Modeling the axial-torsional response of metallic strands accounting for the deformability of the internal contact surfaces: Derivation of the symmetric stiffness matrix

A new formulation for the evaluation of the axial-torsional response of single-layer metallic strands is presented. The proposed model fully accounts for the contraction of the helix radius of the external wires due to both the Poisson effect and the local deformation (flattening) of the internal contact surfaces. Closed form equations are found for the coefficients of the cross sectional elastic stiffness matrix of the strand. Differently from other models of the literature that include the effects of the radial contraction of the wire helices, the proposed stiffness matrix is symmetric. The proposed expressions for the terms of the stiffness matrix are remarkably compact and simple, making them an attractive tool for analytical developments and design calculations. Extensive comparisons with experimental, analytical and Finite Element results of the literature show that the proposed expressions are accurate over a wide range of strand constructions and within a loading range sufficiently extended to cover most practical service conditions.