Critical buckling loads of the perfect Hollomon's power-law columns

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.

► Formulas for critical buckling loads and shapes are derived for Hollomon's beam columns.
► These reduce to classical Euler's formulae when Hollomon's and Hooke's law coincide.
► For large slenderness ratios, our loads are less conservative than the Engesser's loads.
► Loads for beams with circular and rectangular cross sections are computed.