KSCE Journal of Civil Engineering

, Volume 23, Issue 3, pp 1283–1292

# A Recursive Algorithm for Determining the Profile of the Spatial Self-anchored Suspension Bridges

• Tao Li
• Zhao Liu
Structural Engineering

## Abstract

Determining the final state of a suspension bridge involves the optimization problem to obtain the cable tensions which can balance the dead load. For the long-span suspension bridges, the optimization problem is complex because there can be hundreds of variables to identify in this process. In present work, the simultaneous equations describing the equilibrium state of the cable system are set up. With the proposed recursive algorithm, these equations, which shall include a number of unknown variables, are simplified into a concise form in which exist only three unknowns. On this basis, the coupled three nonlinear equations are solved by the proposed method of the Interacting Influence Matrix (IIM) optimization. After solving the coupled equation, all the unknown parameters including the tensions and positions of the cables can be determined analytically. Last, an example is used to demonstrate the correctness and effectiveness of the proposed processes.

## Keywords

recursive algorithm self-anchored suspension bridge spatial cable IIM optimization unstrained length

## References

1. Ahmadi-kashani, K. and Bell, A. J. (1988). “The analysis of cables subject to uniformly distributed loads.” Engineering Structures, vol. 10, no. 3, pp. 174–184. DOI: 10.1016/0141-0296(88)90004-1.
2. An, X., Gosling, P. D., and Zhou, X. (2016). “Analytical structural reliability analysis of a suspended cable.” Structural Safety, vol. 58, pp. 20–30. DOI: 10.1016/j.strusafe.2015.08.001.
3. Gil, H. and Cho, C. (1998). “Yong Jong grand suspension bridge, Korea.” Structural Engineering International, vol. 8, no. 2, pp. 97–98.
4. Jun, K. H., CX, L., YP, Z., and CW, D. (2010). “System transformation program and control principles of suspender tension for a selfanchored suspension bridge with two towers and large transverse inclination spatial cables.” J China Civil Eng, vol. 43, no. 11, pp. 94–101. DOI: 10.15951/j.tmgcxb.2010.11.003 (in Chinese).Google Scholar
5. 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.” Computers & Structures, vol. 128, no. 5, pp. 272–285. DOI: 10.1016/j.compstruc.2013.06.014.
6. Karoumi, R. (1999). “Some modeling aspects in the nonlinear finite element analysis of cable supported bridges.” Computers & Structures, vol. 71, no. 4, pp. 397–412. DOI: 10.1016/S0045-7949(98)00244-2.
7. 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.” International Journal of Steel Structures, vol. 12, no. 2, pp. 157–174. DOI: 10.1007/s13296-012-2002-1.
8. Kim, K. S. and Lee, H. S. (2001). “Analysis of target configurations under dead loads for cable-supported bridges.” Computers & Structures, vol. 79, no. 29, pp. 2681–2692. DOI: 10.1016/S0045-7949(01)00120-1.
9. Kim, H. K., Lee, M. J., and Chang, S. P. (2002). “Non-linear shapefinding analysis of a self-anchored suspension bridge.” Engineering Structures, vol. 24, no. 12, pp. 1547–1559. DOI: 10.1016/S0141-0296(02)00097-4.
10. Kim, S. E. and Thai, H. T. (2010). “Nonlinear inelastic dynamic analysis of suspension bridges.” Engineering Structures, vol. 32, no. 12, pp. 3845–3856. DOI: 10.1016/j.engstruct.2010.08.027.
11. Li, J. H., Feng, D. M., Li, A. Q., and Yuan, H. H. (2016). “Determination of reasonable finished state of self-anchored suspension bridges.” Journal of Central South University, vol. 23, no. 1, pp. 209–219. DOI: 10.1007/s11771-016-3064-6.
12. Martins, A. M. B., Simoes, L. M. C., and Negrao, J. (2016), “Optimum design of concrete cable-stayed bridges.” Eng. Optimiz., vol. 48, no. 5, pp. 772–791. DOI: 10.1080/0305215x.2015.1057057.
13. 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.” Engineering Structures, vol. 31, no. 9, pp. 2162–2170. DOI: 10.1016/j.engstruct.2009.03.018.
14. Sun, J., Manzanarez, R., and Nader, M. (2002). “Design of looping cable anchorage system for new san francisco-Oakland Bay Bridge Main Suspension Span.” Journal of Bridge Engineering, vol. 7, no. 6, pp. 315–324. DOI: 10.1061/(ASCE)1084-0702(2002)7:6(315).
15. Sun, Y., Zhu, H. P., and Xu, D. (2015). “New method for shape finding of self-anchored suspension bridges with three-dimensionally curved cables.” Journal of Bridge Engineering, Vol. 20, No. 2, DOI: 10.1061/(asce)be.1943-5592.0000642.Google Scholar
16. 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.” Engineering Structures, vol. 110, pp. 184–208. DOI: 10.1016/j.engstruct.2015.11.040.
17. Tur, M., Garcia, E., Baeza, L., and Fuenmayor, F. J. (2014). “A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary.” Engineering Structures, vol. 71, pp. 234–243. DOI: 10.1016/j.engstruct.2014.04.015.
18. Wang, H. L. and Qin, S. F. (2016). “Q Shape finding of suspension bridges with interacting matrix.” European Journal of Environmental and Civil Engineering, vol. 20, no. 8, pp. 831–840. DOI: 10.1080/19648189.2015.1084379.
19. Wang, P. H., Tseng, T. C., and Yang, C. G. (1993). “Initial shape of cablestayed bridges.” Computers & Structures, vol. 47, no. 1, pp. 111–123. DOI: 10.1016/0045-7949(93)90095-U.
20. Zhang, J., Liu, A., Ma, Z.J., Huang, H., Mei, L., and Li, Y. (2013). “Behavior of self-anchored suspension bridges in the structural system transformation.” Journal of Bridge Engineering, vol. 18, no. 8, pp. 712–721. DOI: 10.1061/(ASCE)BE.1943-5592.0000422.
21. 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.” Structural Engineering International, vol. 20, no. 3, pp. 303–307. DOI: 10.2749/101686610792016673.