Performance-based design optimization under the set of earthquake records using the uniform deformation theory

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.