On the hysteretic bending behavior of slack metallic cables

Short and slack stranded metallic cables are encountered in several technical applications to connect different structures or different parts of the same structural system. A couple of relevant examples are provided by flexible-bus conductors used in high-voltage electrical substations or passive damping devices installed on overhead electrical lines, such as Bretelle dampers. Bending behavior of metallic cables is nonlinear and non-holonomic due to the onset and propagation of relative sliding phenomena between the wires. While taut suspended cables have been widely studied in the literature under the classic assumptions of small sag and perfect flexibility, whenever dealing with short and slack cables, the aforementioned hypotheses typically cease to be valid, and the bending stiffness contribution plays a significative role in the determination of the overall structural response. In the present paper, two different modeling strategies for the description of the bending behavior of short and slack stranded cables are presented. The first (discrete bending model) describes the cable as a composite structural element made of wires, which are individually modeled as curved elastic thin rods interacting through normal and tangential contact forces. The second (phenomenological bending model), instead, relies on a description of the cable bending process based on an application of the well-known Bouc-Wen hysteresis model. Applications of the proposed models are presented both at the cross-sectional and at the structural levels. The systematic comparison between theoretical and experimental results allows to assess the performance of the two proposed bending models when used with “nominal” values of the model parameters, which are estimated only on the base of the knowledge of the material and geometric properties of the strand. Moreover, a back-analysis of the model parameters is carried out to get an insight on internal mechanical parameters of the cable and on the overall cross-sectional bending response (e.g. bending stiffness values).