Elastica and buckling load of simple tapered columns with constant volume

Numerical methods are developed for solving the elastica and the buckling load of simply supported tapered columns subjected to compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sectional shapes are considered, whose material volumes are always held constant. The column model is based on Bernoulli±Euler beam theory. The Runge±Kutta and Regula±Falsi methods are used to solve the buckling load and the postbuckling de¯ected shape vs load. Extensive numerical results, including the equilibrium paths, the shapes of elastica and the buckling loads are presented in non-dimensional forms. By varying the section ratio, the strongest columns are identi®ed for each taper and cross-sectional shape.