Finite Extension of an Elastic Strand With a Central Core

Abstract

This paper deals with the finite extension of an elastic strand with a central core surrounded by a single layer of helical wires subjected to axial forces and twisting moments. The central core is considered as a straight rod of circular cross section and the helical wires are regarded as slender curved rods with circular cross section. The theory of slender curved rods is used in the analysis. Geometrical nonlinearities due to the reductions in helical angle and cross section of the core and wires are included. It is found that as a result of the contact between the central core and helical wires, a separation between helical wires can occur during the extension of the strand. Stresses in the core and wires as well as the contact forces between the core and wires are analyzed for strands with various helical angles subjected to different axial forces. Examples are presented for the finite extension of strands with fixed ends and strands with free ends.