Stability of slender columns on an elastic foundation with generalised end conditions

Abstract

Slender columns' lateral stability under compressive axial loads is presented, with uninhibited, partially inhibited and totally inhibited end side-sway, including the effects of semi-rigid connections and a uniformly distributed lateral elastic foundation (Winkler's type) throughout its entire span. The proposed classification of prismatic columns on an elastic foundation and the corresponding stability equations are general and relatively simple to apply, yielding exact results when compared to other analytical methods. The buckling load was obtained by making the determinant of a 4 × 4 matrix equal to zero for columns having side-sway uninhibited or partially inhibited at both ends, and of a 3 × 3 matrix for columns having side-sway inhibited at one or both ends. The effect of semi-rigid connections on the buckling load of five classical column cases is fully discussed and the results compared to those arising from other analytical methods.