KSCE Journal of Civil Engineering

, Volume 4, Issue 4, pp 201–211 | Cite as

SFEM-based seismic risk analysis of nonlinear structures using sequential RSM

  • Jungwon Huh
Structural Engineering


A finite element-based reliability analysis approach is proposed to estimate the risk of structures under short duration dynamic loadings including seismic loading in the time domain. The proposed approach is parallel to the deterministic finite element method, except that it can incorporate the information on the uncertainty in the essential variables present in the problem under consideration. In the algorithm, the incorporation of uncertainties of all the seismic loading and resistance-related parameters is successfully accomplished by using the concepts of response surface method, the first-order reliability method, and an iterative linear interpolation scheme. Therefore, the rational integration of these methods with a finite element formulation leads to the stochastic finite element-based algorithm. It is capable of capable of capturing any special features that can be handled by the finite element method, making it a robust reliability assessment technique. One of its distinguishing features is that actual earthquake loading time histories can be used to excite structures so that the realistic loading conditions can be simulated. Furthermore, it has the potential to estimate the risk associated with both the serviceability and the strength limit states. The algorithm has been extensively verified using the Monte Carlo simulation technique. Although two examples are given for the steel frame building structure in this paper, applicability of the proposed approach can be easily extended to other types of structures.


first order reliability method reliability index response surface method serviceability limit state stochastic finite element method strength limit state 


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  1. 1.
    American Institute of Steel Construction (1994)Manual of Steel Construction: Load and Resistance Factor Design. AISC, Chicago, Illinois.Google Scholar
  2. 2.
    Bucher, C.G. and Bourgund, U. (1990). “A fast and efficient response surface approach for structural reliability problems.”Structural Safety, Vol. 7, pp. 57–66.CrossRefGoogle Scholar
  3. 3.
    Bucher, C. G., Chen, Y. M., and Schüller, G. I. (1989). “Time variant reliability analysis utilizing response surface approach,”Reliability and Optimization of Structural Systems ’88: Proc., 2 nd IFIP WG7.5 Conf., Springer-Verlag, Berlin, Germany, pp. 1–14.Google Scholar
  4. 4.
    Haldar, A. and Mahadevan, S. (2000).Probability, Reliability and Statistical Methods in Engineering Design. John Wiley & Sons, New York, N.Y.Google Scholar
  5. 5.
    Haldar, A. and Nee, K. M. (1989). “Elasto-Plastic Large Deformation Analysis of PR Steel Frames for LRFD.”Computers and Structures, Vol. 31, No. 5, pp. 811–823.CrossRefGoogle Scholar
  6. 6.
    Huh, J. (1999).Dynamic Reliability Analysis for Nonlinear Structures Using Stochastic Finite Element Method, PhD dissertation, The University of Arizona, Tucson, Arizona, U.S.A.Google Scholar
  7. 7.
    Huh, J. and Haldar, A. (1999). “Reliability Analysis of Nonlinear Frames under Seismic Loadings.”13th ASCE Engineering Mechanics Division Conference (CD-ROM proceeding), Baltimore, Maryland.Google Scholar
  8. 8.
    Khuri, A. I. and Cornell, J. A. (1996).Response Surfaces Designs and Analyses. Marcel Dekker, New York, N.Y.MATHGoogle Scholar
  9. 9.
    Kondon, K. and Atluri, S. N. (1987). “Large-deformation, elasto-plastic analysis of frames under nonconservative loading, using explicity derived tangent stiffnesses based on assumed stresses.”Computational Mechanics, Vol. 2, No. 1, pp. 1–25.Google Scholar
  10. 10.
    Kim, S. H. and Na, S. W. (1997). “Response surface method using vector projected sampling points.”Structural Safety, Vol. 19, No. 1, pp. 3–19.CrossRefGoogle Scholar
  11. 11.
    Leger, P. and Dussaults, S. (1992). “Seismic-energy dissipation in MDOF structures.”Journal of Structural Engineering, ASCE, Vol. 118, No. 5, pp. 1251–1269.CrossRefGoogle Scholar
  12. 12.
    Lucas, J. M. (1974). Optimum Composite Designs.Technometrics, Vol. 16, No. 4, pp. 561–567.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Rajashekhar, M. R. and Ellingwood, B. R. (1993). “A new look at the response surface approach for reliability analysis.”Structural Safety, Vol. 12, pp. 205–220.CrossRefGoogle Scholar
  14. 14.
    Uang, C. M., Yu, Q. S., Sadre, A., Bonowitz, D., and Youssef, N. (1995). “Performance of a 13-Story Steel Moment-Resisting Frame damaged in the 1994 Northridge Earthquake, Technical Report SAC 95-04, SAC Joint Venture.Google Scholar

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© KSCE and Springer jointly 2000

Authors and Affiliations

  1. 1.Dept. of Civil Eng.Yonsei UniversitySeoulKorea

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