Buckling of Tapered Heavy Columns with Constant Volume

This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered with regular polygons cross-section whose volume constant. Five end conditions for are considered. The differential equation governing shapes column derived based equilibrium equations buckled elements. numerically integrated using direct integration method, eigenvalue obtained determinant search method. accuracy method verified against existing solutions particular cases. effects side number, taper ratio, self-weight, condition load mode shape investigated. contribution acting alone to response also explored. For a given volume, especially, length its stress distribution different geometries estimated.