Flexural-torsional buckling of variable and open cross-section members

This work gives the exact solutions for the coupled flexural-torsional buckling loads of variable and open cross-section columns, loaded by variable axial force. Both the cross-section dimensions and the axial load can vary along the column as polynomial expressions. The proposed solution is based on a new finite-element method for getting the exact stiffness matrix for the member, including the effects of the axial loading. The buckling load is found as the load that causes the stiffness matrix determinant to become 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.