Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analytical study on cable shape and its lateral and vertical sags for earth-anchored suspension bridges with spatial cables

  • Gen-min Tian (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Wen-ming Zhang (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Jia-qi Chang (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Zhao Liu (Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
  • Received : 2021.07.16
  • Accepted : 2023.07.06
  • Published : 2023.08.10
⟨ Previous Next ⟩

Abstract

Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

Keywords

Acknowledgement

This study was financially supported by the National Key R&D Program of China (No. 2022YFB3706703), the National Natural Science Foundation of China (No. 52078134), the Postgraduate Research & Practice Innovation Program of the Jiangsu Province of China (No. KYCX22_0220), and the Research and Development Project of China Communications Construction (grant No. YSZX-02-2021-01-B), which are gratefully acknowledged.

References

  1. Andreu, A., Gil, L. and Roca, P. (2006), "A new deformable catenary element for the analysis of cable net structures", Comput. Struct., 84(29-30), 1882-1890. http://doi.org/10.1016/j.compstruc.2006.08.021.
  2. Cao, H.Y., Zhou, Y.L., Chen, Z.J. and Abdel Wahab, M. (2017), "Form-finding analysis of suspension bridges using an explicit Iterative approach", Struct. Eng. Mech., 62(1), 85-95. http://doi.org/10.12989/sem.2017.62.1.085.
  3. Chen, Z.J., Cao, H.Y., Ye, K., Zhu, H.P, and Li, S.F. (2015), "Improved particle swarm optimization-based form-finding method for suspension bridge installation analysis", J. Comput. Civil Eng., 29(3), 04014047. http://doi.org/10.1061/(ASCE)CP.1943-5487.0000354.
  4. Chen, Z.J., Cao, H.Y. and Zhu, H.P. (2013), "An iterative calculation method for suspension bridge,s cable system based on exact catenary theory", Balt. J. Road Bridge Eng., 8(3), 196-204. http://doi.org/10.3846/bjrbe.2013.25.
  5. Gil, H. and Choi, Y. (2001), "Cable erection test at pylon saddle for spatial suspension bridge", J. Bridge Eng., 6(3), 183-188. http://doi.org/10.1061/(ASCE)1084-0702(2001)6:3(183).
  6. Huang, P.M. and Li, C.J. (2023), "Review of the main cable shape control of the suspension bridge", Appl. Sci., 13(5), 3106. https://doi.org/10.3390/app13053106.
  7. Huang, Y. and Lan, W.R. (2006), "Static analysis of cable structure", Appl. Math. Mech., 27(10), 1425-1430. http://doi.org/CNKI:SUN:YYSL.0.2006-10-015. 10-015
  8. Irvine, H.M. (1975), "Statics of suspended cables", J. Eng. Mech. Div., 101(3), 187-205. http://doi.org/10.1016/S0022-460X(75)80142-8.
  9. Irvine, H.M. (1981), Cable Structures, MIT Press, Cambridge.
  10. 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. http://doi.org/10.1016/j.compstruc.2013.06.014.
  11. 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. http://doi.org/10.1155/2015/923508.
  12. Karoumi, R. (1999), "Some modeling aspects in the nonlinear finite element analysis of cable supported bridges", Comput. Struct., 71(4), 397-412. http://doi.org/10.1016/S0045-7949(98)00244-2.
  13. Kim, H.K., Lee, M.J. and Chang, S.P. (2002), "Non-linear shapefinding analysis of a self-anchored suspension bridge", Eng. Struct., 24(12), 1547-1559. http://doi.org/10.1016/S0141-0296(02)00097-4.
  14. 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. http://doi.org/10.1007/s13296-012-2002-1.
  15. Kim, K.S. and Lee, H.S. (2001), "Analysis of target configurations under dead loads for cable-supported bridges", Comput. Struct., 79(29-30), 2681-2692. http://doi.org/10.1016/S0045-7949(01)00120-1.
  16. Kim, M.Y., Jung, M.R. and Attard, M.M. (2019), "Unstrained length-based methods determining an optimized initial shape of 3-dimensional self-anchored suspension bridges", Comput. Struct., 217, 18-35. https://doi.org/10.1016/j.compstruc.2019.03.008.
  17. Li, C., Li, Y. and He, J. (2019), "Experimental study on torsional behavior of spatial main cable for a self-anchored suspension bridge", Adv. Struct. Eng., 22(14), 3086-3099. http://doi.org/10.1177/1369433219857840.
  18. Li, C.X. (2014), Static Nonlinear Theory and Practice of Modern Suspension Bridge, China Comm Press Co, Ltd, Beijing. (in Chinese)
  19. Li, C.X., Ke, H.J., Liu, H.B. and Xia, G.Y. (2010), "Determination of finished bridge state of self-anchored suspension bridge with spatial cables", Eng. Mech., 27(5), 137-146. (in Chinese)
  20. Li, J.H., Feng, D.M., Li, A.Q. and Yuan, H.H. (2016), "Determination of reasonable finished state of self-anchored suspension bridges", J. Cent. South Univ., 23(1), 209-219. http://doi.org/10.1007/s11771-016-3064-6.
  21. Li, T. and Liu, Z. (2019), "A recursive algorithm for determining the profile of the spatial self-anchored suspension bridges", KSCE J. Civil Eng., 23(3), 1283-1292. http://doi.org/10.1007/s12205-019-0542-z.
  22. Li, T., Liu, Z. and Zhang, W.M. (2020), "Analysis of suspension bridges in construction and completed status considering the pylon saddles", Eur. J. Environ. Civil. Eng., 26(9), 4280-4295. https://doi.org/10.1080/19648189.2020.1848637.
  23. Luo, X.H., Xiao, R.C. and Xiang, H.F. (2004), "Cable shape analysis of suspension bridge with spatial cables", J. Tongji Univ., 32, 1349-1354. (in Chinese)
  24. Rezaiee-Pajand, M., Mokhtari, M. and Masoodi, A.R. (2018), "A novel cable element for nonlinear thermo-elastic analysis", Eng. Struct., 167, 431-444. http://doi.org/10.1016/j.engstruct.2018.04.022.
  25. Shen, R., Qi, D. and Tang, M. (2011), "Model test study of the static property of the jiangdong bridge in hangzhou", China Civil Eng. J., 44(1), 74-80. (in Chinese)
  26. Song, C.L., Xiao, R.C. and Sun, B. (2020), "Improved method for shape finding of long-span suspension bridges", Int. J. Steel Struct., 20(1), 247-258. http://doi.org/10.1007/s13296-019-00283-7.
  27. Such, M., Jimenez-Octavio, J.R., Carnicero, A. and Lopez-Garcia, O. (2009), "An approach based on the catenary equation to deal with static analysis of three dimensional cable structures", Eng. Struct., 31(9), 2162-2170. http://doi.org/10.1016/j.engstruct.2009.03.018.
  28. Sun, J., Manzanarez, R. and Nader, M. (2002), "Design of looping cable anchorage system for new San Francisco-Oakland Bay Bridge main suspension span", J. Bridge Eng., 7(6), 315-324. http://doi.org/10.1061/(ASCE)1084-0702(2002)7:6(315).
  29. Sun, Y., Zhu, H.P. and Xu, D. (2015), "New method for shape finding of self-anchored suspension bridges with three-dimensionally curved cables", J Bridge Eng., 20(2), 04014063. http://doi.org/10.1061/(ASCE)BE.1943-5592.0000642.
  30. 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. http://doi.org/10.1016/j.engstruct.2015.11.040.
  31. Suzuki, Y., Miyata, E.S. and Iverson, S.C. (1996), "Static analyses of the triangular running skyline system: a three-dimensionally movable logging cable system", Comput. Struct., 60(4), 579-592. http://doi.org/10.1016/0045-7949(95)00426-2.
  32. Tang, M.L., Qiang, S.Z. and Shen, R.L. (2003), "Segmental catenary method of calculating the cable curve of suspension bridge", J. China Railw. Soc., 25(1), 87-91. (in Chinese)
  33. Wan, J.W., Wang, Q., Liao, H.L. and Li, M.S. (2017), "Study on aerodynamic coefficients and responses of the integrated catwalk of Halogaland Bridge", Wind Struct., 25(3), 215-232. http://doi.org/10.12989/was.2017.25.3.215. 
  34. Wang, X.M., Frangopol, D.M., Dong, Y., Lei, X.M. and Zhang, Y.F. (2018), "Novel technique for configuration transformation of 3D curved cables of suspension bridges: Application to the Dongtiao River Bridge", J. Perform. Constr. Facil., 32(4), 04018045. http://doi.org/10.1061/(ASCE)CF.1943-5509.0001189.
  35. Wang, X.M., Wang, H., Zhang, J., Sun, Y., Bai, Y.T., Zhang, Y.F. and Wang, H.C. (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.
  36. Wei, J.D., Guan, M.Y., Cao, Q. and Wang, R.B. (2018), "Spatial combined cable element for cable-supported bridges", Eng. Comput., 36(1), 204-225. http://doi.org/10.1108/EC-05-2018-0243.
  37. Xiao, R.C., Chen, M.H. and Sun, B. (2017), "Determination of the reasonable state of suspension bridges with spatial cables", J. Bridge Eng., 22(9), 04017060. http://doi.org/10.1061/(ASCE)BE.1943-5592.0001106
  38. Yang, M.G., Chen, Z.Q. and Hua, X.G. (2010), "A new two-node catenary cable element for the geometrically non-linear analysis of cable-supported structures", Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci., 224(6), 1173-1183. http://doi.org/10.1243/09544062JMES1816.
  39. Zhang, J.P., Liu, A.R., Ma, Z.J., Huang, H.Y., Mei, L.B. and Li, Y.H. (2013), "Behavior of self-anchored suspension bridges in the structural system transformation", J. Bridge Eng., 18(8), 712-721. http://doi.org/10.1061/(ASCE)BE.1943-5592.0000422.
  40. 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. http://doi.org/10.1016/j.engstruct.2018.05.039.
  41. Zhang, W.M., Zhang, Z.H., Tian, G.M. and Chang, J.Q. (2023), "Determining the reasonable completed bridge state of a self-anchored suspension bridge with a spatial cable system based on minimum bending strain energy: An analytical algorithm", J. Bridge Eng., 28(5), 04023018. http://doi.org/10.1061/JBENF2.BEENG-5857.
  42. Zhang, Z.H., Zhang, J.Y., Hao, W.S., Dai, J.G. and Shen, Y. (2010), "Hangzhou Jiangdong Bridge designed as a spatial self-anchored suspension bridge, China", Struct. Eng. Int., 20(3), 303-307. http://doi.org/10.2749/101686610792016673.
  43. Zhou, G.P., Li, A.Q., Li, J.H., Duan, M.J., Xia, Z.Y., Zhu, L., Spencer, B.F. and Wang, B. (2019), "Test and numerical investigations on the spatial mechanics characteristics of extra-wide concrete self-anchored suspension bridge during construction", Int. J. Distrib. Sens. Netw., 15(12), 1550147719891561. http://doi.org/10.1177/1550147719891561.
  44. Zhu, W.L., Ge, Y.J., Fang, G.S. and Cao, J.X. (2021), "A novel shape finding method for the main cable of suspension bridge using nonlinear finite element approach", Appl. Sci., 11(10), 4644. https://doi.org/10.3390/app11104644.