Estimation of main cable tension force of suspension bridges based on ambient vibration frequency measurements

- Journal title : Structural Engineering and Mechanics
- Volume 56, Issue 6, 2015, pp.939-957
- Publisher : Techno-Press
- DOI : 10.12989/sem.2015.56.6.939

Title & Authors

Estimation of main cable tension force of suspension bridges based on ambient vibration frequency measurements

Wang, Jun; Liu, Weiqing; Wang, Lu; Han, Xiaojian;

Wang, Jun; Liu, Weiqing; Wang, Lu; Han, Xiaojian;

Abstract

In this paper, a new approach based on the continuum model is proposed to estimate the main cable tension force of suspension bridges from measured natural frequencies. This approach considered the vertical vibration of a main cable hinged at both towers and supported by an elastic girder and hangers along its entire length. The equation reflected the relationship between vibration frequency and horizontal tension force of a main cable was derived. To avoid to generate the additional cable tension force by sag-extensibility, the analytical solution of characteristic equation for anti-symmetrical vibration mode of the main cable was calculated. Then, the estimation of main cable tension force was carried out by anti-symmetric characteristic frequency vector. The errors of estimation due to characteristic frequency deviations were investigated through numerical analysis of the main cable of Taizhou Bridge. A field experiment was conducted to verify the proposed approach. Through measuring and analyzing the responses of a main cable of Taizhou Bridge under ambient excitation, the horizontal tension force of the main cable was identified from the first three odd frequencies. It is shown that the estimated results agree well with the designed values. The proposed approach can be used to conduct the long-term health monitoring of suspension bridges.

Keywords

tension force;main cable;suspension bridge;continuum model;anti-symmetrical vibration;

Language

English

Cited by

References

1.

Yim, J.S., Wang, M.L., Shin, S.W., Yun, C.B., Jung, H.J., Kim, J.T. and Eem, S.H. (2013), "Field application of elasto-magnetic stress sensors for monitoring of cable tension force in cable-stayed bridges", Smart Struct. Syst., 12(3-4), 465-482.

2.

Casas, J.R. (1994), "A combined method for measuring cable forces: The Cable-Stayed Alamillo Bridge, Spain", Struct. Eng. Int., 4(4), 235-240.

3.

Fang, Z. and Wang, J.Q. (2012), "Practical formula for cable tension estimation by vibration meyhod", J. Bridge Eng., ASCE, 17(1), 161-164.

4.

Ricciardi, G. and Saitta, F. (2008), "A continuous vibration analysis model for cables with sag and bending stiffness", Eng. Struct., 30(5), 1459-1472.

5.

Nam, H. and Nghia, N.T. (2011), "Estimation of cable tension using measured natural frequencies", Procedia Eng., 14, 1510-1517.

6.

Zui, H., Shinke, T. and Namita Y.H.(1996), "Practical formulas for estimation of the cable tension by vibration method", J. Struct. Eng., ASCE, 124(10), 651-656.

7.

Yen, W.H.P., Mehrabi, A.B. and Tabatabai, H. (1997), "Evaluation of stay cable tension using a nondestructive vibration technique", Proceedings of the 15th Structures Congress, ASCE, New York, USA, April.

8.

Mehrabi, A.B. and Tabatabai, H. (1998), "Unified finite difference formulation for free vibration of cables", J. Struct. Eng., ASCE, 124(11), 1313-1322.

9.

Dan, D., Chen, Y. and Yan, X. (2014), "Determination of cable force based on the corrected numerical solution of cable vibration frequency equations", Struct. Eng. Mech., 50(1), 37-52.

10.

Kim, B.H., Park, T., Shin, H. and Yoon, T.Y. (2007), "A comparative study of the tension estimation methods for cable supported bridges", Steel Struct., 7(1), 77-84.

11.

Kim, M.Y., Kwon, S.D. and Kim, N.I. (2000), "Analytical and numerical study on free vertical vibration of shear-flexible suspension bridges", J. Sound Vib., 238(1), 65-84.

12.

McKenna, P.J. and Walter, W. (1987), "Nonlinear oscillations in a suspension bridge", Arch. Ration. Mech. An., 98 (2), 167-177.

13.

Lazer, A.C. and McKenna, P.J. (1990), "Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis", SIAM Rev., 32(4), 537-578.

14.

Glover, J., Lazer, A.C. and McKenna, P.J. (1989), "Existence and stability of large-scale nonlinear oscillations in suspension bridges", Z. Angew. Math. Phys., 40(2), 172-200.

15.

Holubova-Tajcova, G. (1999), "Mathematical modeling of suspension bridges", Math. Comput. Simulat., 50(1-4),183-197.

16.

McKenna, P.J. and Moore, K.S. (2002), "The global structure of periodic solutions to a suspension bridge mechanical model", IMA J. Appl. Math., 67(5), 459-478.

17.

Humphreys, L.D. and McKenna, P.J. (2005), "When a mechanical system goes nonlinear: Unexpected responses to low-periodic shaking", Math. Assoc. Am., 112(10), 861-875.

18.

Turmo, J. and Luco, J.E. (2010), "Effect of hanger flexibility on dynamic response of suspension bridges", J. Eng. Mech., ASCE, 136(12), 1444-1459.

19.

Konstantakopoulos, T.G. and Michaltsos, G.T. (2010), "A mathematical model for a combined cable system of bridges", Eng. Struct., 32(9), 2717-2728.

20.

Luco, J.E. and Turmo, J. (2010), "Linear vertical vibrations of suspension bridges: a review of continuum models and some new results", Soil Dyn Earthq. Eng., 30(9), 769-781.

21.

Ni, Y.Q., Ko, J.M. and Zheng, G. (2002), "Dynamic analysis of large-diameter sagged cables taking into account flexural rigidity", J. Sound Vib., 257(2), 301-319.

22.

Kim, B.H. and Park, T. (2007), "Estimation of cable tension using the frequency-based system identification method", J. Sound Vib., 304(3-5), 660-676.

23.

Wang, H., Li, A.Q. and Li, J. (2010), "Progressive finite element model calibration of a long-span suspension bridge based on ambient vibration and static measurements", Eng. Struct., 32(9), 2546-2556.

24.

Brownjohn, J.M.W., Xia, P.Q., Hao, H. and Xia, Y. (2001), "Civil structure condition assessment by FE model updating: methodology and case studies", Finite Elem. Anal. Des., 37(10), 761-775.

25.

Schlune, H., Plos, M. and Gylltoft, K. (2009), "Improved bridge evaluation through finite element model updating using static and dynamic measurements", Eng. Struct., 31(7), 1477-1485.

26.

Liao, W.Y., Ni, Y.Q. and Zheng, G. (2012), "Tension force and structural parameter identification of bridge cables", Adv. Struct. Eng., 15(6), 983-995.

27.

Timoshenko, S.P. and Young, D.H. (1965), Theory of Structures, McGraw-Hill Book Company, New York, USA.

28.

Steinman, D.B. (1953), A Practical Treatise on Suspension Bridges, Wiley, New York, USA.

29.

Irvine, H.M. and Caughey, T.K. (1974), "The linear theory of free vibration of a suspended cable", Proceedings of the Royal Society of London, Serious A, London, UK, December.