Improved extensional crushing mechanics of prismatic columns with various cross-sections

This work derives the theoretical prediction of the impact behaviour of single thin-walled prismatic columns with various cross-sections based on an improved extensional collapse element. The extensional crushing mechanics were reviewed and improved to calculate the impact crushing characteristics of any single thin-walled prismatic columns: that is, square, hexagonal, octagonal and circular columns. The general equations to predict the mean crushing force and axial instantaneous crushing force of the single thin-walled prismatic versus the folding angle or axial displacement were derived theoretically. Furthermore, using the extensional collapse mode, the maximum (peak) crushing force was theoretically predicted during the first folding process. Lastly, the impact of the columns obtained by the improved theoretical solution was compared via numerical simulation.