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Numerical simulation of structural response is a challenging issue in earthquake engineering and there has been remarkable progress in this area in the last decade. Endurance Time (ET) method is a new response history based analysis procedure for seismic assessment and structural design in which structures are subjected to a gradually intensifying dynamic excitation and their seismic performance is evaluated based on their responses at different excitation levels. Generating appropriate artificial dynamic excitation is essential in this type of analysis. In this paper, an optimization procedure is presented for computation of the intensifying acceleration functions utilized in the ET method and the results of this procedure are discussed. A set of the ET acceleration functions (ETAFs) is considered which has been produced utilizing numerical optimization considering 2048 acceleration points as optimization variables by an unconstrained optimization procedure. The ET formulation is then modified from the continuous time condition into the discrete time state thus the optimization problem is reformulated as a nonlinear least squares problem. In this way, a second set of the ETAFs is generated which better satisfies the proposed objective function. Subsequently, acceleration points are increased to 4096, for 40 seconds duration, and the third set of the ETAFs is produced using a multi level optimization procedure. Improvement of the ETAFs is demonstrated by analyzing several SDOF systems.

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Estimation of collapse performance is primarily conducted through Collapse Fragility Curves (CFC’s). The EDP-based approach is the main scheme for attaining such curves and employs IDA. Obtaining CFC’s from IDA results is tremendously time consuming and computationally demanding. Introduction of more efficient methods of seismic analysis, can potentially improve this issue. The Endurance Time (ET) method is a straightforward method for dynamic analysis of structures subjected to multilevel excitation intensities. In this paper, collapse analysis using ET analysis results to obtain EDP-based CFC’s, has been explained and demonstrated by a model. For verification, the resulting CFC has been compared to that obtained by IDA.

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Endurance Time Method (ET) is a dynamic analysis in which structures are subjected to intensifying accelerograms that are optimized in a way that seismic performance of structures can be estimated at different hazard levels with the best possible accuracy. For the currently available ET accelerograms, regardless of the shaking characteristic, an excitation level is recognized as a representative of a specific hazard level, when the acceleration and the displacement spectrum produced by the ET accelerograms up to that excitation level will be compatible with the acceleration and the displacement spectrum associated with that hazard level. This study compares the shaking characteristics of the current ET accelerograms with the ground motions. For this purpose, distribution of plastic cycles and the equivalent number of the cycles are considered as shaking properties of a motion. This study suggests a procedure to achieve the best possible consistency between the equivalent number of cycles of the current ET records and the ground motions. Moreover, a procedure to generate the new generation and optimization of the ET accelerograms which are more consistent with the ground motions are suggested.

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Endurance Time method is a time history dynamic analysis in which structures are subjected to increasing excitations. These excitations are known as endurance time excitation functions (ETEF). This study proposes a new method for generating ETEFs. In the proposed method, a new basis function for representing ETEFs is introduced. This type of ETEFs representation creates an intelligent space for this ETEFs simulating optimization problem. The proposed method is then applied in order to simulate new ETEFs. To investigate the efficiency of this proposed optimization space, newly generated ETEFs are compared with those simulated by conventional approaches. Results show an improvement in the accuracy of ETEFs as well as the reduction in the required computational time.