Buckling loads for variable cross-section members with variable axial forces

Abstract

This work gives exact solutions for the buckling loads of variable cross-section columns, loaded by variable axial force, for several boundary conditions. Both the cross-section bending stiffness and the axial load can vary along the column as polynomial expressions. The proposed solution is based on a new method that enables one to get the stiffness matrix for the member including the effects of the axial loading. The buckling load is found as the load that makes the determinant of the stiffness matrix equal zero. Several examples are given and compared to published results to demonstrate the accuracy and flexibility of the method. New exact results are given for several other cases.