Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Reliability analysis of uncertain structures using earthquake response spectra

  • Received : 2011.02.21
  • Accepted : 2011.03.11
  • Published : 2011.09.25
⟨ Previous Next ⟩

Abstract

This paper develops a probabilistic methodology for the seismic reliability analysis of structures with random properties. The earthquake loading is assumed to be described in terms of response spectra. The proposed methodology takes advantage of the response spectra and thus does not require explicit dynamic analysis of the actual structure. Uncertainties in the structural properties (e.g. member cross-sections, modulus of elasticity, member strengths, mass and damping) as well as in the seismic load (due to uncertainty associated with the earthquake load specification) are considered. The structural reliability is estimated by determining the failure probability or the reliability index associated with a performance function that defines safe and unsafe domains. The structural failure is estimated using a performance function that evaluates whether the maximum displacement has been exceeded. Numerical illustrations of reliability analysis of elastic and elastic-plastic single-story frame structures are presented first. The extension of the proposed method to elastic multi-degree-of-freedom uncertain structures is also studied and a solved example is provided.

Keywords

References

  1. Abbas, A.M. (2006), "Critical seismic load inputs for simple inelastic structures", J. Sound Vib., 296, 949-967. https://doi.org/10.1016/j.jsv.2006.03.021
  2. Abbas, A.M. and Manohar, C.S. (2005a), "Reliability-based critical earthquake load models. Part 1: Linear structures", J. Sound Vib., 287, 865-882. https://doi.org/10.1016/j.jsv.2004.12.002
  3. Abbas, A.M. and Manohar, C.S. (2005b), "Reliability-based critical earthquake load models. Part 2: Nonlinear structures", J. Sound Vib., 287, 883-900. https://doi.org/10.1016/j.jsv.2004.12.003
  4. Abbas, A.M. and Manohar, C.S. (2007), "Reliability-based vector nonstationary random critical earthquake excitations for parametrically excited systems", Struct. Safety, 29, 32-48. https://doi.org/10.1016/j.strusafe.2005.11.003
  5. Ang, A-H.S. and Tang, W.H. (1984), Probability concepts in engineering planning and design, Volume II Design decision, risk and reliability, John Wiley & Sons, NY.
  6. ASCE (2003), Minimum design loads for buildings and other structures, revision of ASCE-98. ASCE, Structural Engineering Institute.
  7. Bender, B.K. and Perkins, D.M. (1993), "Treatment of parameter uncertainty and variability for a single seismic hazard map", Earthq. Spectra, 9(2), 165-195. https://doi.org/10.1193/1.1585711
  8. Boore, D.M. (1983), "Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra", B. Seismol. Soc. Am., 73, 1865-1894.
  9. Brune, J.N. (1970), "Tectonic stress and the spectra of seismic shear waves from earthquakes", J. Geophys. Res., 75, 4997-5009. https://doi.org/10.1029/JB075i026p04997
  10. Chopra, A.K. (2007), Dynamics of structures, 3rd Ed., Prentice Hall, NJ.
  11. Collins, K.R. (1995), "A reliability-based dual level seismic design procedure for building structures", Earthq. Spectra, 11(3), 417-429. https://doi.org/10.1193/1.1585821
  12. Cornell, C.A. (1968), "Engineering seismic risk analysis", B. Seismol. Soc. Am., 58, 1583-11606.
  13. COSMOS (2005), Consortium organizations for strong-motion observation systems, http://db.cosmos-eq.org.
  14. Davenport, A.G. and Hill-Carroll, P. (1986), "Damping in tall buildings; its variability and treatment in design", Building Motion in Wind, Proc., ASCE Convention, Seatle, WA.
  15. Ditlevsen, O. (1981), Uncertainty modeling, McGraw-Hill, New York.
  16. Grigoriu, M. (1984), Risk, structural engineering and human error, Editor, University of Waterloo Press, Canada.
  17. Gupta, S. and Manohar, C.S. (2006), "Reliability analysis of randomly vibration structures with parameter uncertainties", J. Sound Vib., 297, 1000-1024. https://doi.org/10.1016/j.jsv.2006.05.010
  18. Haldar, A. and Mahadevan, S. (2000), Probability, reliability and statistical methods in engineering design, John Wiley and Sons, Inc., NY.
  19. Haldar, A. and Mahadevan, S. (2000), Reliability assessment using stochastic finite element analysis, John Wiley and Sons, Inc., NY.
  20. Haviland, R.A. (1976), "Study of the uncertainties in the fundamental translational periods and damping values for real buildings", Res. Rep. No. 5, pub. No. R76-12, Dept of Civil Eng., MIT, Cambridge, MA.
  21. IBC (2003), International building code, International code council Inc., USA.
  22. Iyengar, R.N. and Rao, P.N. (1979), "Generation of spectrum compatible accelerograms", Earthq. Eng. Struct. Dyn., 7, 253-263. https://doi.org/10.1002/eqe.4290070305
  23. Kareem, A. and Sun, W.J. (1990), "Dynamic response of structures with uncertain damping", Eng. Struct., 12, 2-8. https://doi.org/10.1016/0141-0296(90)90032-N
  24. Lin, Y.K. (1967), Probabilistic theory of structural dynamics, McGraw-Hill, New York.
  25. Manohar, C.S. and Ibrahim, R.A. (1999), "Progress in structural dynamics with stochastic parameter variations: 1987-1998", Appl. Mech. Rev., 52(5), 177-197. https://doi.org/10.1115/1.3098933
  26. McGuire, R.K. (1995), "Probabilistic seismic hazard analysis and design earthquake: closing the loop", B. Seismol. Soc. Am., 85, 1275-1284.
  27. Moller, O. and Foschi, R.O. (2003), "Reliability evaluation in seismic design: a response surface methodology", Earthq. Spectra, 19(3), 579-603. https://doi.org/10.1193/1.1598200
  28. Muscolino, G., Ricciardi, G. and Impollonia, N. (2000), "Improved dynamic analysis of structures mechanical uncertainties under deterministic inputs", Probabilist. Eng. Mech., 15, 199-212. https://doi.org/10.1016/S0266-8920(99)00021-1
  29. Nigam, N.C. (1983), Introduction to random vibration, MIT press, London.
  30. Nowak, A.S. (1986), Modeling human error, Editor, ASCE, New York.
  31. Rackwitz, R. (2002), "Reliability analysis - a review and some perspectives", Struct. Safety 23, 365-395.
  32. Rackwitz, R. and Fiessler, B. (1978), "Structural reliability under combined random load sequences", Comput. Struct., 9(5), 484-494.
  33. Wen, Y.K. (1995), "Building reliability and code calibration", Earthq. Spectra, 11(2), 269-296. https://doi.org/10.1193/1.1585815
  34. Wen, Y.K. and Wu, C.L. (2001), "Uniform hazard ground motions for mid-america cities", Earthq. Spectra, 17(2), 359-284. https://doi.org/10.1193/1.1586179

Cited by

  1. Reliability Analysis of Semiactive Magnetorheological Dampers Subjected to Harmonic Excitations vol.5, 2013, https://doi.org/10.1155/2013/643927
  2. Influence of some relevant parameters in the seismic vulnerability of RC bridges vol.3, pp.3, 2011, https://doi.org/10.12989/eas.2012.3.3_4.365
  3. Analysis of structural dynamic reliability based on the probability density evolution method vol.45, pp.2, 2011, https://doi.org/10.12989/sem.2013.45.2.201
  4. Application of first-order reliability method in seismic loss assessment of structures with Endurance Time analysis vol.14, pp.5, 2018, https://doi.org/10.12989/eas.2018.14.5.437
  5. Reliability-based design of tuned-mass dampers with soil−structure interaction vol.172, pp.1, 2011, https://doi.org/10.1680/jencm.17.00018
  6. Seismic fragility analysis of wood frame building in hilly region vol.20, pp.1, 2021, https://doi.org/10.12989/eas.2021.20.1.097
  7. Response Spectrum with Uncertain Damping Using Artificial Neural Networks vol.56, pp.None, 2011, https://doi.org/10.4028/www.scientific.net/jera.56.136