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A general approach is presented for the estimation of expected failure rates of structures per unit time, which accounts for uncertainties about mechanical and geometrical properties, as well as about live load and seismic excitation. Such an approach is applied to one‐, three‐, and nine‐story frames with nonlinear behavior, subjected to random sequences of simulated accelerograms corresponding to soft and hard types of ground. Conclusions are reached concerning the influence of several concepts on the probability of failure of the structures analyzed, including: (1) The influence of the spatial statistical correlation among the mechanical properties of the structural members is relatively small as compared to that of other variables; (2) the number of degrees of freedom has a great influence on the probability of failure; (3) for small coefficients of variation of the available ductility, the probabilities of structural failure …