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

Simple approximate formulas for postbuckling deflection of heavy elastic columns