Postbuckling of Elastic Columns with Second-Mode Imperfection

Abstract

Initial imperfections of columns are often assumed to have the shape of the first buckling mode. In this technical note, the imperfection has the shape of the second mode. An elastica analysis is performed, and numerical results are obtained for two cases with the use of a shooting method. For the example of a pinned column, bifurcation occurs at a load slightly higher than the critical load for the perfect system. With further increase in load, the deflection changes smoothly from an antisymmetric shape with one node to a shape with no nodes. For the cantilevered-column example, a limit point occurs just beyond the critical load for the perfect system, and the equilibrium shape jumps from one state to another. As the load is increased further, the deflection passes smoothly to the other side of the column and loses its inflection point.