Endurance Time (ET) method is a response history based analysis procedure that can be used for estimating the seismic response

of structures at different excitation levels in each response history. This seismic analysis method utilizes specific intensifying

acceleration functions to analyze seismic behaviors. One of the potential applications of the ET method is in the seismic

assessment of shell structures. In this study, a procedure for linear seismic analysis of shell structures is proposed and

applications of this method is investigated for several cases of shell structures. These structures are analyzed under three ET

acceleration functions in one direction and the results are compared to time history analysis considering seven actual earthquake

records. Moreover, the results of the ET method are compared to response spectrum analysis method. The outcomes of the study

reveal that the ET method predicts the linear seismic performance of shell structures with acceptable precision and significant

reduction in analysis time. Furthermore, it is conluded that scattering of results of three ET analysis is very low and one analysis

can be used instead of three. Finally, the comparison between THA and RSM results verify that response spectuarm method is a

conservative method which occasionally encounters problems to evaluate bending stresses of shell structures

From practical point of view, optimum design of structures under time variable loadings faces many challenges. Issues such as time-dependent behavior of constraints and the computational costs of the gradients could be mentioned. In order to prevent such difficulties, in this paper, response spectrum method has been utilized instead of applying direct time history method. Additionally, seismic design of structures is defined as a design for a specific response spectra not for an individual acceleration time history. Furthermore, here, in order to guarantee the global optimal designs, the obtained results from gradient-based method are compared with those from the discrete optimization technique (Genetic algorithm). As well, the P-Delta effects are considered in a seismic analysis. In addition, many practical constraints according to the Iranian national building code (NBC) are included in the optimization problem. The developed MATLAB based computer program is utilized to solve the numerical examples of low, intermediate and relatively high-rise braced and un-braced steel frames.