Bulletin of Earthquake Engineering

, Volume 9, Issue 2, pp 561–579 | Cite as

Dimensional analysis of the earthquake-induced pounding between inelastic structures

  • Elias G. Dimitrakopoulos
  • Nicos Makris
  • Andreas J. Kappos
Original Research Paper

Abstract

In this paper the seismic response of inelastic structures with unilateral contact is revisited with dimensional analysis. All physically realizable contact types are captured via a non-smooth complementarity approach. The implementation of formal dimensional analysis leads to a condensed presentation of the response and unveils remarkable order even though two different types of non-linearity coexist in the response: the boundary non-linearity of unilateral contact and the inelastic behaviour of the structure itself. It is shown that regardless the intensity and frequency content of the excitation, all response spectra become self-similar when expressed in the appropriate dimensionless terms. The proposed approach hinges upon the notion of the energetic length scale of an excitation which measures the persistence of ground shaking to impose deformation demands. Using the concept of persistency which is defined for excitations with or without distinct pulses, the response is scaled via meaningful novel intensity measures: the dimensionless gap and the dimensionless yield displacement. The study confirms that contact may have a different effect on the response displacements of inelastic structures depending on the spectral region. In adjacent inelastic structures, such as colliding buildings or interacting bridge segments, contact is likely to alter drastically the excitation frequencies’ at which the system is most vulnerable. Finally, it is shown that the proposed approach yields maximum response displacements which correlate very well with the persistency of real earthquakes for a bridge system with considerably complex behaviour.

Keywords

Pounding Unilateral contact Earthquake engineering Non-linear structural dynamics dimensional analysis Bridges 

Abbreviations

DA

Dimensional Analysis

LCP

Linear Complementarity Problem

MSSS

Multi-Span Simply-Supported

PGA

Peak Ground Acceleration

SDOF

Single Degree Of Freedom

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References

  1. Barenblatt G (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press, CambridgeGoogle Scholar
  2. DesRoches R, Muthukumar S (2002) Effect of pounding and restrainers on seismic response of multiple-frame bridges. J Struct Eng 128(7): 860CrossRefGoogle Scholar
  3. Dicleli M (2008) Performance of seismic-isolated bridges with and without elastic-gap devices in near-fault zones. Earthq Eng Struct Dyn 37(6): 935–954CrossRefGoogle Scholar
  4. Dimitrakopoulos EG (2010) Analysis of a frictional oblique impact observed in Skew bridges. Nonlinear Dyn 60: 575–595CrossRefGoogle Scholar
  5. Dimitrakopoulos EG, Kappos AJ, Makris N (2009a) Dimensional analysis of yielding and pounding structures for records without distinct pulses. Soil Dyn Earthq Eng 29(7): 1170–1180CrossRefGoogle Scholar
  6. Dimitrakopoulos EG, Makris N, Kappos AJ (2009b) Dimensional analysis of the earthquake-induced pounding between adjacent structures. Earthq Eng Struct Dyn 38(7): 867–886CrossRefGoogle Scholar
  7. Dimitrakopoulos EG, Makris N, Kappos AJ (2010) Dimensional analysis of the earthquake response of a pounding oscillator. J Eng Mech (ASCE) 136(3): 299–310CrossRefGoogle Scholar
  8. Jankowski R, Wilde K, Fujino Y (1998) Pounding of superstructure segments in isolated elevated bridge during earthquakes. Earthq Eng Struct Dyn 27(5): 487–502CrossRefGoogle Scholar
  9. Leine RI, Van Campen DH, Glocker CH (2003) Nonlinear dynamics and modeling of various wooden toys with impact and friction. J Vib Control 9(1–2): 25–78Google Scholar
  10. Makris N, Chang S (2000) Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures. Earthq Eng Struct Dyn 29(1): 85–107CrossRefGoogle Scholar
  11. Makris N, Black CJ (2004a) Dimensional analysis of rigid-plastic and elastoplastic structures under pulse-type excitations. J Eng Mech 130(9): 1006CrossRefGoogle Scholar
  12. Makris N, Black CJ (2004b) Dimensional analysis of bilinear oscillators under pulse-type excitations. J Eng Mech 130(9): 1019CrossRefGoogle Scholar
  13. Makris N, Psychogios T (2006) Dimensional response analysis of yielding structures with first-mode dominated response. Earthq Eng Struct Dyn 35(10): 1203–1224CrossRefGoogle Scholar
  14. Malhotra PK (1998) Dynamics of seismic pounding at expansion joints of concrete bridges. J Eng Mech 124(7): 794CrossRefGoogle Scholar
  15. Malhotra PK, Huang MJ, Shakal AF (1995) Seismic interaction at separation joints of an instrumented concrete bridge. Earthq Eng Struct Dyn 24(8): 1055–1067CrossRefGoogle Scholar
  16. Rathje EM, Abrahamson NA, Bray JD (1998) Simplified frequency content estimates of earthquake ground motions. J Geotech Geoenviron Eng 124(2): 150CrossRefGoogle Scholar
  17. Ruangrassamee A, Kawashima K (2001) Relative displacement response spectra with pounding effect. Earthq Eng Struct Dyn 30(10): 1511–1538CrossRefGoogle Scholar
  18. Saadeghvaziri M, Yazdanimotlagh A (2008) Seismic behavior and capacity/demand analyses of three multi-span simply supported bridges. Eng Struct 30(1): 54–66CrossRefGoogle Scholar
  19. Saadeghvaziri M, Yazdani-Motlagh AR, Rashidi S (2000) Effects of soil–structure interaction on longitudinal seismic response of MSSS bridges. Soil Dyn Earthq Eng 20(1–4): 231–242CrossRefGoogle Scholar
  20. Sedov L (1992) Similarity and dimensional methods in mechanics. CRC Press, Boca Raton FlaGoogle Scholar
  21. Vega J, del Rey I, Alarcon E (2009) Pounding force assessment in performance-based design of bridges. Earthq Eng Struct Dyn 38(13): 1525–1544CrossRefGoogle Scholar
  22. Wen Y (1975) Approximate method for nonlinear random vibration 102(EM4): 389–401Google Scholar
  23. Wen Y (1976) Method for random vibration of hysteretic systems 102(EM2): 249–263Google Scholar
  24. Zanardo G, Hao H, Modena C (2002) Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion. Earthq Eng Struct Dyn 31(6): 1325–1345CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Elias G. Dimitrakopoulos
    • 1
  • Nicos Makris
    • 2
  • Andreas J. Kappos
    • 3
  1. 1.Department of EngineeringUniversity of CambridgeCambridgeUK
  2. 2.Department of Civil EngineeringUniversity of PatrasPatrasGreece
  3. 3.Department of Civil EngineeringAristotle University of ThessalonikiThessalonikiGreece

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