Effect of Cable Vibrations on Cable-Stayed Bridges during Large Earthquakes
Publication: Journal of Bridge Engineering
Volume 29, Issue 3
Abstract
Support movements cause nonlinear vibrations in cables, but it is unclear how exactly the cables in cable-stayed bridges respond to the complicated support movements induced by earthquakes. In this study, we employed a displacement approach that separated the cable vibrations into pseudostatic and relative dynamic responses. The former depicted the cable response under static loadings, the latter were caused by the dynamic components of the pseudostatic components. A three-dimensional finite-element model of a cable-stayed bridge was established, with the exact pseudostatic response of the cables included. The cable vibrations were determined following seismic displacements at the cable–deck and cable–tower connections. It was revealed that the cable vibrations were significant both during and after the shaking from the earthquake, and that the maximum response was reached after the shaking in most cases. The longitudinal and vertical seismic inputs mainly cause parametric and in-plane resonant vibrations, whereas the transverse inputs triggered out-of-plane resonant vibrations in the cables. The cable vibrations were more significant when high spectral accelerations of the ground motions occurred in the vibration periods of the cables. It was concluded that the nonlinear cable vibrations should be taken into consideration under larger earthquake conditions.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 52108445 and 52178124) and the Education Department of Guangdong Province (No. 2022GXJK294). This support is gratefully acknowledged.
References
Abdel-Ghaffar, A. M., and M. A. Khalifa. 1991. “Importance of cable vibration in dynamics of cable-stayed bridges.” J. Eng. Mech. 117 (11): 2571–2589. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:11(2571).
Ali, H. M., and A. M. Abdel-Ghaffar. 1995. “Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings.” Comput. Struct. 54 (3): 461–492. https://doi.org/10.1016/0045-7949(94)00353-5.
Antonio, P. D. C., J. Martins, F. Branco, and J. L. Lilien. 1996. “Oscillations of bride stay cables induced by periodic motions of deck and/or towers.” J. Eng. Mech. 122 (7): 613–622.
Benedettini, F., G. Rega, and R. Alaggio. 1995. “Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions.” J. Sound Vib. 182 (5): 775–798. https://doi.org/10.1006/jsvi.1995.0232.
Chadwell, C. B. 2003. Seismic response of single tower cable-stayed bridges. Berkeley, CA: Univ. of California.
Chen, L., L. Sun, Y. Xu, F. Di, Y. Xu, and L. Wang. 2020. “A comparative study of multi-mode cable vibration control using viscous and viscoelastic dampers through field tests on the Sutong Bridge.” Eng. Struct. 224: 111226. https://doi.org/10.1016/j.engstruct.2020.111226.
Costa, A., J. Martins, F. Branco, and J. L. Lilien. 1996. “Oscillations of bridge stay cable induced by periodic motions of deck and/or towers.” J. Eng. Mech. 122 (7): 613–622.
Demšić, M., M. Uroš, A. Jaguljnjak Lazarević, and D. Lazarević. 2019. “Resonance regions due to interaction of forced and parametric vibration of a parabolic cable.” J. Sound Vib. 447: 78–104. https://doi.org/10.1016/j.jsv.2019.01.036.
Gao, D., W. Chen, E. Christophe, and H. Li. 2018. “Multi-mode responses, rivulet dynamics, flow structures and mechanism of rain–wind induced vibrations of a flexible cable.” J. Fluids Struct. 82: 154–172. https://doi.org/10.1016/j.jfluidstructs.2018.06.017.
Georgakis, C. T., and C. A. Taylor. 2005. “Nonlinear dynamics of cable stays. Part 1: Sinusoidal cable support excitation.” J. Sound Vib. 281 (3–5): 537–564. https://doi.org/10.1016/j.jsv.2004.01.022.
Gheorghiu, C., F. Yamazaki, T. Ganev, and H. Ishizaki. 1998. “Seismic response of the Higashi-Kobe Bridge during the 1995 Hyogoken-Nanbu Earthquake.” Bull. Earthquake Resistant Struct. Res. Center 31: 23–39.
Gimsing, N. J., and C. T. Georgakis. 2012. Cable supported bridges: Concept and design. 3rd ed. London: Wiley.
Gonzalez Buelga, A., S. A. Neild, D. J. Wagg, and J. H. G. Macdonald. 2008. “Modal stability of inclined cables subjected to vertical support excitation.” J. Sound Vib. 318: 565–579. https://doi.org/10.1016/j.jsv.2008.04.031.
Guan, Z., J. Li, W. Guo, and H. Qu. 2019. “Design and validation of a shaking-table test model on a long-span cable-stayed bridge with inverted-Y-shaped towers.” Eng. Struct. 201: 109823. https://doi.org/10.1016/j.engstruct.2019.109823.
Irvine, M. H. 1981. Cable structures. Cambridge, UK: The MIT Pr.
Irvine, H. M., T. K. Caughey, and G. B. Whitham. 1974. “The linear theory of free vibrations of a suspended cable.” Proc. R. Soc. London 341 (1626): 299–315. https://doi.org/10.1098/rspa.1974.0189.
Karoumi, R. 1999. “Some modeling aspects in the nonlinear finite element analysis of cable supported bridges.” Comput. Struct. 71 (4): 397–412. https://doi.org/10.1016/S0045-7949(98)00244-2.
Kim, H.-K., M. Shinozuka, and S.-P. Chang. 2004. “Geometrically nonlinear buffeting response of a cable-stayed bridge.” J. Eng. Mech. 130 (7): 848–857. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:7(848).
Kitazawa, M., J. Noguchi, and T. Yamagami. 1993. “Design of the Higashi-Kobe Bridge, Japan.” Struct. Eng. Int. 3 (4): 226–228. https://doi.org/10.2749/101686693780607714.
Lee, C., and N. C. Perkins. 1995. “Three-dimensional oscillations of suspended cables involving simultaneous internal resonances.” Nonlinear Dyn. 8 (1): 45–63. https://doi.org/10.1007/BF00045006.
Lin, K., Y.-L. Xu, X. Lu, Z. Guan, and J. Li. 2021. “Digital twin-based collapse fragility assessment of a long-span cable-stayed bridge under strong earthquakes.” Autom. Constr. 123 (2): 103547. https://doi.org/10.1016/j.autcon.2020.103547.
Long, Y., and H. Kang. 2022. “Analysis of 1:1 internal resonance of a CFRP cable with an external 1/3 subharmonic resonance.” Nonlinear Dyn. 107 (4): 3425–3441. https://doi.org/10.1007/s11071-021-07174-9.
Macdonald, J. H. G., M. S. Dietz, S. A. Neild, A. Gonzalez-Buelga, A. J. Crewe, and D. J. Wagg. 2010. “Generalised modal stability of inclined cables subjected to support excitations.” J. Sound Vib. 329 (21): 4515–4533. https://doi.org/10.1016/j.jsv.2010.05.002.
Martínez-Rodrigo, M. D., and A. Filiatraul. 2015. “A case study on the application of passive control and seismic isolation techniques to cable-stayed bridges: A comparative investigation through non-linear dynamic analyses.” Eng. Struct. 99: 232–252. https://doi.org/10.1016/j.engstruct.2015.04.048.
Mckenna, F. 2011. “Opensees: A framework for earthquake engineering simulation.” Comput. Sci. Eng. 13 (4): 58–66. https://doi.org/10.1109/MCSE.2011.66.
Perkins, N. C. 1992. “Modal interactions in the non-linear response of elastic cables under parametric/external excitation.” Int. J. Non Linear Mech. 27 (2): 233–250. https://doi.org/10.1016/0020-7462(92)90083-J.
Rega, G. 2004. “Nonlinear vibrations of suspended cables—Part I: Modeling and analysis.” Appl. Mech. Rev. 57 (6): 443–478. https://doi.org/10.1115/1.1777224.
Srinil, N., G. Rega, and S. Chucheepsakul. 2003. “Large amplitude three-dimensional free vibrations of inclined sagged elastic cables.” Nonlinear Dyn. 33 (2): 129–154. https://doi.org/10.1023/A:1026019222997.
Sun, C., X. Zhou, and S. Zhou. 2021. “Nonlinear responses of suspended cable under phase-differed multiple support excitations.” Nonlinear Dyn. 104 (2): 1097–1116. https://doi.org/10.1007/s11071-021-06354-x.
Wang, L., and Y. Zhao. 2009. “Large amplitude motion mechanism and non-planar vibration character of stay cables subject to the support motions.” J. Sound Vib. 327 (1–2): 121–133. https://doi.org/10.1016/j.jsv.2009.06.013.
Wang, P. H., T. C. Tseng, and C. G. Yang. 1993. “Initial shape of cable-stayed bridges.” Comput. Struct. 46 (6): 1095–1106. https://doi.org/10.1016/0045-7949(93)90095-U.
Warminski, J., D. Zulli, G. Rega, and J. Latalski. 2016. “Revisited modelling and multimodal nonlinear oscillations of a sagged cable under support motion.” Meccanica 51 (11): 2541–2575. https://doi.org/10.1007/s11012-016-0450-y.
Warnitchai, P., Y. Fujino, and T. Susumpow. 1995. “A non-linear dynamic model for cables and its application to a cable-structure system.” J. Sound Vib. 187 (4): 695–712. https://doi.org/10.1006/jsvi.1995.0553.
Wilson, E. 1996. Three-dimensional static and dynamic analysis of structures: A physical approach with emphasis on earthquake engineering. Berkeley, CA: Computers & Structures.
Wu, Q., K. Takahashi, and S. Nakamura. 2004. “Non-linear response of cables subjected to periodic support excitation considering cable loosening.” J. Sound Vib. 271 (1): 453–463. https://doi.org/10.1016/S0022-460X(03)00513-3.
Wu, Q., K. Takahashi, T. Okabayashi, and S. Nakamura. 2003. “Response characteristics of local vibrations in stay cables on an existing cable-stayed bridge.” J. Sound Vib. 261 (3): 403–420. https://doi.org/10.1016/S0022-460X(02)01088-X.
Yi, J. 2023. “Modeling and analysis of cable vibrations in cable-stayed bridges under near-fault ground motions.” Eng. Struct. 277: 115443. https://doi.org/10.1016/j.engstruct.2022.115443.
Yi, J., and J. Li. 2017. “Longitudinal seismic behavior of a single-tower cable-stayed bridge subjected to near-field earthquakes.” Shock Vib. 2017: 1675982.
Yi, J., and J. Li. 2021. “Modelling of stay cables with large earthquake-induced force variations in cable-stayed bridges.” Structures 33: 627–636. https://doi.org/10.1016/j.istruc.2021.04.034.
Yi, J., and Y. Liu. 2023. “Vibrations of a taut horizontal cable subjected to axial support excitations considering nonlinear quasi-static responses.” Struct. Eng. Mech. 86 (2): 221–235.
Ying, Z. G., Y. Q. Ni, and J. M. Ko. 2006. “Parametrically excited instability of a cable under two support motions.” Int. J. Struct. Stab. Dyn. 6 (1): 43–58. https://doi.org/10.1142/S0219455406001794.
Zarate, B. A., and J. M. Caicedo. 2015. “Effects of cable dynamics in the modeling of cable-stayed bridges under seismic excitation.” Int. J. Struct. Stab. Dyn. 15 (4): 1450061. https://doi.org/10.1142/S0219455414500618.
Zhao, Y., Z. Guo, C. Huang, L. Chen, and S. Li. 2018. “Analytical solutions for planar simultaneous resonances of suspended cables involving two external periodic excitations.” Acta Mech. 229 (2): 4393–4411. https://doi.org/10.1007/s00707-018-2224-1.
Zhong, J., J.-S. Jeon, and W.-X. Ren. 2018. “Risk assessment for a long-span cable-stayed bridge subjected to multiple support excitations.” Eng. Struct. 176: 220–230. https://doi.org/10.1016/j.engstruct.2018.08.107.
Zong, Z., X. Huang, L. I. Yale, and Z. Xia. 2016. “Evaluation of the collapse failure modes of cable-stayed bridge model under strong earthquake excitations.” China Sci. Pap. 11 (7): 721–727.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 29 • Issue 3 • March 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 8, 2023
Accepted: Nov 15, 2023
Published online: Jan 12, 2024
Published in print: Mar 1, 2024
Discussion open until: Jun 12, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.