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Abstract: In recent years nonlinear static analysis method has been widely used in the field of performance based earthquake engineering. Whereas the capabilities of this method is well recognized, it still has inherent shortcomings. Accordingly, by considering aspects such as nonlinear properties of members, higher modes effect, and the computational cost, the accuracy of the method should be investigated. Although an enormous study have been carried out to improve the pushover analysis, the proposed methods are almost deterministic and cannot directly consider the seismic records uncertainties. Toward this challenge, the present study aims to examine the requirements of inelastic static analysis method through a comparison with incremental dynamic analysis results. The general purpose of the pushover method is to yield the maximum story responses (shear and drift) expected during the earthquake. For this reason, the selection of the dynamic response absolute maxima is discussed and different criteria are investigated; maximum displacement versus corresponding base shear, maximum displacement versus maximum base shear and, finally, maximum base shear versus corresponding displacement. Therefore, using the information obtained from dynamic analysis, the characteristic of the proper lateral forces that can represent the average of the maximum effect of the ensemble of earthquake records and consider the inherent records uncertainties, can be obtained. So, to derive the characteristics of equivalent lateral forces based on the dynamic response of the system, four different lateral force profiles can be considered; (1) F1: lateral forces create the same average story forces as dynamic analysis, (2) F2: the profile and intensity of the lateral forces that produce the average of the maximum story shear induced by seismic record ensemble, (3) D1: the lateral force profile is chosen in a way that it can produce the same maximum story drifts as dynamic analysis, and (4) D2: the forces that their responses best represent the average of the story lateral displacement in dynamic analysis. The comparisons are performed for three levels of the typical small, medium and high-rise buildings denoted as four, twelve and twenty-story shear frames. The mathematical model of the frames are chosen as the smoothly varying differential Bouc–Wen model. Because of the versatility and mathematical tractability of the Bouc-Wen model, by altering different parameters of the model, it can simulate various structural behavior with any degree of nonlinearity. The estimated responses are compared to those resulted from the nonlinear dynamic analysis. The comparison procedure in the validation process is conducted in two levels; structural global level results (base shear and roof displacement) and story level results (the story drift and lateral force profiles). Furthermore, using the considered characteristics of the lateral load profile, the probabilistic capacity curve which has the potential to be used for assessing different parts of the structure for different performance levels is extracted. As we expect from static nonlinear analysis the demand of the stories should reach their maximum. In fact, in the low-rise structure when the roof displacement reach its maximum, all of the stories also lean towards their maximum demands. By increasing the structures height (followed with higher modes effect), the result of classic pushover analysis cannot correctly estimate the demands and it differs from the result of dynamic analysis.

Keywords: Bouc-Wen model, stochastic linearization, probabilistic capacity curve, extreme value

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