Dynamic buckling of columns by biaxial moments and uniform end torque

A new concept of uniform torque is proposed for the dynamic torsional buckling analysis. A dynamic biaxial moments and torque buckling theory is presented for analysis in structural dynamics. Second-order effects of the axial force, biaxial moments and torque are considered. The consistent natural boundary moments and forces are derived to ensure the symmetry of the dynamic stiffness matrix in fulfilling the requirement of the reciprocal theorem and conservation of energy. The exact dynamic stiffness matrix is obtained using power series expansion. The derivatives of the analytical dynamic stiffness matrix with respect to different loading and geometric parameters are derived explicitly for sensitivity and continuation analyses. Generally distributed axial force can be analyzed without difficulty. It is pointed out that non-uniform sections may not be handled by power series due to the convergent problem. Global pictures for all kinds of linear dynamic buckling are given for the first time. The methodology is based on finite element formulation and therefore it can easily be extended to analyze structural frames.