Tapered thin open section beams on elastic foundation—I. Buckling analysis

This work presents exact solutions for the coupled flexural-torsional axial buckling loads of tapered beams with a thin-walled open section resting on an elastic foundation. Vlasov's coupled differential equations are employed and an exact series solution is obtained for the case in which the cross-sectional dimensions are a polynomial function of the axial coordinate. A solution is also obtained by the finite element method using tapered elements with cubic shape functions. The results of axial buckling load are presented for different cross-sections for various boundary conditions at the ends. The effect of the parameters of the elastic foundation is investigated.