The Representation of Cables Subjected to General Loading

Abstract

This paper is concerned with the development of a general 3D cable element suitable for use in the analysis of cable structures such as guyed masts and underwater cable systems. The element can adequately model structural cables subjected to completely general loading. The loading may be specified as a function of a Lagrangian coordinate along either the strained or the unstrained length of the cable, and/or as a function of the deformed geometry of the cable. This element is particularly suitable for use in situations where there is a strong interaction between the loading and cable profiles. Examples of structures in which such situations arise are subsea cable systems subjected to current loading and guyed masts under the action of wind and ice loading.In the development of the general cable element, two sets of quantities, i.e. equivalent nodal forces and the tangent stiffness relationships, need to be evaluated. Consideration of equilibrium and compatibility conditions together with the constitutive relationship for a single hanging cable subjected to external loading has led to the development of three simultaneous non-linear equations. The unknowns in these equations are determined using the Newton-Raphson technique to obtain the equivalent nodal forces. Initial estimates are found using simple but accurate formulae which have been developed for this purpose. Based on these equations a method for the determination of the tangent stiffness relationship for the general cable element is described. This method is shown to be particularly efficient in terms of computation.In order to demonstrate the versatility of the general cable element it has been used in the analysis of a stay of a guyed mast and an undersea guyed tower.