Critical Buckling Loads of the Perfect Hollomon's Power-law Columns

TL;DR

This paper derives analytical formulas for the critical buckling loads and shapes of perfect plastic columns with constant cross-sections, extending classical elastic buckling theory to plastic materials using Hollomon's power-law.

Contribution

It introduces explicit formulas for plastic buckling loads and shapes of columns, extending Euler's elastic buckling theory to plastic materials with Hollomon's law.

Findings

Derived formulas for plastic buckling loads of circular and rectangular columns.

Presented deformed shapes using generalized trigonometric functions.

Compared plastic buckling loads with classical Euler-Engesser results.

Abstract

In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Hollomon's power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and comparisons to the classical result of the Euler-Engesser reduced-modulus loads are also presented.