Structural Engineering and Mechanics

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Assessment of deformations and internal forces in the suspension bridge under eccentric live loads: Analytical algorithm

  • Zhang, Wenming (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Lu, Xiaofan (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Chang, Jiaqi (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Tian, Genmin (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Xia, Lianfeng (Henan Polytechnic)
  • Received : 2021.10.19
  • Accepted : 2021.11.16
  • Published : 2021.12.25
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Abstract

Suspension bridges bear large eccentric live loads in rush hours when most vehicles travel in one direction on the left or right side of the bridge. With the increasing number and weight of vehicles and the girder widening, the eccentric live load effect on the bridge behavior, including bending and distortion of the main girder, gets more pronounced, even jeopardizing bridge safety. This study proposes an analytical algorithm based on multi-catenary theory for predicting the suspension bridge responses to eccentric live load via the nonlinear generalized reduced gradient method. A set of governing equations is derived to solve the following unknown values: the girder rigid-body displacement in the longitudinal direction; the horizontal projection lengths of main cable's segments; the parameters of catenary equations and horizontal forces of the side span cable segments and the leftmost segments of middle span cables; the suspender tensions and the bearing reactions. Then girder's responses, including rigid-body displacement in the longitudinal direction, deflections, and torsion angles; suspenders' responses, including the suspender tensions and the hanging point displacements; main cables' responses, including the horizontal forces of each segment; and the longitudinal displacement of the pylons' tower top under eccentric load can be calculated. The response of an exemplar suspension bridge with three spans of 168, 548, and 168 m is calculated by the proposed analytical method and the finite element method in two eccentric live load cases, and their results prove the former's feasibility. The nonuniform distribution of the live load in the lateral direction is shown to impose a greater threat to suspension bridge safety than that in the longitudinal direction, while some other specific features revealed by the proposed method are discussed in detail.

Keywords

Acknowledgement

The work described in this paper was financially supported by the National Natural Science Foundation of China under Grants 52078134 and 51678148, the Natural Science Foundation of Jiangsu Province (BK20181277), and the National Key R&D Program of China (No. 2017YFC0806009), which are gratefully acknowledged.

References

  1. Arco, D.C. and Aparicio, A.C. (2001), "Preliminary static analysis of suspension bridges", Eng. Struct., 23(9), 1096-1103. https://doi.org/10.1016/S0141-0296(01)00009-8.
  2. Bridge Science Research Institute (1996), Major Bridge Engineering Bureau of the Ministry of Railways Suspension Bridge, Science and Technology Document Press, Beijing.
  3. Cao, H.Y, Qian, X., Chen, Z.J. and Zhu, H.P. (2017), "Layout and size optimization of suspension bridges based on coupled modelling approach and enhanced particle swarm optimization", Eng. Struct., 146, 170-183. https://doi.org/10.1016/j.engstruct.2017.05.048.
  4. Cao, H.Y, Qian, X., Zhou, Y., Chen, Z.J. and Zhu, H.P. (2018), "Feasible range for midtower lateral stiffness in three-tower suspension bridges", J. Bridge Eng., 23, 06017009 https://orcid.org/0000-0002-6183-256X. https://doi.org/10.1061/(asce)be.1943-5592.0001196
  5. Chai, S.B., Xiao, R.C. and Wang, X.L. (2016), "Approximate calculation for deformation of multi-tower suspension bridges", Struct. Eng. Int., 26, 45-51. https://doi.org/10.2749/101686616X14480232444324.
  6. Choi, D.H., Gwon, S.G., Yoo, H. and Na, H.S. (2013), "Nonlinear static analysis of continuous multi-span suspension bridges", Int. J. Steel Struct., 13, 103-115. https://doi.org/10.1007/s13296-013-1010-0.
  7. Clemente, P., Nicolosi, G. and Raithel, A. (2000), "Preliminary design of very long-span suspension bridges", Eng. Struct., 22(12), 1699-1706. https://doi.org/10.1016/S0141-0296(99)00112-1.
  8. Grigorjeva, T., Juozapaitis, A. and Kamaitis, Z. (2010), "Static analysis and simplified design of suspension bridges having various rigidity of cables", J. Civil Eng. Manage., 16, 363-371. https://doi.org/10.3846/jcem.2010.41
  9. Grigorjeva, T., Juozapaitis, A. and Karnaitis, Z. (2006), "Simplified engineering method of suspension bridges with rigid cables under action of symmetrical and asymmetrical loads", Balt. J. Road Bridge Eng., 1, 11-20.
  10. Grigorjeva, T., Juozapaitis, A., Kamaitis, Z. and Paeglitis, A. (2008), "Finite element modelling for static behaviour analysis of suspension bridges with varying rigidity of main cables", Balt. J. Road Bridge Eng., 3, 121-128. https://doi.org/10.3846/1822-427X.2008.3.121-128
  11. Jung, M.R., Shin, S.U., Attard, M.M. and Kim, M.Y. (2015), "Deflection theory for self-anchored suspension bridges under live load", J. Bridge Eng., 20, 04014093. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000687.
  12. Lasdon, L.S., Waren, A.D., Jain, A. and Ratner, M. (1976), "Design and testing of a generalized reduced gradient code for nonlinear programming", ACM Tran. Math. Softw., 4(1), 34-50. https://doi.org/10.1145/355769.355773
  13. Niu, W.J. and Yu, H.T. (2016), "A new analytic solution to determine internal load of small span suspension bridge", KSCE J. Civil Eng., 20, 1419-1428. https://doi.org/10.1007/s12205-015-0598-3.
  14. Ohshima, H., Sato, K. and Watanabe, N. (1984), "Structural analysis of suspension bridges", J. Eng. Mech. 110, 392-404. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:3(392).
  15. Park, K.J., Kim, D.Y. and Hwang, E.S. (2018), "Investigation of live load deflection limit for steel cable stayed and suspension bridges", Int. J. Steel Struct., 18, 1252-1264. https://doi.org/10.1007/s13296-018-0108-9.
  16. Shi, X.F., Zhou, Z.J. and Ruan, X. (2016), "Failure analysis of a girder bridge collapse under eccentric heavy vehicles", J. Bridge Eng., 21, 05016009. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000964.
  17. Sun, Y., Zhu, H.P. and Xu, D. (2016), "A specific rod model based efficient analysis and design of hanger installation for self-anchored suspension bridges with 3D curved cables", Eng. Struct., 110, 184-208. https://doi.org/10.1016/j.engstruct.2015.11.040.
  18. Tang, M.C. (2017), "Super-long span bridges", Struct. Infrastr. Eng., 13, 722-730. https://doi.org/10.1080/15732479.2016.1187635.
  19. Wang, H.L., Qin, S.F., Huang, C.L. and Ge, X.M. (2010), "Living load nonlinear analysis of self-anchored cable-stayed suspension bridges", Appl. Mech. Mater., 29, 1583-1587. https://doi.org/10.4028/www.scientific.net/AMM.29-32.1583.
  20. Wang, X.L., Chai, S.B. and Xu, Y. (2016), "Deformation characteristics of double-cable multispan suspension bridges", J. Bridge Eng., 21, 06015007. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000858.
  21. Wang, X.M., Wang, H., Sun, Y., Mao, X. and Tang, S. (2020), "Process-independent construction stage analysis of self-anchored suspension bridges", Autom. Constr., 117, 103227. https://doi.org/10.1016/j.autcon.2020.103227.
  22. Wang, X.M., Wang, H., Zhang, J., Sun, Y., Bai, Y., Zhang, Y. and Wang, H. (2021), "Form-finding method for the target configuration under dead load of a new type of spatial self-anchored hybrid cable-stayed suspension bridges", Eng. Struct., 227, 111407. https://doi.org/10.1016/j.engstruct.2020.111407.
  23. Wollmann, G.P. (2001. "Preliminary analysis of suspension bridges", J. Bridge Eng., 6(4), 227-233. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:4(227).
  24. Zhang, W.M., Chang, J.Q. and Tian, G.M. (2022) "FEM-based shape-finding and force-assessment of suspension bridges via completed loop adjustment", J. Bridge Eng., 27(1), 04021098. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001804.
  25. Zhang, W.M., Shi, L.Y., Li, L. and Liu, Z. (2018), "Methods to correct unstrained hanger lengths and cable clamps' installation positions in suspension bridges", Eng. Struct., 171, 202-213. https://doi.org/10.1016/j.engstruct.2018.05.039.
  26. Zhang, W.M., Yang, C.Y. and Chang, J.Q. (2021), "Cable shape and construction parameters of triple-tower double-cable suspension bridge with two asymmetrical main spans", J. Bridge Eng., 26(2), 04020127. https://orcid.org/0000-0002-8272-1121. https://doi.org/10.1061/(asce)be.1943-5592.0001674
  27. Zhang, W.M., Yang, C.Y., Wang, Z.W. and Liu, Z. (2019), "An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans", Eng. Struct., 199, 109595. https://doi.org/10.1016/j.engstruct.2019.109595.