Application of Exact Element-Method on Calculation of Form-Finding and Unstressed Length of Cable

Abstract:

The problem of form-finding for the suspended cable is actually the problem of determining all key points coordinates on main cable, which are by equilibrium relation on the horizontal force, main cable sagitta and lifting point force under the precondition of determining the endpoints boundary conditions of cable segment. According from the static equilibrium relationship of cable element, based on the analysis of its analytical solution process, in this paper, the cable elements are divided into two types in accordance withthe vertical distribution load along the arc length and along the string length , the corresponding shape curve of cable element is the parabola and the catenary, and with parabolic results as its initial value for the iteration of nonlinear solution, then cable element eventually converge for the catenary. And based on the exact coordinates results ,the calculation method of the length without stress is presented,and compiled corresponding computational procedures. By comparing the results of form-finding and the cable-length in non-stress according to program compiled and the results from the finite element software and the measured value of Aizhai suspension bridge, compared with the nonlinear finite element method,it confirmed the method requireing smaller dividing element density, the convergence speed is quicker and the results can ensure the precision.

• Periodical: Applied Mechanics and Materials (Volumes 405-408)
• Pages: 1699-1708
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.405-408.1699
• Online since: September 2013
• Authors: Zhou Li, Yuan Cheng Wei, Rong Hui Wang, Jia Lun Li, Peng Zhang
• Keywords: Exact Coordinates, Form-Finding, Iteration, Suspension Cable

References

[1] SHEN Shi-zhao. XU Chong-bao. Suspension Cable Structure Design[M], BEIJING: China Architecture and Building Press, (1997).

[2] XIANG Yang, SHEN Shi-zhao. Initial Form-finding Analysis of Cable Structures[J]. Journal of Harbin University of Civil Engineering and Architecture, 1997, 30(3): 29-33.

[3] YAN Jing-tong, GAO ri. Comparison And Analysis Between Two Form-finding Methods For Cable Net Structures[J]. Steel Structure 2002, 17(1): 4-6.

[4] SCHEK H K. The force densities method for form-finding and computation of general nets[J]. Computer Methods in Applied Mechanics Engineering, 1974. 3(1): 115-134.

DOI: 10.1016/0045-7825(74)90045-0

[5] BARNES M R. Dynamic relaxation analysis of tension networks[A]. Proceedings of the International Conference on Tension Structure[C]. London, April, (1974).

[6] Zhou meng-bo. Suspension bridge manual [M], Beijing: China Communications Press, 2003. 8.

[7] YUAN Si, CHENG Da-ye, YE Kang-sheng. Exact Element Method for Form-finding Analysis of Cable Structures [J]. Journal of Building Structures 2005, 26(2): 46-51.

[8] Wang Xin-ming. ANSYS Engineering structure numerical analysis[M], Beijing: China Communications Press, 2007. 10.