Analytical model for the bending of parallel wire cables considering interactions among wires

Abstract

Bending behaviors can be critical in simulating cables, such as the local effects close to cable end regions or dynamic properties of short cables. Wires form up the cable and tend to slip relative to each other under bending load. Complex interactions among wires make the modeling of cables challenging. In this work, we propose an analytical model for bending parallel wire cables in which the cable cross section with layered wires is idealized as a composite section of the laminated beam. The slips and interactive forces among wires are modeled by the interfacial slips and the resulting interactive forces at the interfaces of the composite section. In this way, the bending cable can transform into an in-plane stress state laminated beam. The state space method is then applied to solve the problem, and the numerical results agree well with the experimental results and analytical formulations in the literature. Bending stiffness of the cable differs from lower bound to upper bound according to the anti-slip ability among wires, from full-slip state to no-slip state. The overall deflection, as well as the local deformations and stresses of the bending cable, can be simultaneously obtained. These results show that the present model is efficient and accurate in simulating bending cables, which is capable of extending to more cable studies.