Critical load for buckling of non-prismatic columns under self-weight and tip force

The stability of elastic columns with variable cross-section under self-weight and concentrated end load is considered. A simple and easy-to-implement approach is suggested. Different end conditions are dealt with. The governing equation subject to associated boundary conditions for Euler–Bernoulli columns is transformed into an integral equation, and critical buckling load is then evaluated by seeking the lowest eigenvalue of the resulting integral equation. Numerical examples of the critical buckling load for prismatic and non-prismatic columns under self-weight and end force are given, and the effectiveness of this method for buckling analysis of tapered columns is validated. For several frequently encountered end supports, the influence of the taper ratio on the critical buckling load is discussed.