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NEW TRENDS IN SEISMIC DESIGN OF STRUCTURES
Edited by: N.D. Lagaros, Y. Tsompanakis and M. Papadrakakis
Practical Methods for Uncertainty Analysis in Seismic Design
National University of Colombia, Manizales, Colombia
J.E. Hurtado, "Practical Methods for Uncertainty Analysis in Seismic Design", in N.D. Lagaros, Y. Tsompanakis and M. Papadrakakis, (Editors), "New Trends in Seismic Design of Structures", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 2, pp 29-58, 2015. doi:10.4203/csets.37.2
Keywords: random vibration, Monte Carlo simulation, robust design, reliability based design, total probability theorem, point estimates, stratified sampling.
Current trends in earthquake engineering favor the consideration of actual nonlinear structural performance as well as the uncertainties in actual seismic design. While a good amount of literature has been published on performance-based design, the development of practical methods for incorporating uncertainty analysis in seismic design with reasonable accuracy and computational effort is still required. This chapter is a contribution to the development of such practical techniques, some of which are herein presented for the first time. The two main design options in relation to uncertainty, namely robust design optimization (RDO) and reliability-based design optimization (RBDO), are presented first. Generally speaking, the first option depends on an accurate and realistic evaluation of the statistical low order moments of the structural responses. It is shown that the use of the random vibration analysis connection with the point estimate technique allows a fast and accurate solution of this problem. On the other hand, for the RBDO case, it is necessary to compute failure probabilities for each trial model in the optimization process. To solve this need, a powerfulmethod for improving the probability estimates yielded by approximate methods such as analytical (i.e. non Monte Carlo) random vibration analysis is proposed. The method is based on the total probability theorem used for extrapolating the random vibration analysis with the help of a few Monte Carlo simulations, whose number is further reduced by means of a special sampling technique named backward stratified sampling. With an example involving a base isolated building, it is shown that the method requires only a small number of Monte Carlo simulations to yield excellent accuracy.
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