An Upper Bound on the Failure Probability for Linear Structures

[+] Author and Article Information
L. H. Koopmans, C. Qualls

Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, N. Mex.

J. T. P. Yao

School of Civil Engineering, Purdue University, Lafayette, Ind.

J. Appl. Mech 40(1), 181-185 (Mar 01, 1973) (5 pages) doi:10.1115/1.3422921 History: Received October 01, 1971; Online July 12, 2010


This paper establishes a new upper bound on the failure probability of linear structures excited by an earthquake. From Drenick’s inequality max|y(t)| ≤ MN, where N2 = ∫ h2 , M2 , = ∫ x2 , x(t) is a nonstationary Gaussian stochastic process representing the excitation of the earthquake, and y(t) is the stochastic response of the structure with impulse response function h(τ), we obtain an exponential bound computable in terms of the mean and variance of the energy M2 . A numerical example is given.

Copyright © 1973 by ASME
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