either pinned or free at the opposite end. For the case of the free-free beam, it can have arbitrary initial translational and rotational velocities. Impact can occur anywhere within the beam span, although the contact is frictionless. It is shown that, when the beam response governs, the initial impact is likely governed by shear, and therefore, Euler-Bernoulli beam theory is not a good modeling choice in general. Results based on a wood log hitting concrete, steel, and wood columns reveal the behavior governing the impact force time history. A simple design formula for the initial maximum impact force is shown to be quite accurate. The impact duration is governed by either the longitudinal wave speed in the pole or the shear wave speed in the column. In addition, the energy transfer between translational and rotational kinetic energies and strain energies is used to analyze the impact vibrational motion; this analysis reveals both the initial dependence on shear deformation and the transfer of the associated energy to bending energy. The significance of including rotary inertia is also demonstrated.