Skip to main content
SpringerLink
Log in

Oblique frictional unilateral contacts perceived in curved bridges

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The pounding at the deck and abutment interface of a curved bridge, which occurs during earthquakes after closing the gap, directly leads to the deck unseating, in-plane deck rotation and torsional damage to the columns of the bridge. The study in hand assumes the deck of the curved bridge as a completely rigid body to analyse the multi-body oblique frictional impact at the deck–abutment interaction. Extending other authors’ work, a linear complementarity formulation is implemented for computing the unilateral contact to identify the effects of different impact states, such as stick and forward or backward slip, depending on the initial conditions during single or double impact. Stick and slip conditions during single impact are evaluated for different pre-impact rotations and ratios of transverse to normal pre-impact relative velocities. Also, the inward and outward slips during double impact, which represent the possibility of the deck being out-off lane, and the possibility of post-impact deck rotation are estimated for several curved geometries. The results show the curved bridge is very susceptible for in-plane deck rotation and out-off lane misalignment during the deck–abutment pounding.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. (AASHTO), A.A.o.S.H.a.T.O.: Section 6: Foundation and abutment design. In: (AASHTO) Guide specifications of bridges. Washington, DC (2011)

  2. (AASHTO), A.A.o.S.H.a.T.O.: Chapter 4: analysis and design requirements. In: (AASHTO) Guide specifications of bridges. Washington, DC (2011)

  3. Yashinsky, M., Karshenas, M.: Fundamentals of seismic protection for bridges. National Information Centre of Earthquake Engineering (2003)

  4. Jennings, P.C.: Engineering features of the San Fernando earthquake of February 9, 1971 (1971)

  5. CENTER, J.B.E.: Damage to Highway Bridges Caused by the 2011 Tohoku-Oki Earthquake. In. Tokyo (2011)

  6. Chouw, N., Hao, H.: Pounding damage to buildings and bridges in the 22 February 2011 Christchurch earthquake. Int J Prot Struct. 3(2), 123–140 (2012)

    Article  Google Scholar 

  7. Cole, G., Bull, D., Dhakal, R., Carr, A.: Interbuilding pounding damage observed in the 2010 Darfield earthquake. Bull. N. Z. Soc. Earthq. Eng. 43(4), 382 (2010)

    Google Scholar 

  8. Cole, G.L., Dhakal, R.P., Turner, F.M.: Building pounding damage observed in the 2011 Christchurch earthquake. Earthq. Eng. Struct. Dyn. 41(5), 893–913 (2012)

    Article  Google Scholar 

  9. Elnashai, A.S., Gencturk, B., Kwon, O.-S., Hashash, Y.M., Kim, S.J., Jeong, S.-H., Dukes, J.: The Maule (Chile) earthquake of February 27, 2010: development of hazard, site specific ground motions and back-analysis of structures. Soil Dyn. Earthq. Eng. 42, 229–245 (2012)

    Article  Google Scholar 

  10. Priestley, M.N., Seible, F., Calvi, G.M.: Seismic Design and Retrofit of Bridges. Wiley, London (1996)

    Book  Google Scholar 

  11. Wieser, J., Zaghi, A.E., Maragakis, M., Buckle, I.: A methodology for the experimental evaluation of seismic pounding at seat-type abutments of horizontally curved bridges. Bridges 10, 9780784412367.9780784412055 (2014)

  12. Saad, A., Sanders, D.H., Buckle, I.: Impact of rocking foundations on horizontally curved bridge systems subjected to seismic loading. Bridges 10, 9780784412367.9780784412056 (2014)

  13. Dimitrakopoulos, E.: Analysis of a frictional oblique impact observed in skew bridges. Nonlinear Dyn. 60(4), 575–595 (2010). doi:10.1007/s11071-009-9616-7

    Article  MATH  Google Scholar 

  14. Dimitrakopoulos, E.G.: Nonsmooth analysis of the impact between successive skew bridge-segments. Nonlinear Dyn. 74(4), 911–928 (2013)

    Article  MathSciNet  Google Scholar 

  15. Kim, S.: GIS-based regional risk analysis approach for bridges against earthquakes. Dissertation, Department of Civil Engineering, State University of New York at Buffalo (1993)

  16. Maleki, S.: Seismic modeling of skewed bridges with elastomeric bearings and side retainers. J. Bridge Eng. 10(4), 442–449 (2005). doi:10.1061/(ASCE)1084-0702(2005)10:4(442)

    Article  Google Scholar 

  17. Maragakis, E.A., Jennings, P.C.: Analytical models for the rigid body motions of skew bridges. Earthq. Eng. Struct. Dyn. 15(8), 923–944 (1987). doi:10.1002/eqe.4290150802

    Article  Google Scholar 

  18. Zhu, P., Abe, M., Fujino, Y.: Modelling three-dimensional non-linear seismic performance of elevated bridges with emphasis on pounding of girders. Earthq. Eng. Struct. Dyn. 31(11), 1891–1913 (2002)

    Article  Google Scholar 

  19. Saadeghvaziri, M.A., Yazdani-Motlagh, A.: Seismic behavior and capacity/demand analyses of three multi-span simply supported bridges. Eng. Struct. 30(1), 54–66 (2008)

    Article  Google Scholar 

  20. Kaviani, P., Zareian, F., Taciroglu, E.: Seismic behavior of reinforced concrete bridges with skew-angled seat-type abutments. Eng. Struct. 45, 137–150 (2012)

    Article  Google Scholar 

  21. Kawashima, K., Shoji, G.: Effect of restrainers to mitigate pounding between adjacent decks subjected to a strong ground motion. In: Proceedings of the 12th World Conference on Earthquake Engineering (2000)

  22. Kawashima, K., Tirasit, P.: Effect of nonlinear seismic torsion on the performance of skewed bridge piers. J. Earthq. Eng. 12(6), 980–998 (2008)

    Article  Google Scholar 

  23. Anagnostopoulos, S.A.: Pounding of buildings in series during earthquakes. Earthq. Eng. Struct. Dyn. 16(3), 443–456 (1988). doi:10.1002/eqe.4290160311

    Article  Google Scholar 

  24. Anagnostopoulos, S.A., Spiliopoulos, K.V.: An investigation of earthquake induced pounding between adjacent buildings. Earthq. Eng. Struct. Dyn. 21(4), 289–302 (1992)

    Article  Google Scholar 

  25. Goyal, S., Pinson, E.N., Sinden, F.W.: Simulation of dynamics of interacting rigid bodies including friction II: software system design and implementation. Eng. Comput. 10(3), 175–195 (1994)

    Article  Google Scholar 

  26. Jankowski, R.: Non-linear viscoelastic modelling of earthquake-induced structural pounding. Earthq. Eng. Struct. Dyn. 34(6), 595–611 (2005)

    Article  Google Scholar 

  27. Muthukumar, S., DesRoches, R.: A Hertz contact model with non-linear damping for pounding simulation. Earthq. Eng. Struct. Dyn. 35(7), 811–828 (2006)

    Article  Google Scholar 

  28. Ye, K., Li, L., Zhu, H.: A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthq. Eng. Struct. Dyn. 38(9), 1135–1142 (2009)

    Article  Google Scholar 

  29. Brogliato, B.: Nonsmooth Mechanics: Models, Dynamics and Control. Springer, Berlin (2012)

    MATH  Google Scholar 

  30. Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  31. Wriggers, P., Laursen, T.A.: Computational Contact Mechanics, vol. 30167. Springer, Berlin (2006)

    Book  MATH  Google Scholar 

  32. Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.) Nonsmooth Mechanics and Applications. International Centre for Mechanical Sciences, vol. 302, pp. 1–82. Springer, Vienna (1988)

    Chapter  Google Scholar 

  33. Panagiotopoulos, P.D.: Dynamic and incremental variational inequality principles, differential inclusions and their applications to co-existent phases problems. Acta Mech. 40(1–2), 85–107 (1981). doi:10.1007/BF01170692

    Article  MathSciNet  MATH  Google Scholar 

  34. Panagiotopoulos, P.D.: Nonconvex energy functions. Hemivariational inequalities and substationarity principles. Acta Mech. 48(3–4), 111–130 (1983). doi:10.1007/BF01170410

    Article  MathSciNet  MATH  Google Scholar 

  35. Banerjee, A., Chanda, A., Das, R.: Historical origin and recent development on normal directional impact models for rigid body contact simulation: a critical review. Arch. Comput. Methods Eng. (2016). doi:10.1007/s11831-016-9164-5

  36. Abbas, H., Paul, D., Godbole, P., Nayak, G.: Soft missile impact on rigid targets. Int. J. Impact Eng. 16(5), 727–737 (1995)

    Article  Google Scholar 

  37. Klarbring, A., Björkman, G.: A mathematical programming approach to contact problems with friction and varying contact surface. Comput. Struct. 30(5), 1185–1198 (1988). doi:10.1016/0045-7949(88)90162-9

    Article  MATH  Google Scholar 

  38. Kraus, P.R., Fredriksson, A., Kumar, V.: Modeling of frictional contacts for dynamic simulation. In: Proceedings of IROS 1997 Workshop on Dynamic Simulation: Methods and Applications, pp. 1–10 (1997)

  39. Glocker, C.: Set-Valued Force Laws: Dynamics of Non-smooth Systems, vol. 1. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

  40. Leine, R., Van Campen, D., Glocker, C.H.: Nonlinear dynamics and modeling of various wooden toys with impact and friction. J. Vib. Control 9(1–2), 25–78 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  41. Payr, M., Glocker, C.: Oblique frictional impact of a bar: analysis and comparison of different impact laws. Nonlinear Dyn. 41(4), 361–383 (2005). doi:10.1007/s11071-005-8200-z

    Article  MathSciNet  MATH  Google Scholar 

  42. Theodosiou, C., Natsiavas, S.: Dynamics of finite element structural models with multiple unilateral constraints. Int. J. Non-linear Mech. 44(4), 371–382 (2009)

    Article  MATH  Google Scholar 

  43. Zhang, H., Brogliato, B., Liu, C.: Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data. Multibody Syst. Dyn. 32(1), 1–25 (2014)

    Article  MathSciNet  Google Scholar 

  44. Chanda, A., Banerjee, A., Das, R.: Sensitivity analysis of the impact parameters on the seismic response of straight bridges. Paper Presented at the 2nd Australasian Conference on Computational Mechanics, Brisbane, Australia, 30 November–1 December

  45. Chanda, A., Banerjee, A., Das, R.: The application of the most suitable impact model(s) for simulating the seismic response of a straight bridge under impact due to pounding. Int. J. Sci. Eng. Res. 7(2), 25–36 (2016)

    Google Scholar 

  46. Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts, vol. 421. Springer, Berlin (2000)

    MATH  Google Scholar 

  47. Lemke, C.E.: The dual method of solving the linear programming problem. Naval Res. Logist. Q. 1(1), 36–47 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  48. Lemke, C.E.: On Complementary Pivot Theory. Department of Mathematics, Rensselaer Polytechnic Institute, New York (1967)

    MATH  Google Scholar 

  49. Kane, T.R., Levinson, D.A.: Dynamics, Theory and Applications. McGraw Hill, New York (1985)

    Google Scholar 

  50. Marghitu, D.B., Stoenescu, E.D.: Rigid body impact with moment of rolling friction. Nonlinear Dyn. 50(3), 597–608 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Auckland, 20 Symonds Street, Auckland, 1010, New Zealand

    Arnab Banerjee, Avishek Chanda & Raj Das

Authors
  1. Arnab Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Avishek Chanda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raj Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arnab Banerjee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banerjee, A., Chanda, A. & Das, R. Oblique frictional unilateral contacts perceived in curved bridges. Nonlinear Dyn 85, 2207–2231 (2016). https://doi.org/10.1007/s11071-016-2824-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2824-z

Keywords

Search

Navigation