Abstract
Steel wire ropes have wide application in a variety of engineering fields such as ocean engineering and civil engineering. The stress calculation for steel wire ropes is of crucial importance when conducting strength and fatigue analyses. In this study, we performed a finite element analysis of single-strand steel wire ropes. For the geometric modeling, we used an analytic geometry of space method. We established helical line equations and used the coordinates of the contact points. The finite-element model was simplified using the periodic law. Periodic boundary conditions were used to simulate a wire strand of infinite length under tensile strain, for which we calculated the cross-sectional stresses and inner forces. The results showed that bending and torsion moments emerged when the wire strand was under tensile load. In some cases, the bending stress reached 18% of the tensile stress, and the torsion stress reached 29% of the tensile stress, which means that the total stress was higher than the nominal stress. Whereas in earlier studies, a conservative prediction of nominal stress was not possible, the results of our strength and fatigue analyses were more conservative.
Similar content being viewed by others
References
Aboudi, J., Arnold, S. M., and Bednarcyk, B. A., 2013. Chapter 3-Fundamentals of the mechanics of multiphase materials. In: Micromechanics of Composite Materials. Aboudi, J., et al., eds., Oxford, Butterworth-Heinemann, 87–145.
Cao, X., and Wu, W., 2018. The establishment of a mechanics model of multi-strand wire rope subjected to bending load with finite element simulation and experimental verification. International Journal of Mechanical Sciences, 142–143: 289–303.
Chen, Y., Meng, F., and Gong, X., 2017. Full contact analysis of wire rope strand subjected to varying loads based on semi-analytical method. International Journal of Solids and Structures, 117: 51–66.
Chen, Y., Tan, H., and Qin, W., 2020. Semi-analytical analysis of the interwire multi-state contact behavior of a three-layered wire rope strand. International Journal of Solids and Structures, 202: 136–152.
Costello, G. A., 1997. Static response of a wire rope. In: Theory of Wire Rope. Costello, G. A., ed., Springer New York, New York, 44–57.
Hertz, H., 1882. On the contact of elastic solids. Journal für die reine und angewandte Mathematik (Crelles Journal), 92: 156–171.
Jiang, W. G., 2012. A concise finite element model for pure bending analysis of simple wire strand. International Journal of Mechanical Sciences, 54(1): 69–73.
Jiang, W. G., Henshall, J. L., and Walton, J. M., 2000. A concise finite element model for three-layered straight wire rope strand. International Journal of Mechanical Sciences, 42(1): 63–86.
Jiang, W. G., Warby, M. K., and Henshall, J. L., 2008. Statically indeterminate contacts in axially loaded wire strand. European Journal of Mechanics—A: Solids, 27(1): 69–78.
Liu, L., Zheng, S., and Liu, D., 2020. Effect of lay direction on the mechanical behavior of multi-strand wire ropes. International Journal of Solids and Structures, 185–186: 89–103.
Love, A. E. H., 1944. A Treatise on the Mathematical Theory of Elasticity. Primary Source Edition. Dover Publications, Cambridge, UK, 529–530.
Meng, F., Chen, Y., Du, M., and Gong, X., 2016. Study on effect of inter-wire contact on mechanical performance of wire rope strand based on semi-analytical method. International Journal of Mechanical Sciences, 115–116: 416–427.
Minaei, A., Daneshjoo, F., and Goicolea, J. M., 2020. Experimental and numerical study on cable breakage equivalent force in cable-stayed structures consisting of low-relaxation seven-wire steel strands. Structures, 27: 595–606.
Montoya, A., Waisman, H., and Betti, R., 2012. A simplified contact-friction methodology for modeling wire breaks in parallel wire strands. Computers & Structures, 100–101: 39–53.
Peng, X., and Cao, J., 2002. A dual nomogenization and finite element approach for material characterization of texile composites. Composites, 33(1): 45–56.
Stanova, E., Fedorko, G., Fabian, M., and Kmet, S., 2011. Computer modelling of wire strands and ropes part II: Finite element-based applications. Advances in Engineering Software, 42(6): 322–331.
Xia, Z., Zhang, Y., and Ellyin, F., 2003. A unified periodical boundary conditions for representative volume elements of composites and applications. International Journal of Solids and Structures, 40(8): 1907–1921.
Xiang, L., Wang, H. Y., Chen, Y., Guan, Y. J., and Dai, L. H., 2017. Elastic-plastic modeling of metallic strands and wire ropes under axial tension and torsion loads. International Journal of Solids and Structures, 129: 103–118.
Xiang, L., Wang, H. Y., Chen, Y., Guan, Y. J., Wang, Y. L., and Dai, L. H., 2015. Modeling of multi-strand wire ropes subjected to axial tension and torsion loads. International Journal of Solids and Structures, 58: 233–246.
Yu, Y., Chen, Z., Liu, H., and Wang, X., 2014. Finite element study of behavior and interface force conditions of seven-wire strand under axial and lateral loading. Construction and Building Materials, 66: 10–18.
Zhang, P., Duan, M., Ma, J., and Zhang, Y., 2019a. A precise mathematical model for geometric modeling of wire rope strands structure. Applied Mathematical Modelling, 76: 151–171.
Zhang, Z., Wang, X., and Li, Q., 2019b. Responds of a helical triple-wire strand with interwire contact deformation and friction under axial and torsional loads. European Journal of Mechanics—A: Solids, 73: 34–46.
Acknowledgements
This study is funded by the National Natural Science Foundation of China (No. 51879188), and the Key R&D Project of Hebei Province (No. 1827350D).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tang, Y., He, X., Li, Y. et al. Stress Analysis of Wire Strands by Mesoscale Mechanics. J. Ocean Univ. China 21, 1118–1132 (2022). https://doi.org/10.1007/s11802-022-4923-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11802-022-4923-4