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Performance-based design optimization (PBDO) is a relatively new concept in structural seismic design optimization. One of the PBDO methods which has been introduced in recent years is the optimization based on the uniform deformation theory. This method is quite different from other optimization techniques and formed based on the concept of structural performance and uniform distribution of deformation demands in the structure subjected to the seismic excitation. The aim of this method is to assign specific sections to elements such that all of the elements can reach their allowable deformation capacity during the earthquake. According to this theory, inefficient material is gradually shifted from the strong to weak areas leads to a uniform deformation (ductility) state at the end of a repetitive process. Although the base of this theory and proposed algorithm is to attain a uniform state of deformation in the whole structure, but the allowable limit of deformation values defined in PBD codes is not constant for all of structural elements. Additionally, in these codes, some actions of structural elements may be controlled by deformation and some controlled by force. Therefore, by considering the acceptance criteria of PBD codes, it is not possible to reach a uniform deformation state in the whole structure. Hence, in this paper uniform distribution of demand capacity ratio (DCR) is considered instead of uniform state of deformation. Historical review of applying this methodology shows that researchers mostly have used it to the optimum design of the structures under the earthquake records separately. Since earthquakes are random by nature, it is unlikely that the same earthquake ground motion will be repeated at some future time. This reveals that design based only one earthquake is insufficient and it is necessary to consider several earthquakes in checking the dynamic responses of a building. This paper presents an algorithm to PBDO of steel moment frames under set of ground motion records using the basic concepts of the uniform deformation theory. The proposed method consists of two phases. In the first phase of the search, to enhance the convergence rate, the search space of design variables is assumed to be continuous. Additionally in this phase of the search, only the deformation-controlled elements may vary. In the Second phase of the search, first for each structural element groups, the nearest discrete section to the imaginary section achieved in the first phase is identified and selected and then the structure is analyzed again and the DCRs are controlled. In this phase, acceptance criteria for both deformation and forced-controlled elements are supposed to be satisfied. Efficiency of the proposed algorithm is demonstrated in the optimum design of two baseline steel moment frames under a set of ground motion records. Results indicate that the proposed algorithm has a high speed to reach the optimum solution. The results are also compared with the optimum designs obtained by pushover analysis. It is shown that the optimization based on the pushover analysis results higher frame weight than time history analysis.

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One of the effective ways to mitigate earthquake damage in structures is passive control of structures. Yielding metallic dampers economic passive control devices. Not only yielding metallic dampers are easy to erect, but they can also be used as a passive control systems easily. In this paper, the aim is to develop a design procedure for steel structures equipped with a combination of yielding metallic dampers so that, dampers will experience specific nonlinear behavior when subjected to various seismic hazard levels. For this purpose, the first step is providing seismic hazard spectra with different return periods for the intended site of construction. In this research, this step has been taken by using the Tehran probabilistic analysis hazard project data and then plotting uniform hazard spectra with 75-year, 475-year, 975-year and 2475-year return periods. After determination of uniform hazard spectra with mentioned return periods, behaviors of structures equipped with yielding metallic dampers have been investigated in the form of one-storey one-span, one-storey two-span and multi storey multi span frames. Required equations for behavior of these structures under monotonic loading is developed. In the beginning of design process, the performance criteria for the structure and the damper is set and by using the derived equations, design of single degree of freedom frames based on performance criteria has been carried out. These single degree of freedom structures have different periods and strength reduction factors. After designing the single degree freedom structures, nonlinear static analysis results have been compared with result of nonlinear time history analysis. For this purpose, 7 earthquake records have been chosen and scaled based on Iranian code of practice for seismic resistant design of buildings and used for dynamic analysis. Results showed that all performance criteria of 75-year and 475-year hazard levels have been satisfied but for 975-year and 2475-year hazard levels, six cases have not satisfied the desired critera with 6 percent error. In order to verify the presented numerical analysis of multi degree of freedom structures, an experimental study has been chosen and the results of these two works have been compared. This verification showed that the presented analysis can model the structures and dampers with acceptable accuracy. Performance criteria of multi degree freedom structures have also been proposed. Three, 3-storey, 6-storey and 9-storey buildings equipped with dampers have been designed and based on proposed method and the desired performance of dampers have been achieved. Time history analysis have been carried out for each return period. For these analyises, 7 earthquake records were chosen and scaled based on Iranian code of practice for seismic resistant design of buildings. Comparison of performance point displacement levels and the displacements obtained from 28 nonlinear analyses, showed up to 13 percent error. Meanwhile, the displacement levels of each set of dampers for 75-year, 475-year, 975-year and 2475-year return periods, confirmed efficiency of proposed design method and all dampers met the mentioned performance criteria. The results also showed that when hazard level increased, the difference between the results of nonlinear time history analyses and static nanlinear analyses have also increased.

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Seismic design codes provide different equations for estimating displacement demands in various buildings and structures. Such equations were usually obtained by performing regression analysis over the obtained data from numerical models under different nonlinear analyzes. On the other hand, the application of artificial earthquakes is allowed to be considered for design and demand assessment in structures when there is a lack of suitable ground motions for a specific region and site. Since the accuracy of such relations affects the reliability of demand estimating in structures, it is required to assess the efficiency of such predictive relations. Moreover, it is essential to assess the efficiency of those relations for artificially generated earthquakes. Hence, in this study, the estimated demands from the design and assessment codes relations are evaluated for artificially generated ground motions. In this regard, regulations in the fourth edition of the Iranian seismic design code (also known as Standard 2800) and the last revision of the Iranian seismic evaluation code of practice (also known as Code-360) are considered. Estimated demands from these codes are compared to the results from the nonlinear time-history analysis of a group of single degree of freedom (SDOF) systems. Although an SDOF system can not represent the complete behavior of a complex building, for the low to medium-rise buildings with a fundamental vibration first mode, such an idealization is acceptable. In this regard, a group of SDOF systems with the elastic-perfectly-plastic (EPP) nonlinear behavior was considered. SDOF systems have vibration periods between 0.1s to 2.0s (as low to medium-rise buildings) with strength reduction factors (R_μ) of 2 to 8 to cover most of the common lateral resisting systems. These systems were analyzed under the action of 24 artificially generated ground motion records. Earthquake records were generated based on three different envelop shapes including compound shape, exponential shape, and Saragoni and Hart shape. These envelop shapes are representing the general form of an earthquake accelerogram and try to impose the real characteristics of an earthquake on the generated record. After employing the time-history analysis on each SDOF system, the mean of the maximum displacement demands of SDOF systems was obtained and compared to those from the estimating equations in Standard 2800 and Code-360. It is observed that estimated demands from Standard 2800 are closer to those from time-history analysis when compared with the obtained results from Code-360. Among the considered strength reduction factors, it was observed that SDOF systems with larger R_μ lead to a higher difference between the time-history results and those from codes. This is more predominant over the period range of 0.1s to 0.8s. So, relations in both codes are required to be modified for better demand estimating. In this regard, a method is proposed for modifying the available equations in the prementioned codes to accurately predict the displacement demands in systems under the action of artificially generated ground motions. A comparison between the results from the modified equations and those from the nonlinear time-history analysis shows the efficiency of the proposed method.