A Novel Modal Combination Rule Under Multi-component Ground Motion

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

Traditional earthquake-resistant design philosophy involves estimation of peak elastic response for a specified seismic hazard, which in turn requires a modal combination rule for multi degree-of-freedom systems. Commonly used modal combination rule CQC3 estimates just the largest response peaks, while the other higher-order peaks are assumed to be of no significance. The CQC3 rule is based on use of white noise idealization of excitation and is therefore inappropriate for application when the dominant frequencies of the system are outside the frequency-band of significant energy in the excitation. Considering the possibility that structural damage in the post-yield regime can be correlated with the higher-order peaks, a new modal combination rule is developed for the ordered peak response of multi-storied buildings excited by the multi-component ground motions. The proposed rule is formulated using the stationary random vibration theory without any assumption regarding the cross-correlation between different modes and the nature of the input excitation. Results show that the proposed rule outperforms the CQC3 rule, and in addition, estimates the higher-order peaks in a simple way with a significant level of accuracy comparable to that for the largest peak.

Keywords

Ground Motion Spectral Displacement Peak Factor MDOF System Multistoried Building 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    Goodman LE, Rosenblueth E, Newmark N (1953) Aseismic design of firmly founded elastic structures. Trans ASCE 120:782–802Google Scholar
  2. 2.
    Rosenblueth E, Elorduy J (1969) Response of linear systems to certain transient disturbances. In: Proceedings of the fourth world conference on earthquake engineering, vol 1. Santiago, pp 185–196Google Scholar
  3. 3.
    Der Kiureghian A (1981) A response spectrum method for random vibration analysis of MDOF systems. Earthq Eng Struct Dyn 9:419–435CrossRefGoogle Scholar
  4. 4.
    Wilson EL, Der Kiureghian A, Bayo E (1981) A replacement for the SRSS method in seismic analysis. Earthq Eng Struct Dyn 9:187–194CrossRefGoogle Scholar
  5. 5.
    Singh M, Mehta K (1983) Seismic design response by an alternative SRSS rule. Earthq Eng Struct Dyn 11:771–783CrossRefGoogle Scholar
  6. 6.
    Der Kiureghian A, Nakamura Y (1993) CQC modal combination rule for high-frequency modes. Earthq Eng Struct Dyn 22:943–956CrossRefGoogle Scholar
  7. 7.
    Gupta V (1994) Higher order peaks in the seismic response of multistoried buildings. Report 94-03, Department of Civil Engineering, IIT, KanpurGoogle Scholar
  8. 8.
    Amini A, Trifunac M (1985.) Statistical extension of response spectrum superposition. Soil Dyn Earthq Eng 4(2):54–63Google Scholar
  9. 9.
    Gupta I, Trifunac M (1987) Order statistics of peaks in earthquake response of multi-degree-of-freedom systems. Earthq Eng Eng Vib 7(4):15–50Google Scholar
  10. 10.
    Gupta V, Trifunac M (1989) Investigation of building response to translational and rotational earthquake excitations. Report CE 89-02, University of Southern California, Los AngelesGoogle Scholar
  11. 11.
    Sadhu A (2007) Ordered Peak Response under multi-component ground motion via modal combination rule and its correlation with nonlinear response. M.Tech. Thesis, Department of Civil Engineering, Indian Institute of Technology, KanpurGoogle Scholar
  12. 12.
    O’Hara G, Cunnif P (1963) Elements of normal mode theory. Report 6002, Naval Research Laboratory, Washington, DCGoogle Scholar
  13. 13.
    Chu SL, Amin M, Singh S (1972) Spectral treatment of actions of three earthquake components on structures. Nucl Eng Des 21:126–136CrossRefGoogle Scholar
  14. 14.
    Newmark N (1975) Seismic design criteria for structures and facilities—Trans-Alaska pipeline system. Proceedings of the U.S. national conference on earthquake engineering, Ann Arbor, pp 94–103Google Scholar
  15. 15.
    Rosenblueth E, Contreras H (1977) Approximate design for multicomponent earthquakes. J Eng Mech Div, Proceedings of ASCE 103:881–893Google Scholar
  16. 16.
    Smeby W, Kiureghian AD (1985) Modal combination rules for multicomponent earthquake excitation. Earthq Eng Struct Dyn 13:1–12CrossRefGoogle Scholar
  17. 17.
    Menun C, Kiureghian AD (1998) A replacement for the 30%, 40% and SRSS rules for multicomponent seismic analysis. Earthq Spectra 14:153–163CrossRefGoogle Scholar
  18. 18.
    Hernandez J, Lopez O (2002) Response to three-component seismic motion of arbitrary direction. Earthq Eng Struct Dyn 31:55–77CrossRefGoogle Scholar
  19. 19.
    Penzien J, Watabe M (1975) Characteristics of 3-dimensional earthquake ground motions. Earthq Eng Struct Dyn 3:365–373CrossRefGoogle Scholar
  20. 20.
    Gupta V (2002) Developments in response spectrum-based stochastic response of structural systems. ISET J Earthq Technol 39(4):347–365Google Scholar
  21. 21.
    Kaul M (1978) Stochastic characterization of earthquake through their response spectrum. Earthq Eng Struct Dyn 6:497–509CrossRefGoogle Scholar
  22. 22.
    Unruh J, Kana D (1981) An iterative procedure for the generation of consistent power/response spectrum. Nucl Eng Des 66(3):427–435CrossRefGoogle Scholar
  23. 23.
    Christian J (1989) Generating seismic design power spectral density functions. Earthq Spectra 5(2):351–368CrossRefGoogle Scholar
  24. 24.
    Gupta V (2008) A new approximation for spectral velocity ordinates at short periods. Earthq Eng Struct Dyn 38(7):941–949CrossRefGoogle Scholar
  25. 25.
    Trifunac M, Brady A (1975) A study on the duration of strong earthquake ground motion. Bull Seismol Soc Am 65(3):581–626Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2012

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Department of Civil and Environmental EngineeringIndian Institute of Technology KanpurKanpurIndia

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