THE VARIATIONAL THEORY OF A CIRCULAR ARCH WITH TORSIONAL SPRINGS AT BOTH EDGES

Abstract. The behavior of arches are nonlinear and sensitive to the buck-ling conditions. The existence of equilibrium states of elastic circular arches with rotational resistance at both edges under normal pressure is investigated. Variational formulation is derived using an energy method. 1. Introduction. In this article, we study the existence of equilibrium states of buckled circular arches under uniform normal pressure. An arch is an elastic structural member restrained at the bases. The buckling of such a ”classical ” arch has been considered by Timoshenko, S.P. and Gere, J.M. [7], Vlasov,V.Z.[8] and Simitses, G.J. [5]. I