An analytical solution for the estimate of the mean crushing force of structures with polygonal and star-shaped cross-sections subjected to axial load

Abstract

The present work is focused on the development of an analytical solution for the estimate of the mean crushing force for structures with polygonal and star-shaped cross-section. The geometrical analysis revealed that polygonal and star-shaped cross-sections could be obtained using a consistent set of equations. A theoretical model for the mean crushing force that can be applied for this entire range of structures was developed, based on the hypothesis of an extensional model applied to the collapse pattern. Literature data were collected and used as a reference for an analysis of the results. For each case, a specific material model was assigned, and crushing process parameter like the effective crushing distance was discussed. A nondimensional analysis of the mean crushing force was performed in order to evaluate the results overall data collected. Finally, the proposed solution was compared with existing, specific, analytical solutions used for the estimate of the mean crushing force and values of the mean crushing force from the literature. The linear regression model applied to the dataset consisting of analytical estimates resulted in a coefficient of determination R2 = 0.983 while for the dataset comprising experimental values, a coefficient of determination R2 = 0.965 was obtained. These results show that this analytical solution can be used, with confidence, to provide a preliminary estimate of the mean crushing force while allowing variations of the shape of the cross-section and, without the need of a specific or particular analytical formula.