Skip to main content
Log in

Dynamic response of cable-stayed bridges due to sudden failure of stays: the 3D problem

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper studies analytically the problem of the sudden failure of a number of stays through a suitable mathematical model, based on the analytical method exposed by authors in previous publications and extended in this study through a 3D analysis. The analysis is carried out by the modal superposition method, and the gathered equations of the problem are solved through the Galerkin procedure and the Duhamel’s Integrals. Characteristic examples are solved and useful diagrams and plots are drawn, while interesting results are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Fleming, J.F.: Non-linear static analysis of cable-stayed bridge structures. Comput. Struct. 10(4), 986–1000 (1979). https://doi.org/10.1016/0045-7949(79)90006-3

    Article  Google Scholar 

  2. Kollbruner, C.F., Hajdin, N., Stipanic, B.: Contribution to the analysis of cable-stayed bridges. Institute for Engineering Research Editions, Schulthess Verlag Zürich, N.48 (1980)

  3. Bruno, D., Grimaldi, A.: Non-linear behavior of long-span cable-stayed bridges. Meccanica 20(4), 303–313 (1985). https://doi.org/10.1007/BF0235268

    Article  Google Scholar 

  4. Gimsing, N., Georgakis, C.H.T.: Cable Supported Bridges: Concept and Design, 3rd edn. Wiley, Chichester (2012)

    Google Scholar 

  5. Khalil, M.S.: Non-linear analysis of cable-stayed bridges at ultimate load level. Can. J. Civ. Eng. 23(5), 1111–1117 (1999). https://doi.org/10.1139/l96-918

    Article  Google Scholar 

  6. Virgoreux, M.: Recent evolution on cable-stayed bridges. Eng. Struct. 21(8), 737–755 (1999). https://doi.org/10.1016/S0141-0296(98)00028-5

    Article  Google Scholar 

  7. Michaltsos, G.T., Ermopoulos, J.C., Konstantakopoulos, T.G.: Preliminary design of cable-stayed bridges for vertical static loads’. Struct. Eng. Mech. 16(1), 1–15 (2003). https://doi.org/10.12989/sem.2003.16.1.00

    Article  Google Scholar 

  8. Freire, A.M.S., Negräo, J.H.O., Lopez, A.V.: Geometrical non-linearities on the static analysis of highly flexible steel cable-stayed bridges. Comput. Struct. 84(31–32), 2128–2140 (2006). https://doi.org/10.1016/j.compstruc.2006.08.047

    Article  Google Scholar 

  9. Fleming, J.F., Egeseli, E.A.: Dynamic behavior of a cable-stayed bridge. Earthq. Eng. Struct. D. 8(1), 1–16 (1980). https://doi.org/10.1002/eqe.4290080102

    Article  Google Scholar 

  10. Nazmy, A.S., Abdel-Ghaffar, A.M.: Non-linear earthquake response analysis of long-span cable- stayed bridges: Theory. Earthq. Eng. Struct. D. 19(1), 45–62 (1990). https://doi.org/10.1002/eqe.4290190106

    Article  Google Scholar 

  11. Abdel-Ghaffar, A.M., Khalifa, M.A.: Importance of cable vibration in dynamics of cable-stayed bridges. J. Eng. Mech. ASCE 117(11), 2571–2589 (1991). https://doi.org/10.1061/(ASCE)0733-9399(1991)117:11(2571)

    Article  Google Scholar 

  12. Chatterjee, P.K., Datta, T.K., Suruna, C.S.: Vibration of cable-stayed bridges under moving vehicles. Struct. Eng. Int. 4(2), 116–121 (1994). https://doi.org/10.2749/101686694780650887

    Article  Google Scholar 

  13. Bruno, D., Colotti, V.: Vibration analysis of cable-stayed bridges. Struct. Eng. Int. 4(1), 23–28 (1994). https://doi.org/10.2749/101686694780602187

    Article  Google Scholar 

  14. Achkire, Y., Preumont, A.: Active tendon control of cable-stayed bridges. Earthq. Eng. Struct. D. 25(6), 585–597 (1996). https://doi.org/10.1002/(SICI)1096-9845(199606)25:6<585::AID-EQE570>3.0.CO;2-I

    Article  Google Scholar 

  15. Michaltsos, G.T.: A simplified model for the dynamic analysis of cable-stayed bridges. Facta Universitatis 3(11), 185–204 (2001)

    MATH  Google Scholar 

  16. Konstantakopoulos, T.G., Michaltsos, G.T., Sophianopoulos, D.S.: A simplified model for the study of the lateral-torsional vibration of cable-stayed bridges. Eurodyn 2002, Munich, September (2002)

  17. Wang, P.H., Liu, M.Y., Huang, Y.T., Lin, L.C.: Influence of lateral motion of cable-stayed bridges. Struct. Eng. Mech. 34(6), 719–738 (2010). https://doi.org/10.12989/sem.2010.34.6.719

    Article  Google Scholar 

  18. Ermopoulos, J., Vlahinos, A., Yang-Cheng, Wang: Stability analysis of cable-stayed bridges. Comput. Struct. 44(5), 1083–1089 (1992). https://doi.org/10.1016/0045-7949(92)90331-S

    Article  Google Scholar 

  19. Bosdogianni, A., Olivari, D.: Wind-induced and Rain-induced oscillations of cable-stayed bridges. J. Wind Eng. Ind. Aerod. 64(2–3), 171–185 (1997). https://doi.org/10.1016/S0167-6105(96)00089-X

    Article  Google Scholar 

  20. Michaltsos, G.T.: Stability of a cable-stayed bridge’s pylon, under time-depended loading (2005). Collection of papers in memory of Academician P.S. Theocharis. Institution of Mechanics Problems and Academy of Sciences, Russia, Inst. Of Mechanics of Nat. Acad. of Sciences, Armenia

  21. Michaltsos, G.T., Raftoyiannis, I.G., Konstantakopoulos, T.G.: Dynamic stability of cable-stayed bridge pylons. Int. J. Struct. Stab. Dyn. 8(4), 627–643 (2008). https://doi.org/10.1142/S021945540800282X

    Article  MathSciNet  MATH  Google Scholar 

  22. S.E.T.R.A. Haubans: Recommandations de la Commission Interministérielle de la Précontrainte, Service d’ Etudes Techniques des Routes et Autoroutes; France (2001)

  23. P.T.I.: Recommandations for stay cable design, testing and installation. Post-Tensioning Institute, USA (2007)

  24. Mozos, C.M.: Theoretical and experimental study on the structural response of cable stayed bridges to a stay failure. PhD Dissertation, Universidad de Castilla-La Manche, Spain (2002)

  25. Del Olmo, C.M.M, Bengoechea, A.C.A.: Cable stayed bridges. Failure of a stay: Dynamic and pseudo-dynamic analysis of structural behaviour. In: Proceedings of the 3rd International Conference on Bridge Maintenance, Safety and Management- Life-Cycle Performance and Cost, The Netherlands (2002)

  26. Mozos, C.M., Aparicio, A.C.: Parametric study on the dynamic response of cable stayed bridges to the sudden failure of a stay, Part I: Bending moment acting on the deck. Eng. Struct. 32(10), 3288–3300 (2010). https://doi.org/10.1016/j.engstruct.2010.07.003

    Article  Google Scholar 

  27. Mozos, C.M., Aparicio, A.C.: Parametric study on the dynamic response of cable stayed bridges to the sudden failure of a stay, Part II: Bending moment acting on the pylons and stress on the stays. Eng. Struct. 32(10), 3301–3312 (2010). 10.1016/j.engstruct.2010.07.002

    Article  Google Scholar 

  28. Mozos, C.M., Aparicio, A.C.: Static strain energy and dynamic amplification factor on multiple degree of freedom systems. Eng. Struct. 31(11), 2756–2765 (2009). https://doi.org/10.1016/j.engstruct.2009.07.003

    Article  Google Scholar 

  29. Ruiz-Teran, A.M., Aparicio, A.C.: Dynamic amplification factors in cable-stayed structures. J. Sound Vib. 300(1–2), 197–216 (2007). https://doi.org/10.1016/j.jsv.2006.07.028

    Article  Google Scholar 

  30. Wolff, M., Starossek, U.: Cable loss and progressive collapse in cable-stayed bridges. Bridge Struct. 5(1), 17–28 (2009). https://doi.org/10.1080/15732480902775615

    Article  Google Scholar 

  31. Starossek, U.: Avoiding disproportionate collapse of major bridges. Struct. Eng. Int. 3, 289–297 (2009). https://doi.org/10.2749/101686609788957838

    Article  Google Scholar 

  32. Wallace, P., Alsharif, M., Hepbun, D., Zhou, C.: Failure modes of underground MW cables: Electrical and Thermal Modelling. Comcol Conference, Milan (2009)

  33. Tang, Z., Zhou, C., Zhou, W.: Analysis of significant factors on cable failure using the Cox Proportional Hazard Model. IEEE 29920, 951–957 (2014). https://doi.org/10.1109/TPWRD.2013.2287025

    Article  Google Scholar 

  34. Chou-Han, D.: Fracture Feature and Failure Cause Analysis of Cable Wire on Bridges. Appl. Mech. Mater. 178–181, 2472–2478 (2012). https://doi.org/10.4028/www.scientific.net/AMM.178-181.2472

    Article  Google Scholar 

  35. Lepidi, M., Gattulli, V., Vestroni, F.: Static and dynamic response of elastic suspended cables with damage. Int. J. Solids Struct. 44(25), 8194–8212 (2007). https://doi.org/10.1016/j.ijsolstr.2007.06.009

    Article  MATH  Google Scholar 

  36. Mapelli, C., Barella, S.: Failure analysis of a cableway rope. Eng. Fail. Anal. 16(5), 1666–1673 (2009). https://doi.org/10.1016/j.engfailanal.2008.12.011

    Article  Google Scholar 

  37. Mahmoud, K.M.: Fracture strength for a high strength steel bridge cable wire with a surface crack. Theor. Appl. Fract. Mec. 48(2), 152–160 (2007). https://doi.org/10.1016/j.tafmec.2007.05.006

    Article  Google Scholar 

  38. Li, C.X., Tang, X.S., Xiang, G.B.: Fatigue crack growth of cable steel wires in a suspension bridge: multiscaling and mesoscopic fracture mechanics. Theor. Appl. Fract. Mec. 53(2), 113–126 (2019). https://doi.org/10.1016/j.tafmec.2010.03.002

    Article  Google Scholar 

  39. Materazzi, A.L., Ubertini, F.: Eigenproperties of suspension bridges with damage. J. Sound Vib. 330(26), 6420–6434 (2011). https://doi.org/10.1016/j.jsv.2011.08.007

    Article  Google Scholar 

  40. Greco, T., Lonetti, P., Pascuzzo, A.: Dynamic analysis of cable-stayed bridges affected by accidental failure mechanisms under moving loads. Math. Probl. Eng. (2013). https://doi.org/10.1155/2013/302706

    Article  MathSciNet  Google Scholar 

  41. Lonetti, P., Pascuzzo, A.: Vulnerability and failure analysis of hybrid cable-stayed suspension bridges subjected to damage mechanisms. Eng. Fail. Anal. 45, 470–495 (2014). https://doi.org/10.1016/j.engfailanal.2014.07.002

    Article  Google Scholar 

  42. Aoki, Y., Valipour, H., Samali, B., Saleh, A.: A study on potential progressive collapse responses of cable-stayed bridges. Adv. Struct. Eng. 16(4), 689–706 (2013). https://doi.org/10.1260/1369-4332.16.4.689

    Article  Google Scholar 

  43. Raftoyiannis, I.G., Konstantakopoulos, T.G., Michaltsos, G.T.: Dynamic response of cable-stayed bridges, subjected to sudden failure of stays–the 2D problem. Coupled Syst. Mech. 3(4), 345–365 (2014). https://doi.org/10.12989/csm.2014.3.4.345

    Article  Google Scholar 

  44. Konstantakopoulos, T.G.: Static and Dynamic problems in C-S-Bridges. Ph.D. Dissertation, Athens, Greece (2004)

  45. Petalas, J.M., Konstantakopoulos, T.G.: The effect of the horizontal components of the cable forces on the static analysis of cable-stayed bridges. In: Proceedings of the 5th National Conference on Metal Structures. Xanthi, Greece (2005)

  46. Michaltsos, G.T., Raftoyiannis, I.G.: Bridges’ Dynamics (e-Book), eISBN: 978-1-60805-220-2, Bentham (2011)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George T. Michaltsos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Michaltsos, G.T., Sophianopoulos, D.S. & Avraam, T.P. Dynamic response of cable-stayed bridges due to sudden failure of stays: the 3D problem. Arch Appl Mech 90, 1431–1456 (2020). https://doi.org/10.1007/s00419-020-01676-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01676-5

Keywords

Navigation