A reliability analysis method has been developed for plane rigid frame structures, with shear walls in all or some of their wall openings, subjected to horizontal in-plane earthquake ground accelerations. The structural reliability is measured here in terms of the probability that, throughout the structure's lifetime, its response will not violate a set of performance criteria selected to represent a safe state of structural behavior.; In this study, the structure is assumed to be safe as long as the response is confined within the linear range of structural behavior. Hence, the linear structural analysis utilizing the finite element method is performed here placing emphasis on the interaction between the shear walls and surrounding frame.; The probabilistic characteristics of the earthquake and structural response are described at two levels: First, an individual earthquake ground acceleration is assumed to be a stationary and Gaussian random process with mean zero and Kanai-Tajimi spectrum. Then, the corresponding stationary response can also be shown to be Gaussian with mean zero with its probabilistic characteristics derived from the random vibration theory. Only the finite duration of such a response process is considered, however, in estimating the structural reliability. This is to reflect, in approximation, the nonstationary nature of both the earthquake ground accelerations and structural responses. Second, an extreme value distribution of Type II is employed to describe the statistical variation of an individual earthquake's intensity, while the Poisson arrival law is used to model the earthquake occurrences.; The modal analysis approach is taken to map the safe domains associated with individual critical internal forces in the (transformed) generalized coordinate vector space. Then, the global reliability, i.e., the reliability of the structure as a whole, is obtained by estimating the probability that the generalized coordinate vector will remain in the domain representing the intersection of these safe domains throughout the structure's lifetime. A number of numerical examples are worked out to implement the theory and to determine the reliabilities of typical rigid frames.
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