Refined Kinematic Relations and Numerical Evaluation of Static Stiffness of Multi-layered Conductors Under Coupled Tension, Torsion, and Bending Loads

The behaviour of helical cable strands under axial and bending actions is governed by the complex interaction of its individual helical wires. In this study, the fundamental expressions for curvature, wire twist, within strands are modified to incorporate the combined influence of wire elongation—a factor largely overlooked in earlier research. Additionally, the resulting shear displacement from this elongation is introduced into the normal and binormal shear force calculations, marking the first inclusion of such effects in coupled axial–bending analysis. Using these kinematic improvements, a mathematical framework is developed to determine the single layer cable stiffness subjected to simultaneous loading patterns. The approach is subsequently applied to multi-layer conductors typical of overhead transmission systems. Numerical outcomes are compared with existing published data, highlighting the differences produced by the enhanced formulation. The results of the numerical analysis through refined kinematic relations for a single-layer 7-wire strand indicates that the elongation of the wire results in a decrease of normal flexural strain by 10% to 12% and bending stiffness by 5%. Where as in case of multilayer conductors (Panther, Zebra, Moose), there is no change in axial and torsional stiffness in comparison with the existing mathematical models, but bending stiffness decreases slightly for Panther and Moose multilayer conductors, thereby validating the novelty of the refined kinematic relations.