A symmetric linear elastic model for helical wire strands under axisymmetric loads

Abstract

Among several mathematical models for predicting the mechanical response of a helical wire strand to axisymmetric tension and torque derived in the literature over five decades, purely tensile wire linear elastic models have the symmetry of a stiffness matrix. Curiously, in those models where wire bending and torsion terms were included there was a lack of symmetry. In this paper the origin of the lack of symmetry in the earlier models has been identified and a symmetric model developed. The correct generalized strains for this purpose were derived using Wempner's theory and verified using Ramsey's theory. The validity of this model has been verified by comparing its results with that of earlier models and experiments available. This linear elastic symmetric model brings forth the much needed agreement between the global (strand) and the local (wire) responses which should help to simplify considerably the analysis of multi-layer strands and multi-strand wire ropes.