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Oct 1, 2005

Structural Response and Reliability Estimates: Slepian Model Approach

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Publication: Journal of Structural Engineering
Volume 131, Issue 10

Abstract

This research study investigates the practicality of using a Slepian model to model the earthquake excitation and structural response behavior of structures during the strong ground motion portion and entire duration of earthquake acceleration records. Of particular interest was the extreme response behavior of basic linear and nonlinear hysteretic oscillators. Predictions for the linear oscillators were found to be good, while predictions for the highly nonlinear oscillators were poorer until corrected for the change in equilibrium position experienced during the motion response behavior. Based upon the experience gained from these examples, a three-story frame whose beam-to-column connections were modeled as trilinear hysteretic systems were investigated. The accuracy of the Slepian response prediction for the seismic response was confirmed and the expected value form was coupled with a drift-based limit state function to estimate a conditional form of the first order structural reliability. Since the coefficient of variation of the seismic demand is not explicitly known, the reliability estimates were bounded based upon observations of typical seismic demand variation in engineered structural systems.

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Acknowledgments

The writers would like to gratefully acknowledge the partial financial support of the U.S. Department of the Interior through U.S. Geological Survey—Earthquake Hazard Reduction Program Grant No. UNSPECIFIED02HQGR0110. In addition, the second writer would also like to acknowledge the additional partial financial support for this study from the R.P. Gregory ’32 Endowed Chair in Civil Engineering at Texas A&M University. Finally, the writers would like to acknowledge the care and detailed review comments by the anonymous reviewers in helping to strengthen this paper.

References

Bendat, J. S., and Piersol, A. G. (1993). Engineering applications of correlation and spectral analysis, 2nd Ed., Wiley, New York.
Bendat, J. S., and Piersol, A. G. (2000). Random data analysis and measurement procedures, 3rd Ed., Wiley, New York.
Ditlevsen, O. (1986). “Elasto-plastic oscillator with Gaussian excitation.” J. Sound Vib., 112, 386–406.
Ditlevsen, O. (1991). “Gaussian excited elasto-plastic oscillator with rare visits to the plastic domain.” J. Sound Vib., 145(3), 443–456.
Ditlevsen, O., and Bognar, L. (1993a). “Associate linear system approach to nonlinear random vibration.” J. Eng. Mech., 119, 638–640.
Ditlevsen, O., and Bognar, L. (1993b). “Plastic displacement distributions of the Gaussian white noise excited elasto-plastic oscillator.” Probab. Eng. Mech., 8, 209–231.
Dymiotis, C., Andreas, K. J., and Chryssanthopoulas, M. K. (1999). “Seismic reliability of RC frames with uncertain drift and member capacity.” J. Struct. Eng., 125(9), 1038–1047.
Evans, M., Hastings, N., and Peacock, B. (2000). Statistical distributions, 2nd Ed., Wiley-Vhc, Weinheim, Germany.
Hart, G. C., and Wong, K. (1999). Structural dynamics for structural engineers, Wiley, New York.
Husid, R. (1969). “The effect of gravity on the collapse of yielding structures with earthquake excitation.” Proc., 4th World Conf. on Earthquake Engineering, Chilean Association on Seismology and Earthquake Engineering, Santiago, Chile, Vol. 2, A4-31–A4-43.
Kac, M., and Slepian, D. (1959). “Large excursions of Gaussian processes.” Ann. Math. Stat., 30, 1215–1228.
Leadbetter, M. R., Lindgren, G., and Rootzen, H. (1983). Extremes and related properties of random sequences and processes, Springer, New York.
Lindgren, G. (1970). “Some properties of a normal process near a local maximum.” Ann. Math. Stat., 41(6), 1870–1883.
Lindgren, G. (1981). “Jumps and bumps on random roads.” J. Sound Vib., 78, 383–395.
Lindgren, G. (1984). “Use and structure of Slepian models for prediction and direction in crossing and extreme value theory.” Statistical extremes and applications, J. Tiago de Oliveira, ed., NATO ASI Series, Reidel, Dordrecht, The Netherlands, 261–284.
Niedzwecki, J. M., van de Lindt, J. W., Gage, J. H., and Teigen, P. S. (2000). “Design estimates of surface wave interaction with compliant deepwater platforms.” Ocean Eng., 27, 867–888.
Page, R. A., Blume, J. A., and Joyner, W. B. (1975). “Earthquake shaking and damage to buildings.” Science, 189(4203), 601–608.
Park, Y., and Ang, A. (1985). “Mechanistic seismic damage model for reinforced concrete.” J. Struct. Eng., 111(4), 722–739.
Randrup-Thomsen, S., and Ditlevsen, O. (1997). “One-floor building as elasto-plastic oscillator subject to and interacting with Gaussian base motion.” Probab. Eng. Mech., 12(1), 49–56.
Randrup-Thomsen, S., and Ditlevsen, O. (1999). “Experiments with elasto-plastic oscillator.” Probab. Eng. Mech., 14, 161–167.
Slepian, D. (1961). “The one-sided barrier problem for Gaussian noise.” Bell Syst. Tech. J., 41, 463–501.
Slepian, D. (1962). “On the zeros of Gaussian noise.” Time series analysis, M. Rosenblatt, ed., Wiley, New York, 104–115.
Tarp-Johansen, N., and Ditlevsen, O. (1999). “Slepian modeling as a computational method in random vibration analysis of hysteretic structures.” Proc., 3rd International Conf. Computational Stochastic Mechanics, Thera-Santorini, Greece, A. A. Balkema, Rotterdam, The Netherlands, 67–78.
Tarp-Johansen, N., and Ditlevsen, O. (2000). “Time between plastic displacements of elasto-plastic oscillators subject to Gaussian white noise.” Proc., Int. Conf. on Monte Carlo Simulation.
van de Lindt, J. W., and Goh, G. (2004). “Earthquake duration effect on structural reliability.” J. Struct. Eng., 130(5), 821–826.
van de Lindt, J. W., and Niedzwecki, J. M. (2003). “Identification of the ground motion parameters that control structural damage using a Slepian process model.” Final Rep. to the U.S. Dept. of the Interior, U.S. Geological Survey, Reston, Va.
Vanmarcke, E. H., and Lai, S.-S. P. (1980). “Strong-motion duration and RMS amplitude of earthquake records.” Bull. Seismol. Soc. Am., 70(4), 1293–1307.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 131Issue 10October 2005
Pages: 1620 - 1628

History

Received: Mar 5, 2004
Accepted: Jan 4, 2005
Published online: Oct 1, 2005
Published in print: Oct 2005

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Notes

Note. Associate Editor: Vinay Kumar Gupta

Authors

Affiliations

J. W. van de Lindt, M.ASCE [email protected]
Associate Professor, Dept. of Civil Engineering, Colorado State Univ., Fort Collins, CO 80523-1372 (corresponding author). E-mail: [email protected]
J. M. Niedzwecki, F.ASCE
R. P. Gregory 32 Chair Professor, Texas A&M Univ., Dept. of Civil Engineering, College Station, TX 77843-3136.

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