Authors' Reply to Discussion by Hagedorn, P., Eckstein, M., Heffel, E., and Wagner, A. of “The Temporal Evolution of Buckling in a Dynamically Impacted Column”

The authors are pleased to acknowledge the interest in our work by Hagedorn et al. [1]. In response, we wish to clarify the equations used by Ji and Waas [2]. To this end, we show the derivations of the governing equations for a perfectly flat Euler–Bernoulli column and the corresponding geometrically imperfect column, both of which are impacted at one end. In doing so, we point out that the equations used by Ji and Waas [2] are a consistent set of equations that result due to the smallness of the magnitude of the initial geometrical imperfection. If this smallness assumption is relaxed, the total energy approach shown in Ref. [1] lead to a fully coupled set of nonlinear equations. After deriving the complete set of equations for a geometrically perfect and a geometrically imperfect impacted column, a discussion is included where we...