Markov Model for Seismic Reliability Analysis of Degrading Structures
Publication: Journal of Structural Engineering
Volume 119, Issue 6
Abstract
A Markov model is proposed to evaluate seismic performance and sensitivity to initial state of structural systems and determine the vulnerability of structures exposed to one or more earthquakes. The method of analysis is based on the seismic hazard modeled by a filtered Poisson process, nonlinear dynamic analysis for estimating structural response to earthquakes, uncertainty in initial damage state, and failure conditions incorporating damage accumulation during consecutive seismic events. Simple structures designed by the seismic design code are used to illustrate the proposed method. Effects of uncertainty in the initial state of these systems on seismic reliability are also investigated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Algermissen, S. T., and Perkins, D. M. (1976). “A probabilistic estimate of maximum acceleration in rock in the contiguous United States.” U.S. Geological Survey open‐file report, U.S. Geological Survey, Washington, D.C., 76–416.
2.
Algermissen, S. T., Perkins, D. M., Thenhaus, P. C., Hanson, S. L., and Bender, B. L. (1982). “Probabilistic estimates of maximum acceleration and velocity in rock in the contiguous United States.” U.S. Geological Survey Open‐File Report, U.S. Geological Survey, Washington, D.C., 82–1033.
3.
Algermissen, S. T. (1983). An introduction to the seismicity of the United States; monograph series. Earthquake Engrg. Res. Inst., Berkeley, Calif.
4.
Baber, T. T., and Wen, Y.‐K. (1980). “Stochastic equivalent linearization for hysteretic degrading multistorey structures.” Structural research series no. 471, Dept. of Civil Engineering, University of Illinois at Urbana‐Champaign, Ill.
5.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proc., 4th Conf. on Nonlinear Oscillation, Prague, Czechoslovakia.
6.
Bulirsch, R., and Stoer, J. (1966). “Numerical treatment of ordinary differential equations by extrapolation methods.” Numerische Mathematik, Berlin, 8, 1–13.
7.
Cornell, C. A. (1968). “Engineering seismic risk analysis.” Bull. of the Seismological Soc. of Am., 58(5), 1583–1606.
8.
Ellingwood, B., Galambos, T. V., MacGregor, J. C., and Cornell, C. A. (1980). “Development of a probability based load criterion for American national standard A58.” Nat. Bureau of Standards special publication no. SP 577, Nat. Bureau of Standards, Washington, D.C.
9.
Gear, C. W. (1971). Numerical initial value problems in ordinary differential equations. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
10.
Hurty, C. W., and Rubinstein, M. F. (1964). Dynamics of structures. Prentice Hall, Inc., Englewood Cliffs, N.J.
11.
Huťa, A. (1957). “Contribution à la formule de sixième ordre dans la méthode de Runge‐Kutta‐Nyström,” Acta Fac. Rerum Natur. Univ. Comenian. Math., 2, 21–24.
12.
Kutta, W. (1901). “Beitraz zur näherungsweisen Integration totaler Differentialgleichungen.” Zeitschreft fur Mathematik und Physik, 46, 435–453.
13.
Lai, P. S‐S. (1982). “Statistical characterization of strong motions using power spectral density functions.” Bull. of the Seismological Soc. of Am., 72(1), 259–274.
14.
Lambert, J. D. (1973). Computational methods in ordinary differential equations. John Wiley & Sons, London, England.
15.
Meirovitch, L. (1967). Analytical methods in vibration. The Macmillan Co., New York, N.Y.
16.
O'Connor, M. J., and Ellingwood, B. (1987). “Reliability of nonlinear structures with seismic loading.” J. Struct. Engrg., ASCE, 113(5), 1011–1028.
17.
Parzen, E. (1962). Stochastic processes. Holden‐Day, San Francisco, Calif.
18.
Rahman, S., and Grigoriu, M. (1989). “Reliability based design codes.” Proc. Int. Conf. of Structural Safety and Reliability, ASCE, New York, N.Y.
19.
Rahman, S., and Grigoriu, M. (1990). “Probabilistic evaluation of seismic performance of structural systems.” Proc., 4th U.S. Nat. Conf. on Earthquake Engineering, Earthquake Engrg. Res. Inst., Palm Springs, California.
20.
Rahman, S., and Grigoriu, M. (1990). “Local and global damage indices in seismic analysis.” Proc., 9th Symp. on Earthquake Engineering, University of Roorkee, Roorkee, India.
21.
Rahman, S. (1991). “A Markov model for local and global damage indices in seismic analysis,” PhD thesis, Cornell University, Ithaca, N.Y.
22.
Runge, C. (1895). “Über die numerische Auflösung von Differentialgleichungen.” Annals of Mathematics, 46, 167–178.
23.
Shampine, L. F., and Gear, C. W. (1979). “A user's view of solving stiff ordinary differential equations.” SIAM Rev., 21, 1–17.
24.
Sues, R. H., Mau, S. T., and Wen, Y.‐K. (1988). “System identification of degrading hysteretic restoring forces.” J. Engrg. Mech., 114(5), 833–846.
25.
Uniform Building Code. (1988). International Conference of Building Officials, Whittier, Calif.
26.
Wen, Y.‐K. (1976). “Method for random vibration of hysteretic systems.” J. Engrg. Mech., ASCE, 102(2), 249–263.
27.
Wen, Y.‐K. (1980). “Equivalent linearization for hysteretic systems under random excitations.” J. Appl. Mech., 47(1), 150–154.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 119 • Issue 6 • June 1993
Pages: 1844 - 1865
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Mar 3, 1992
Published online: Jun 1, 1993
Published in print: Jun 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.