Buckling capacities of braced heavy columns under an axial load

Abstract

The stability of heavy columns which are subjected to an axial load and may be restrained by several elastic braces or internal supports is investigated. The buckling loads are determined by minimizing the generalized Rayleigh quotient (which is derived from the Timoshenko energy approach) subject to some equality constraints on the deflection curve, imposed by the presence of lateral restraints. On the basis of the convergence studies made on the energy solutions, two terms of the trigonometric series are found to be sufficient for approximating the deflection curve of unrestrained columns. Consequently, simple approximate formulas can be obtained by solving the quadratic characteristic equation supplied from the Rayleigh-Ritz energy approach. These formulas are more accurate and in rather simpler forms when compared to the well known Kato's formulas. © 1988.