Advertisement

Archive of Applied Mechanics

, Volume 89, Issue 11, pp 2281–2312 | Cite as

Static and dynamic responses of suspended arch bridges due to failure of cables

  • D. S. SophianopoulosEmail author
  • G. T. Michaltsos
  • H. I. Cholevas
Original
  • 155 Downloads

Abstract

A mathematical model is proposed to investigate the behavior of a suspended arch bridge, subjected to sudden failure of cables. The main aim of this study is to analyze the effects produced by potential cables failure scenarios on the deformations and stresses of the bridge. The studied suspended arch bridge has a dense arrangement of cables, but the method described herein may be easily extended to the case of a sparse arrangement of cables. The theoretical formulation is based on a continuum approach, which has been used in the literature to analyze such bridges. Finally, the equations obtained are solved using the Duhamel’s integrals and the Laplace transform. For an exemplary bridge, results are obtained for the cases of failure of one, two and five cables, and important conclusions for structural design purposes are drawn.

Keywords

Dynamics of bridges Suspended arch bridges Failure of cables Dynamic amplification factor 

List of symbols

Upper case latin

A

Cross-sectional area

E

Modulus of elasticity of steel material (deck and arch)

G

Shear modulus

H(x)

Heaviside function

\(I_c\)

Moment of inertia of the arch at the mid-span section

\(I_y\)

Moment of inertia with respect to y-axis

\(I_z\)

Moment of inertia with respect to z-axis

\(I_{\omega }\)

Warping resistance of the deck

\(J_{px}\)

Rotational mass moment of inertia of the deck

\(I_D\)

Saint-Venant torsional moment of inertia

L

Length of the bridge structure

R

Average geometrical radius of the arch

R(t)

Modal amplitudes

T(t)

Modal amplitudes

UWZ

Shape functions

Lower case latin

a

Subscript denoting properties of the arch

b

Half-width of the deck

c

Subscript denoting properties of the cables

d

Subscript denoting properties of the deck

\(f_0\)

Sag of the arch at the middle of the bridge span

\(f_z(t)\)

Time functions

m

Mass per unit length

\(m_x\)

External moment acting on the deck

\(p_y\)

External applied force with respect to y-axis, acting on the deck

\(p_z\)

External applied force with respect to z-axis, acting on the deck

\(q_c\)

Stress per unit length of cables

\(q_1\)

Stress per unit length of the left line of cables

\(q_2\)

Stress per unit length of the right line of cables

\(q_z(x)\)

Forces developing on the cables

xyz

Axes designation

w

Vertical displacement

z(x)

Length of the cables at position x

Greek

\(\varphi _d\)

Rotational deformation of the arch

\(\upsilon \)

Horizontal displacement

\(\Phi \)

Modal amplitudes

Notes

References

  1. 1.
    Johnston, B.G.: Guide to Stability Design Criteria for Metal Structures. Structural Stability Research Council, 3rd edn. Wiley, Hoboken (1976)Google Scholar
  2. 2.
    Bergmeister, K., Capsoni, A., Corradi, L., Menardo, A.: Lateral elastic stability of slender arches for bridges including deck slenderness. Struct. Eng. Int. 19(2), 149–154 (2009).  https://doi.org/10.2749/101686609788220259 CrossRefGoogle Scholar
  3. 3.
    Pircher, M., Stacha, M., Wagner, J.: Stability of network arch bridges under traffic loading. Proc. Inst. Civ. Eng. Bridge Eng. 166(3), 186–192 (2013).  https://doi.org/10.1680/bren.11.00027 CrossRefGoogle Scholar
  4. 4.
    Wang, Y., Liu, C., Liang, Y., Zhang, S.: Nonlinear stability analysis and completed bridge test on slanting type CFST arch bridges. J. Build. Struct. 36, 107–113 (2015)Google Scholar
  5. 5.
    Zhu, X.-L., Sun, D.-B.: Nonlinear in-plane stability and catastrophe analysis of shallow arches. J. Vib. Shock 35(6), 47–51 (2016)Google Scholar
  6. 6.
    Bruno, D., Lonetti, P., Pascuzzo, A.: An optimization model for the design of network arch bridges. Comput. Struct. 170, 13–25 (2016).  https://doi.org/10.1016/j.compstruc.2016.03.011 CrossRefGoogle Scholar
  7. 7.
    Mannini, C., Belloli, M., Marra, A.M., et al.: Aeroelastic stability of two long-span arch structures: a collaborative experience in two wind tunnel facilities. Eng. Struct. 119, 252–263 (2016).  https://doi.org/10.1016/j.engstruct.2016.04.014 CrossRefGoogle Scholar
  8. 8.
    Zhang, Z.-C.: Creep analysis of long span concrete-filled steel tubular arch bridges. Gongcheng Lixue/Eng. Mech. 24(5), 151–160 (2007)Google Scholar
  9. 9.
    Shao, X., Peng, J., Li, L., Yan, B., Hu, J.: Time-dependent behavior of concrete-filled steel tubular arch bridge. J. Bridge Eng. (ASCE) 15(1), 98–107 (2010).  https://doi.org/10.1061/(ASCE)1084-0702(2010)15:1(98) CrossRefGoogle Scholar
  10. 10.
    Loghman, A., Ghorbanpour Arani, A., Shajari, A.R., Amir, S.: Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite. Arch. Appl. Mech. 81(12), 1853–1864 (2011).  https://doi.org/10.1007/s00419-011-0522-3 CrossRefzbMATHGoogle Scholar
  11. 11.
    Lai, X.-Y., Li, S.-Y., Chen, B.-C.: The influence of addictives on the creep of concrete-filled steel tube. Harbin Gongye Daxue Xuebao/J. Harbin Inst. Technol. 44(SUPPL.1), 248–251 (2012)Google Scholar
  12. 12.
    Granata, M.F., Arici, M.: Serviceability of segmental concrete arch-frame bridges built by cantilevering. Bridge Struct. 9(1), 21–36 (2013)Google Scholar
  13. 13.
    Ma, Y.S., Wang, Y.F.: Creep effects on the reliability of a concrete-filled steel tube arch bridge. J. Bridge Eng. (ASCE) 18(10), 1095–1104 (2013).  https://doi.org/10.1061/(ASCE)BE.1943-5592.0000446 CrossRefGoogle Scholar
  14. 14.
    Zhou, Y.: Concrete creep and thermal effects on the dynamic behavior of a concrete-filled steel tube arch bridge. J. Vibroeng. 16(4), 1735–1744 (2014)Google Scholar
  15. 15.
    Bradford, M.A., Pi, Y.-L.: Geometric nonlinearity and long-term behavior of crown-pinned CFST arches. J. Struct. Eng. (ASCE) (2015).  https://doi.org/10.1061/(ASCE)ST.1943-541X.0001163 CrossRefGoogle Scholar
  16. 16.
    Li, J.-B., Ge, S.-J., Chen, H.: Seismic behavior analysis of a 5-span continuous half-through CFST arch bridge. World Inf. Earthq. Eng. 21(3), 110–115 (2005)Google Scholar
  17. 17.
    Álvarez, J.J., Aparicio, A.C., Jara, J.M., Jara, M.: Seismic assessment of a long-span arch bridge considering the variation in axial forces induced by earthquakes. Eng. Struct. 34, 69–80 (2012).  https://doi.org/10.1016/j.engstruct.2011.09.013 CrossRefGoogle Scholar
  18. 18.
    Huang, F.-Y., Chen, B.-C., Li, J.-Z., Cheng, H.-D.: Shaking tables testing of concrete filled steel tubular single arch rib model under the excitation of rare earthquakes. Gongcheng Lixue/Eng. Mech. 32(7), 64–73 (2015)Google Scholar
  19. 19.
    Sevim, B., Atamturktur, S., Altunişik, A.C., Bayraktar, A.: Ambient vibration testing and seismic behavior of historical arch bridges under near and far fault ground motions. Bull. Earthq. Eng. 14(1), 241–259 (2016).  https://doi.org/10.1007/s10518-015-9810-6 CrossRefGoogle Scholar
  20. 20.
    Lei, S., Gao, Y., Pan, D.: An optimization solution of Rayleigh damping coefficients on arch bridges with closely-spaced natural frequencies subjected to seismic excitations. J. Harbin Inst. Technol. 47(12), 123–128 (2015)Google Scholar
  21. 21.
    Drosopoulos, G.A., Stavroulakis, G.E., Massalas, C.V.: Influence of the geometry and the abutments movement on the collapse of stone arch bridges. Constr. Build. Mater. 22(3), 200–210 (2008).  https://doi.org/10.1016/j.conbuildmat.2006.09.001 CrossRefGoogle Scholar
  22. 22.
    Liu, B., Yang, C., Zhou, K.: Effect of springing displacement on mechanical performance of the buried corrugated steel arch bridge. J. Wuhan Univ. Technol. (Transp. Sci. Eng.) 36(3), 441–444 (2012)Google Scholar
  23. 23.
    Liu, S.-M., Wang, Z.-X., Zhu, C.: Method of temporarily carrying heavy vehicle on masonry arch bridge without strengthening. J. Beijing Univ. Technol. 41(10), 1559–1565 (2015)Google Scholar
  24. 24.
    Yau, J.-D.: Vibration of parabolic tied-arch beams due to moving loads. Int. J. Struct. Stab. Dyn. 6(2), 193–214 (2006).  https://doi.org/10.1142/S0219455406001915 MathSciNetCrossRefGoogle Scholar
  25. 25.
    Yang, J.-X., Chen, W.-Z., Gu, R.: Analysis of dynamic characteristics of short hangers of arch bridge. Bridge Constr. 44(3), 13–18 (2014)Google Scholar
  26. 26.
    Nikkhoo, A., Kananipour, H.: Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 228(13), 2314–2322 (2014).  https://doi.org/10.1177/0954406213518908 CrossRefGoogle Scholar
  27. 27.
    Türker, T., Bayraktar, A.: Structural safety assessment of bowstring type RC arch bridges using ambient vibration testing and finite element model calibration. Measurement 58, 33–45 (2014).  https://doi.org/10.1016/j.measurement.2014.08.002 CrossRefGoogle Scholar
  28. 28.
    Calçada, R., Cunha, A., Delgado, R.: Dynamic analysis of metallic arch railway bridge. J. Bridge Eng. 7(4), 214–222 (2002).  https://doi.org/10.1061/(ASCE)1084-0702(2002)7:4(214) CrossRefGoogle Scholar
  29. 29.
    Chen, S., Tang, Y., Huang, W.-J.: Visual vibration simulation of framed arch bridge under multi-vehicle condition. Gongcheng Lixue/Eng. Mech. 22(1), 218–222 (2005)Google Scholar
  30. 30.
    Wallin, J., Leander, J., Karoumi, R.: Strengthening of a steel railway bridge and its impact on the dynamic response to passing trains. Eng. Struct. 33(2), 635–646 (2011).  https://doi.org/10.1016/j.engstruct.2010.11.022 CrossRefGoogle Scholar
  31. 31.
    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 CrossRefzbMATHGoogle Scholar
  32. 32.
    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 CrossRefGoogle Scholar
  33. 33.
    Mahmoud, K.M.: Fracture strength for a high strength steel bridge cable wire with a surface crack. Theor. Appl. Fract. Mech. 48(2), 152–160 (2007).  https://doi.org/10.1016/j.tafmec.2007.05.006 CrossRefGoogle Scholar
  34. 34.
    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. Mech. 53(2), 113–126 (2019).  https://doi.org/10.1016/j.tafmec.2010.03.002 CrossRefGoogle Scholar
  35. 35.
    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 CrossRefGoogle Scholar
  36. 36.
    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 MathSciNetCrossRefGoogle Scholar
  37. 37.
    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 CrossRefGoogle Scholar
  38. 38.
    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 CrossRefGoogle Scholar
  39. 39.
    Haubans, S.E.T.R.A.: Recommandations de la Commission Interministérielle de la Précontrainte. Service d’ Etudes Techniques des Routes et Autoroutes, France (2001)Google Scholar
  40. 40.
    P.T.I.: Recommendations for Stay Cable Design, Testing and Installation. Post-Tensioning Institute, DC45.1-12, USA (2012)Google Scholar
  41. 41.
    Mozos, C.M.: Theoretical and experimental study on the structural response of cable stayed bridges to a stay failure. Dissertation, Universidad de Castilla-La Manche (2007)Google Scholar
  42. 42.
    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, 16–19 July 2006, Porto, Portugal, CRC PressGoogle Scholar
  43. 43.
    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 CrossRefGoogle Scholar
  44. 44.
    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).  https://doi.org/10.1016/j.engstruct.2010.07.002 CrossRefGoogle Scholar
  45. 45.
    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 CrossRefGoogle Scholar
  46. 46.
    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 CrossRefGoogle Scholar
  47. 47.
    Wolff, M., Starossek, U.: Cable loss and progressive collapse in cable-stayed bridges. Bridge Struct. 5, 17–28 (2009).  https://doi.org/10.1080/15732480902775615 CrossRefGoogle Scholar
  48. 48.
    Starossek, U.: Avoiding disproportional collapse of major bridges. Struct. Eng. Int. 19(3), 289–297 (2009).  https://doi.org/10.2749/101686609788957838 CrossRefGoogle Scholar
  49. 49.
    Konstantakopoulos, T.G., Michaltsos, G.T.: Suspended arch bridges under moving loads—the 2D mathematical model. Int. J. Bridge Eng. 6(1), 91–105 (2018)Google Scholar
  50. 50.
    Kounadis, A.N.: An efficient and simple approximate technique for solving nonlinear initial and boundary-value problems. Comput. Mech. 9(3), 221–231 (1992).  https://doi.org/10.1007/BF00350188 MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Panagiotopoulos, P.: Hemivariational Inequalities: Applications in Mechanics and Engineering. Springer, Berlin (1993)CrossRefGoogle Scholar
  52. 52.
    Mistakidis, E.S., Stavroulakis, G.E.: Nonconvex Optimization in Mechanics: Smooth and Nonsmooth Algorithms, Heuristic and Engineering Applications. Kluwer, London (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • D. S. Sophianopoulos
    • 1
    Email author
  • G. T. Michaltsos
    • 2
  • H. I. Cholevas
    • 1
  1. 1.Department of Civil EngineeringUniversity of ThessalyVólosGreece
  2. 2.National Technical University of AthensAthensGreece

Personalised recommendations