Frictional Dissipation in Axially Loaded Simple Straight Strands

In this paper, an analytical investigation is made of the frictional damping properties of axially loaded metallic cables made from one layer of wires helically wrapped around a central wire. Our efforts are focused on the quantity of energy dissipated through friction due to the motions between wires when a cable is loaded. Although the local interwire pivoting drives the response of the cables studied, a first linear model is built where pivoting is allowed, but friction is not taken into account. Then, a law of friction is established and linearized to extend the linear model into a tractable piecewise linear hysteretic one. Through a variety of examples, it appears that the energy dissipated in friction over a load cycle is very small compared to other sources of dissipation, because axially loaded simple straight strands do not experience fretting-induced failures, except close to terminations. It is also shown that modifying the design of such cables is not expected to significantly improve their damping properties. Thanks to their large axial strength allied with their flexi- bility, cables are used in many applications ranging from ca- ble-stayed bridges and large-span roofs to tension-leg-plat- forms and prestressed concrete structures. In service life, these structures do not experience only static loads, but also cyclic efforts such as vortex-induced vibrations or traffic loads. Then, when the damping properties of a cable are mainly due to friction between its constituent wires, these properties can also be expected to be related in some way to the cable durability, because the interwire wear and fretting phenomena involved in damping can drastically shorten the cable fatigue life. In an attempt to quantify the energy dissipated through friction and correlate it with some basic fatigue data, the frictional damping properties of axially loaded metallic cables are explored in this paper. Although the design of cables is in constant evolution, the study of cable damping properties is still a current research field, even though it was undertaken some decades ago (Pipes 1936; Kawashima and Kimura 1952). A review of experi- mental work on cable damping in transverse vibrations were made recently (Fang and Lyons 1996). As for the axial damp- ing of cables, Hobbs and Raoof (1984) presented a report of the few available experimental results. The cable damping properties due to friction are obviously governed by the geometry and the characteristics of the inter- wire contacts. Hobbs and Raoof (1984) proposed a model for the axial frictional energy dissipation in multilayered spiral strands. Since then, they have also achieved some fatigue pre- dictions (Raoof 1991), but their cable model is based on the homogenization of the cable layers into orthotropic cylindrical sheets and cannot be used for all types of cables. As a first step, the present investigation is limited to axially loaded simple straight strands made from one layer of wires wrapped around a core. If a simple straight strand has no core, or if the core radius is too small, the outside helical wires are