A Bayesian Method to Form the Best Probabilistic Model to Estimate the Seismic Demand of Steel Moment-Resisting Frames

In this article, using a Bayesian statistics method, in order to estimate the seismic demand of Steel Moment-Resisting Frames (SMRFs) at any given Intensity Measure (IM), two probabilistic models,Probabilistic Seismic Demand Model (PSDM), not included collapse probability, and CollapseProbability Model (CPM), are developed. With the aim of selecting the best PSDM, 13 different IM parameters consist of one or more spectral accelerations are defined and evaluated. The Bayesian regression results show that for all defined IM, a linear relation between the logarithm of IM and thelogarithm of demand parameter, drift here, is the best form to define the PSDM, but if a single spectral acceleration is used to define the IM, it is impossible to introduce a unique parameter as IM for all type of SMRFs, because a specific spectral acceleration with the most accuracy to estimated the seismic demandof a stiff frame, may change to the weakest estimator in a deformable frame and vice versa. On the otherhand, if the IM is defined by using the combination of two or more spectral acceleration, one can find a unique IM with almost same accuracy for all modeled frames. Also the results show that a normal distribution is the best probabilistic model to define the CPM.