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Shock and Vibration
Volume 5, Issue 5-6, Pages 355-369

Maximum Displacement Variability of Stochastic Structures Subject to Deterministic Earthquake Loading

L.L. Graham

Department of Civil Engineering, University of Virginia, Charlottesville, VA 22903-2442, USA

Received 8 August 1998; Revised 25 November 1998

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The variability of the maximum response displacement of random frame structures under deterministic earthquake loading are examined in this paper using stochastic finite element techniques. The elastic modulus and the mass density are assumed to be described by cross-correlated stochastic fields. Specifically, a variability response function formulation is used for this problem, which allows for calculation of spectral-distribution-free upper bounds of the maximum displacement variance. Further, under the assumption of prespecified correlation functions describing the spatial variation of the material properties, variability response functions are used to calculate the corresponding maximum displacement variance. Two numerical examples are provided to demonstrate the methodology. Results show that randomness in the material properties can lead to significant uncertainty in the maximum response displacement.