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Structural response under seismic loadings is typically nonlinear and related to many factors, such as structural configurations, material properties, occupancy loads, earthquake hazards and incomplete knowledge of the system. As all these factors have their sources of uncertainties, structural response under seismic loading has its probabilistic nature. Therefore, the random variable for any structural demand follows a multivariate probability distribution over the integration domain defined by the limit states. Examining the probabilistic behaviour of structures under earthquake loadings has to consider the sources of uncertainties from all factors. It is also known that numerical methods, such as the finite element method, are commonly used to predict nonlinear structural response. The probabilistic structural demand is a discrete probability function of its related variables.
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