On the Two-dimensional Static Stiffness of a Parabolic Cable

Abstract

This study proposes the two-dimensional static stiffness of a parabolic cable. Based on that derivative of the total length of a cable is equal to that of its elastic elongation, the stiffness equations for horizontal and vertical directions at the end point of a cable are derived. The off-diagonal terms of the stiffness matrix can be also derived using relationship between the horiwontal and vertical forces at the end point. The proposed equations are verified with the exact solution of the elastic catenary cable and the expression of the parabolic cable based on Ernst's equivalent stiffness for various numerical conditions. The results of the proposed equations show good agreement with those of the catenary solution.