This paper deals with the small extension of linearly elastic two-ply filament yarns. Each filament is treated as a long slender curved rod with circular cross section and helical configuration. Analysis is based on the linear theory of slender curved rods. Two problems are investigated, namely, the extension of a yarn with fixed ends and the extension of a yarn with free ends. In comparison with a previous study of a similar problem, it is found that the method adopted in this paper can provide more accurate results and better geometrical and physical insights into the problem. In this study, the yarn elongation and the filament stress are determined for yarns with various helical angles. The effect of the superposition of a twisting moment on the axial extension is also investigated.

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