Simple approximate formulas for postbuckling deflection of heavy elastic columns

TL;DR

This paper introduces simple analytical formulas to estimate the large deflection of heavy elastic columns under combined loads, simplifying the analysis of post-buckling behavior across various scales.

Contribution

It provides novel, straightforward formulas that relate load, weight, and deflection angle, offering an accessible alternative to complex nonlinear analysis methods.

Findings

Formulas accurately predict large deflections in heavy columns.

Applicable to a wide range of scales from macro to nano.

Facilitates practical analysis of post-buckling behavior.

Abstract

Columnar buckling is a ubiquitous phenomenon that occurs in both living things and man-made objects, regardless of the length scale ranging from macroscopic to nanometric structures. In general, analyzing the post-buckling behavior of a column requires the application of complex mathematical methods because it involves nonlinear problem solving. To complement these complex methods, this study presents simple analytical formulas for the large deflection of a heavy elastic column under combined loads. The analytical formulas relate the concentrated load acting on the tip of the column, the column's own weight, and the deflection angle of the column through a simple mathematical expression. This can assist in obtaining an overall picture of the post-buckling behavior of heavy columns from an application point of view.