Exact Three-Dimensional Elasticity Solution for Buckling of Beam of a Circular Cross-Section

An exact three-dimensional elasticity solution for buckling of a circular cross-section beam with one end fixed and the other end free is obtained. A comparison is made using the approximate solution by Kardomateas and an exact two-dimensional solution by Chattopadhyay and Gu. The buckling loads of both exact solutions are in good agreement with each other, but the buckling load using the approximate solution is slightly higher than the exact solutions. The exact solutions support Engesser's formula rather than Haringx's formula for the buckling load of a beam with transverse shear effect.