Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analytical methods for determining the cable configuration and construction parameters of a suspension bridge

  • Zhang, Wen-ming (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Tian, Gen-min (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Yang, Chao-yu (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University) ;
  • Liu, Zhao (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
  • Received : 2018.10.03
  • Accepted : 2019.08.26
  • Published : 2019.09.25
⟨ Previous Next ⟩

Abstract

Main cable configurations under final dead load and in the unloaded state and critical construction parameters (e.g. unstrained cable length, unstrained hanger lengths, and pre-offsets for tower saddles and splay saddles) are the core considerations in the design and construction control of a suspension bridge. For the purpose of accurate calculations, it is necessary to take into account the effects of cable strands over the anchor spans, arc-shaped saddle top, and tower top pre-uplift. In this paper, a method for calculating the cable configuration under final dead load over a main span, two side spans, and two anchor spans, coordinates of tangent points, and unstrained cable length are firstly developed using conditions for mechanical equilibrium and geometric relationships. Hanger tensile forces and unstrained hanger lengths are calculated by iteratively solving the equations governing hanger tensile forces and the cable configuration, which gives careful consideration to the effect of hanger weight. Next, equations for calculating the cable configuration in the unloaded state and pre-offsets of saddles are derived from the cable configuration under final dead load and the conditions for unstrained cable length to be conserved. The equations for the main span, two side spans and two anchor spans are then solved simultaneously. In the proposed methods, coupled nonlinear equations are solved by turning them into an unconstrained optimization problem, making the procedure simplified. The feasibility and validity of the proposed methods are demonstrated through a numerical example.

Keywords

Acknowledgement

Supported by : NSFC, Natural Science Foundation of Jiangsu Province

References

  1. Cao, H., Zhou, Y., Chen, Z. and Wahab, M.A. (2017), "Formfinding analysis of suspension bridges using an explicit Iterative approach", Struct. Eng. Mech., 62(1), 85-95. https://doi.org/10.12989/sem.2017.62.1.085.
  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), https://doi.org/10.1061/(ASCE)CP.1943-5487.0000354.
  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. Irvine, H.M. (1981), Cable Structures, The MIT Press, Cambridge, Mass, USA.
  5. Jayaraman, H.B. and Knudson, W.C. (1981), "A curved element for the analysis of cable structures", Comp. Struc., 14(3), 25-333. https://doi.org/10.1016/0045-7949(81)90016-X.
  6. 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", Comp. Struct., 128(5), 272-285. https://doi.org/10.1016/j.compstruc.2013.06.014.
  7. Jung, M.R., Min, D.J. and Kim, M.Y. (2015), "Simplified analytical method for optimized initial shape analysis of selfanchored suspension bridges and its verification", Math. Prob. Eng., 2015, 1-14. http://dx.doi.org/10.1155/2015/923508.
  8. Karoumi, R. (2012), "Some modeling aspects in the nonlinear finite element analysis of cable supported bridges", Comp. Struct., 71(4), 397-412. https://doi.org/10.1016/S0045-7949(98)00244-2.
  9. Kim, K.S. and Lee, H.S. (2001), "Analysis of target configurations under dead loads for cable supported bridges", Comp. Struct., 79(29), 2681-2692. https://doi.org/10.1016/S0045-7949(01)00120-1.
  10. Kim, H.K. and Lee, M.J. (2002), "Chang SP. Non-linear shapefinding analysis of a self-anchored suspension bridge", Eng. Struct., 24(12), 1547-1559. https://doi.org/10.1016/S0141-0296(02)00097-4.
  11. Lasdon, L.S., Fox, R.L. and Ratner, M.W. (1974), "Nonlinear optimization using the generalized reduced gradient method", RAIRO Oper. Res. Rech. Oper., 8(3), 73-103.
  12. Lasdon, L.S., Waren, A.D., Jain, A. and Ratner, M. (1978), "Design and testing of a generalized reduced gradient code for nonlinear programming", ACM Trans. Math. Softw., 4(1), 34-50. https://apps.dtic.mil/dtic/tr/fulltext/u2/a025724.pdf. https://doi.org/10.1145/355769.355773
  13. O'Brien, T. (1964), "General solution of suspended cable problems", J. Struct. Div., 93(ST1), 1-26. https://doi.org/10.1061/JSDEAG.0001574
  14. O'Brien, T. and Francis, A.J. (1964), "Cable movements under two-dimensional loads", J. Struct. Div., 90(ST3), 89-123.
  15. 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), https://doi.org/10.1061/(ASCE)BE.1943-5592.0000642.
  16. Thai, H.T. and Kim, S.E. (2011), "Nonlinear static and dynamic analysis of cable structures", Finite Elem. Anal. Des., 47(3), 237-246. https://doi.org/10.1016/j.finel.2010.10.005.
  17. Thai, H.T. and Choi, D.H. (2013), "Advanced analysis of multispan suspension bridges", J. Constr. Steel Res., 90(41), 29-41. https://doi.org/10.1016/j.jcsr.2013.07.015
  18. Wang, P.H. and Yang, C.G. (1996), "Parametric studies on cablestayed bridges", Comp. Struct., 60(2), 243-260. https://doi.org/10.1016/0045-7949(95)00382-7.
  19. 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(2), 1-12. http://dx.doi.org/10.1155/2015/918649.
  20. Wilde, D.J. and Beightler, C.S. (1967), Foundations of Optimization, Prentice-Hall Inc., Englewood Cliffs, NJ, USA.
  21. 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.