Three-Dimensional Parabolic Cable Element for Static Analysis of Cable Structures

Abstract

This paper presents a three-dimensional inclined parabolic cable element for static analysis of cable structures. After a catenary cable element is briefly reviewed, the three dimensional parabolic cable considered in this paper is presented. The derivation of the stiffness matrix for the element is described by equating the total differentiations of the cable length and its elastic elongation, and defining the stiffness as the ratio of the infinitesimal force increment to the infinitesimal length increment. The static equilibrium equation for a two-node cable element and the procedure for nonlinear structural analysis using the Newton-Raphson iterative method are presented as well. The proposed element can consider an inclined cable without the need for a transformation, and has explicit and simple stiffness formulas compared with those of a catenary element. To validate the proposed parabolic cable element, four example models subjected to static loadings are analyzed using the proposed element, and the displacements are compared with those obtained by previous researchers and finite element analysis software. The verification proves that the proposed parabolic cable element offers highly accurate static responses for cable structures.