Evaluation of Maximum Bending Stiffness of Stranded Cables with Refined Kinematic Relations

Abstract

AbstractThe mechanical response of a helically stranded cable depends on the effective stiffness offered by the collective assembly of its constituent wires. This can vary between two extreme conditions, namely a monolithic state, also known as the stick–slip state, wherein all the wires in the cable behave as a single unit with no relative movements among themselves, offering the maximum stiffness for the cable. In the other extreme condition, all the wires are free to move among themselves, with no frictional holding among them, thus offering the minimum stiffness. This paper reviews the various mathematical models that are available for the estimation of maximum bending stiffness and brings out the need for considering a vital parameter known as the ‘wire stretch effect’ that has been neglected by many authors till date. The consequent fundamental changes that occur in the basic kinematic relations are brought out and refined expressions for the internal wire forces and moments are established for the first time in the coupled axial-bending analysis. Further, the shear displacement of the wire due to the stretch has also been included in the wire normal and binormal shear forces. A single-layered cable with core-wire contact has been considered for analysis and the numerical results are evaluated with these new inclusions and are compared with the published results. It is hoped that the refined model suggested in this paper for the accurate estimation of the maximum stiffness, will pave way for more reasonable cable analysis in the subsequent slip stages.KeywordsHelical cable assemblyKinematic relationsEffective stiffness