Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Empirical formulas to estimate cable tension by cable fundamental frequency

  • Ren, Wei-Xin (Department of Civil Engineering, Fuzhou University) ;
  • Chen, Gang (Department of Civil Engineering, Fuzhou University) ;
  • Hu, Wei-Hua (Department of Civil Engineering, Fuzhou University)
  • Received : 2004.11.11
  • Accepted : 2005.03.22
  • Published : 2005.06.20
⟨ Previous Next ⟩

Abstract

The cable tension plays an important role in the construction, assessment and long-term health monitoring of cable structures. The cable vibration equation is nonlinear if cable sag and bending stiffness are included. The engineering implementation of a vibration-based cable tension evaluation is mostly carried out by the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications since the cable sag and bending stiffness are ignored. From the practical point of view, it is necessary to have empirical formulas if they are simple and yet accurate. Based on the solutions by means of energy method and fitting the exact solutions of cable vibration equations where the cable sag and bending stiffness are respectively taken into account, the empirical formulas are proposed in the paper to estimate cable tension based on the cable fundamental frequency only. The applicability of the proposed formulas is verified by comparing the results with those reported in the literatures and with the experimental results carried out on the stay cables in the laboratory. The proposed formulas are straightforward and they are convenient for practical engineers to fast estimate the cable tension by the cable fundamental frequency.

Keywords

References

  1. Casas, J.R. (1994), 'A combined method for measuring cable forces: The cable-stayed Alamillo Bridge', Spain. Struct. Eng. Int., 3, 235-240
  2. Chen, G. (1994), 'Practical formulas for estimation of cable tension by vibration method', M.Sc. Thesis, Fuzhou University
  3. Cunha, A., Caetano, E. and Delgado, R. (2001), 'Dynamic tests on large cable-stayed bridge', J. Bridge Eng., ASCE, 6, 54-62 https://doi.org/10.1061/(ASCE)1084-0702(2001)6:1(54)
  4. Humar, J.L. (1990), Dynamics of Structures. Prentice-Hall, Inc., Englewood Cliffs, N. J
  5. Irvine, H.M. (1981), Cable Structures. The MIT Press, Cambridge, Massachusetts, USA
  6. Irvine, H.M. and Caughey, T.K. (1974), 'The linear theory of free vibration of a suspended cable', Proc. Royal Society of London, England, Series A, 341, 299-315
  7. Leonard, J.W. (1998), Tension Structures. McGraw-Hill Book Company, New York
  8. Mehrabi, A.B. and Tabatabai, H. (1998), 'A unified finite difference formulation for free vibration of cables', J. Struct. Eng., ASCE, 124(11), 1313-1322 https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1313)
  9. Ni, Y.Q., Ko, J.M. and Zheng, G. (2002), 'Dynamic analysis of large-diameter sagged cables taking in account flexural rigidity', J. Sound Vib., 257(2), 301-319 https://doi.org/10.1006/jsvi.2002.5060
  10. Russell, J.C. and Lardner, T.J. (1998), 'Experimental determination of frequencies and tension for elastic cables', J. Eng. Mech., ASCE, 124, 1067-1072 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:10(1067)
  11. Starossek, U. (1991), 'Dynamic stiffuess matrix of sagging cable', J. Struct. Eng., ASCE, 117(12), 2815-2829
  12. Starossek, U. (1994), 'Cable dynamics - A review', Struct. Eng. Int., 3, 171-176
  13. Yen, W.H.P., Mehrabi, A.B. and Tabatabai, H. (1997), 'Estimation of stay cable tension using a non-destructive vibration technique', Building to Last: Proc. of the 15th Structures Congress, ASCE, 1, 503-507
  14. Zheng, G, Ko, J.M. and Ni, Y.Q. (2001), 'Multimode-based evaluation of cable tension force in cable-supported bridges', Smart Structures and Materials 2001: Smart Systems for Bridges, Structures, and Highways 2001, SPIE, 4330, 511-522
  15. Zui, H., Shinke, T. and Namita, Y. (1996), 'Practical formulas for estimation of cable tension by vibration method', J. Struct. Eng., ASCE, 122(6), 651-656 https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(651)

Cited by

  1. Recursive optimization method for monitoring of tension loss in cables of cable-stayed bridges vol.27, pp.15, 2016, https://doi.org/10.1177/1045389X15620043
  2. Real-time identification of time-varying tension in stay cables by monitoring cable transversal acceleration vol.21, pp.7, 2014, https://doi.org/10.1002/stc.1634
  3. Dynamic Brillouin Scattering–Based Condition Assessment of Cables in Cable-Stayed Bridges vol.22, pp.3, 2017, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001010
  4. Determination of cable tensions based on frequency differences vol.25, pp.2, 2008, https://doi.org/10.1108/02644400810855977
  5. New Method for Identifying Internal Forces of Hangers Based on Form-Finding Theory of Suspension Cable vol.22, pp.11, 2017, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001147
  6. Cable Force Calculation Using Vibration Frequency Methods Based on Cable Geometric Parameters vol.31, pp.4, 2017, https://doi.org/10.1061/(ASCE)CF.1943-5509.0001002
  7. Development and sensing properties study of FRP–FBG smart stay cable for bridge health monitoring applications vol.44, pp.4, 2011, https://doi.org/10.1016/j.measurement.2011.01.005
  8. New insights into coherence analysis with a view towards extracting structural natural frequencies under operational conditions vol.77, 2016, https://doi.org/10.1016/j.measurement.2015.08.038
  9. Cable Modal Parameter Identification. II: Modal Tests vol.135, pp.1, 2009, https://doi.org/10.1061/(ASCE)0733-9399(2009)135:1(51)
  10. Measured Frequency for the Estimation of Cable Force by Vibration Method vol.141, pp.2, 2015, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000890
  11. Analysis of a reversible flight control system response to atmospheric turbulence vol.112, pp.1128, 2008, https://doi.org/10.1017/S0001924000002025
  12. Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads vol.329, pp.9, 2010, https://doi.org/10.1016/j.jsv.2009.11.018
  13. FBG force-testing ring for bridge cable force monitoring and temperature compensation vol.223, 2015, https://doi.org/10.1016/j.sna.2015.01.003
  14. Bayesian estimation of tension in bridge hangers using modal frequency measurements vol.3, pp.4, 2016, https://doi.org/10.12989/smm.2016.3.4.349
  15. Determination of cable force based on the corrected numerical solution of cable vibration frequency equations vol.50, pp.1, 2014, https://doi.org/10.12989/sem.2014.50.1.037
  16. Estimation of Cable Tension Force Independent of Complex Boundary Conditions vol.141, pp.1, 2015, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000836
  17. Numerical and experimental dynamic analysis and control of a cable stayed bridge under parametric excitation vol.45, 2012, https://doi.org/10.1016/j.engstruct.2012.06.018
  18. A PSO Driven Intelligent Model Updating and Parameter Identification Scheme for Cable-Damper System vol.2015, 2015, https://doi.org/10.1155/2015/423898
  19. Multistep and Multiparameter Identification Method for Bridge Cable Systems vol.23, pp.1, 2018, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001145
  20. Unified Practical Formulas for Vibration-Based Method of Cable Tension Estimation vol.18, pp.3, 2015, https://doi.org/10.1260/1369-4332.18.3.405
  21. Estimation of tensile force in tie-rods using a frequency-based identification method vol.329, pp.11, 2010, https://doi.org/10.1016/j.jsv.2009.12.009
  22. Vibration Analysis for Monitoring of Ancient Tie-Rods vol.2017, 2017, https://doi.org/10.1155/2017/7591749
  23. Monitoring of the Internal Force of the Flexible Components by Vibration Method vol.45, pp.1, 2017, https://doi.org/10.1520/JTE20160138
  24. Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests vol.317, pp.1-2, 2008, https://doi.org/10.1016/j.jsv.2008.02.048
  25. Detection of Tension Loss in Cables of Cable-Stayed Bridges by Distributed Monitoring of Bridge Deck Strains vol.142, pp.6, 2016, https://doi.org/10.1061/(ASCE)ST.1943-541X.0001463
  26. A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions vol.409, 2017, https://doi.org/10.1016/j.jsv.2017.07.043
  27. Determination of Stay-Cable Forces Using Highly Mobile Vibration Measurement Devices vol.23, pp.2, 2018, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001166
  28. Cluster analysis of stress corrosion mechanisms for steel wires used in bridge cables through acoustic emission particle swarm optimization vol.77, 2017, https://doi.org/10.1016/j.ultras.2017.01.012
  29. A single heavy load airdrop and its effect on a reversible flight control system vol.80, pp.4, 2008, https://doi.org/10.1108/00022660810882764
  30. Estimation of Tension in Cables with Intermediate Elastic Supports Using Finite-Element Method vol.16, pp.5, 2011, https://doi.org/10.1061/(ASCE)BE.1943-5592.0000192
  31. Tension Force and Structural Parameter Identification of Bridge Cables vol.15, pp.6, 2012, https://doi.org/10.1260/1369-4332.15.6.983
  32. Practical Formula for Cable Tension Estimation by Vibration Method vol.17, pp.1, 2012, https://doi.org/10.1061/(ASCE)BE.1943-5592.0000200
  33. Cable Modal Parameter Identification. I: Theory vol.135, pp.1, 2009, https://doi.org/10.1061/(ASCE)0733-9399(2009)135:1(41)
  34. Stay Force Estimation in Cable-Stayed Bridges Using Stochastic Subspace Identification Methods vol.22, pp.9, 2017, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001091
  35. Real-Time Output-Only Identification of Time-Varying Cable Tension from Accelerations via Complexity Pursuit vol.142, pp.1, 2016, https://doi.org/10.1061/(ASCE)ST.1943-541X.0001337
  36. Genetic Algorithm-based tension identification of hanger by solving inverse eigenvalue problem vol.22, pp.6, 2014, https://doi.org/10.1080/17415977.2013.848432
  37. Stay Cable Tension Estimation of Cable-Stayed Bridges Using Genetic Algorithm and Particle Swarm Optimization vol.22, pp.10, 2017, https://doi.org/10.1061/(ASCE)BE.1943-5592.0001130
  38. Free linear vibrations of cables under thermal stress vol.327, pp.1-2, 2009, https://doi.org/10.1016/j.jsv.2009.07.005
  39. On the effects of uniform temperature variations on stay cables vol.5, pp.5, 2015, https://doi.org/10.1007/s13349-015-0140-9
  40. Dynamic behavior monitoring and damage evaluation for arch bridge suspender using GFRP optical fiber Bragg grating sensors vol.44, pp.4, 2012, https://doi.org/10.1016/j.optlastec.2011.10.014
  41. Transverse Oscillation of Precise Cable Drive System vol.522, pp.1662-9795, 2012, https://doi.org/10.4028/www.scientific.net/KEM.522.332
  42. Estimation Method of Cable Tension Based on Iterative Algorithm and Optimization Algorithm vol.353-356, pp.1662-7482, 2013, https://doi.org/10.4028/www.scientific.net/AMM.353-356.3202
  43. Estimation of Tension Force in Short Hangers Using Added Mass Method vol.658, pp.1662-8985, 2013, https://doi.org/10.4028/www.scientific.net/AMR.658.124
  44. A Sensitivity Analysis of Cable Parameters on Tension of a Suspended Cable under Combination Resonances pp.1793-6764, 2018, https://doi.org/10.1142/S0219455419500251
  45. Determining Time Variation of Cable Tension Forces in Suspended Bridges Using Time-Frequency Analysis vol.2018, pp.1687-8094, 2018, https://doi.org/10.1155/2018/1053232
  46. Identification of the tension force in cables with insulators vol.54, pp.1-2, 2019, https://doi.org/10.1007/s11012-018-00941-w
  47. Automated Modal Analysis for Tracking Structural Change during Construction and Operation Phases vol.19, pp.4, 2019, https://doi.org/10.3390/s19040927
  48. NONLINEAR DYNAMIC ANALYSIS OF A CABLE UNDER FIRST AND SECOND ORDER PARAMETRIC EXCITATIONS vol.18, pp.4, 2005, https://doi.org/10.3846/13923730.2012.702994
  49. Experimental study of vibration characteristics of FRP cables based on Long-Gauge strain vol.63, pp.6, 2005, https://doi.org/10.12989/sem.2017.63.6.735
  50. A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions vol.166, pp.None, 2005, https://doi.org/10.1016/j.engstruct.2018.03.070
  51. Validation value of cable force using the accelerometer vol.195, pp.None, 2005, https://doi.org/10.1088/1755-1315/195/1/012022
  52. Tension Identification of Suspenders with Supplemental Dampers for Through and Half-Through Arch Bridges under Construction vol.145, pp.3, 2005, https://doi.org/10.1061/(asce)st.1943-541x.0002255
  53. Tension estimation of hangers with shock absorber in suspension bridge using finite element method vol.21, pp.3, 2005, https://doi.org/10.21595/jve.2018.20054
  54. Cable Tension Monitoring Based on the Elasto-Magnetic Effect and the Self-Induction Phenomenon vol.12, pp.14, 2019, https://doi.org/10.3390/ma12142230
  55. Research on characteristic function for cable inverse analysis based on dynamic stiffness theory and its application vol.194, pp.None, 2019, https://doi.org/10.1016/j.engstruct.2019.05.062
  56. PVDF Nanofiber Sensor for Vibration Measurement in a String vol.19, pp.17, 2005, https://doi.org/10.3390/s19173739
  57. Tension Force Estimation of Cables with Two Intermediate Supports vol.20, pp.3, 2005, https://doi.org/10.1142/s0219455420500327
  58. Controlling deflection of long steel I-shaped girder bridge using two V-shaped pre-tensioning cables vol.27, pp.2, 2020, https://doi.org/10.1007/s11771-020-4317-y
  59. Image‐based back analysis for tension estimation of suspension bridge hanger cables vol.27, pp.4, 2020, https://doi.org/10.1002/stc.2508
  60. Identification of instantaneous tension of bridge cables from dynamic responses: STRICT algorithm and applications vol.142, pp.None, 2005, https://doi.org/10.1016/j.ymssp.2020.106729
  61. Intelligent parameter identification for bridge cables based on characteristic frequency equation of transverse dynamic stiffness vol.39, pp.3, 2005, https://doi.org/10.1177/1461348418814617
  62. Variational Mode Decomposition Based Time-Varying Force Identification of Stay Cables vol.11, pp.3, 2005, https://doi.org/10.3390/app11031254
  63. Frequency-based tension assessment of an inclined cable with complex boundary conditions using the PSO algorithm vol.79, pp.5, 2005, https://doi.org/10.12989/sem.2021.79.5.619
  64. Fully Automated and Robust Cable Tension Estimation of Wireless Sensor Networks System vol.21, pp.21, 2021, https://doi.org/10.3390/s21217229