Structural Engineering and Mechanics

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Form-finding analysis of suspension bridges using an explicit Iterative approach

  • Cao, Hongyou (Department of Civil and Environmental Engineering, National University of Singapore) ;
  • Zhou, Yun-Lai (Department of Civil and Environmental Engineering, National University of Singapore) ;
  • Chen, Zhijun (School of Civil Engineering & Mechanics, Huazhong University of Science & Technology) ;
  • Wahab, Magd Abdel (Division of Computational Mechanics, Ton Duc Thang University)
  • Received : 2016.09.19
  • Accepted : 2017.01.23
  • Published : 2017.04.10
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Abstract

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

Keywords

Acknowledgement

Supported by : Central Universities, National Natural Science Foundation of China

References

  1. Cao, H., Chen, Z., Wu, Q., Zhu, H.P. and Kang, J. (2016), "A simplified model for multi-span suspension bridges based on single cable theory", China J. Highw. Tran., 29(4), 77-84.
  2. Chen, Z., Cao, H., Ye, K., Zhu, H. and Li, S. (2013), "Improved particle swarm optimization-based form-finding method for suspension bridge installation analysis", J. Comput. Civil Eng., 29(3), 04014047.
  3. Chen, Z., Cao, H. and Zhu, H. (2015), "An iterative calculation method for suspension bridge's cable system based on exact catenary theory", Baltic J. Road Bridge Eng., 8(3), 196-204. https://doi.org/10.3846/bjrbe.2013.25
  4. Chen, Z., Cao, H., Zhu, H., Hu, J. and Li, S. (2014), "A simplified structural mechanics model for cable-truss footbridges and its implications for preliminary design", Eng. Struct., 68, 121-133. https://doi.org/10.1016/j.engstruct.2014.02.015
  5. Fan, L., Pan, Y. and Du, G. (1999), "Study on the fine method of calculating the erection-parameters of long-span suspension bridges", Chin Civil Eng. J., 32, 20-25.
  6. Faroughi, S., Kamran, M.A. and Lee, J. (2014), "A Genetic algorithm approach for 2-D tensegrity form finding", Adv. Struct. Eng., 17(11), 1669-1679. https://doi.org/10.1260/1369-4332.17.11.1669
  7. Gimsing, N.J. and Georgakis, C.T. (2011), Cable Supported Bridges: Concept and Design, John Wiley & Sons.
  8. Irvine, H.M. (1981), Cable Structures, The MIT Press, Cambridge.
  9. Jung, M.R., Min, D.J. and Kim, M.Y. (2013), "Nonlinear analysis methods based on the unstrained element length for determining initial shaping of suspension bridges under dead loads", Comput. Struct., 128, 272-285. https://doi.org/10.1016/j.compstruc.2013.06.014
  10. Jung, M.R., Min, D.J. and Kim, M.Y. (2015), "Simplified analytical method for optimized initial shape analysis of self-anchored suspension bridges and its verification", Math. Prob. Eng., 2015, Article ID 923508, 14.
  11. 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
  12. Kim, H.K. and Kim, M.Y. (2012), "Efficient combination of a TCUD method and an initial force method for determining initial shapes of cable-supported bridges", Int. J. Steel Struct., 12(2), 157-174. https://doi.org/10.1007/s13296-012-2002-1
  13. Kim, H.K., Lee, M.J. and Chang, S.P. (2002), "Non-linear shape-finding analysis of a self-anchored suspension bridge", Eng. Struct., 24(12), 1547-1559. https://doi.org/10.1016/S0141-0296(02)00097-4
  14. Kim, K.S. and Lee, H.S. (2001), "Analysis of target configurations under dead loads for cable-supported bridges", Comput. Struct., 79(29), 2681-2692. https://doi.org/10.1016/S0045-7949(01)00120-1
  15. Kim, M.Y ., Kim, D.Y., Jung, M.R. and Attard, M.M. (2014), "Improved methods for determining the 3 dimensional initial shapes of cable-supported bridges", Int. J. Steel Struct., 14(1), 83-102. https://doi.org/10.1007/s13296-014-1009-1
  16. Koohestani, K, and Guest, S.D. (2013), "A new approach to the analytical and numerical form-finding of tensegrity structures", Int. J. Solid. Struct., 50(19), 2995-3007. https://doi.org/10.1016/j.ijsolstr.2013.05.014
  17. Lonetti, P, and Pascuzzo, A. (2014), "Optimum design analysis of hybrid cable-stayed suspension bridges", Adv. Eng. Softw., 73, 53-66. https://doi.org/10.1016/j.advengsoft.2014.03.004
  18. Lund, E. (1994), "Finite element based design sensitivity analysis and optimization", Institute of Mechanical Engineering, Aalborg University, Denmark.
  19. Luo, X.H. (2004), "Numerical analysis method for cable system of suspension bridges", J. Tongji Univ., 4, 5.
  20. O'Brien, T. (1967), "General solution of suspended cable problems", J. Struct. Div., 93(1), 1-26.
  21. O'Brien, W.T. and Francis, A.J. (1964), "Cable movements under two-dimensional loads", ASCE J. Struct. Div., 90, 89-123.
  22. Sun, Y., Zhu, H.P. and Xu, D. (2014), "New method for shape finding of self-anchored suspension bridges with three-dimensionally curved cables", J. Bridge Eng., 20(2), 04014063.
  23. 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
  24. Wang, P.H. and Yang, C.G. (1996), "Parametric studies on cable-stayed bridges", Comput. Struct., 60(2), 243-260. https://doi.org/10.1016/0045-7949(95)00382-7
  25. Wang, S., Zhou, Z., Gao, Y. and Huang, Y. (2015), "Analytical calculation method for the preliminary analysis of self-anchored suspension bridges", Math. Prob. Eng., 2015, Article ID 918649, 12.
  26. Wriggers, P. (2008), Nonlinear Finite Element Methods, Springer Science & Business Media.
  27. Zhang, L.Y., Li, Y., Cao, Y.P. and Feng, X.Q. (2014), "Stiffness matrix based form-finding method of tensegrity structures", Eng. Struct., 58, 36-48. https://doi.org/10.1016/j.engstruct.2013.10.014

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