Because of earthquake uncertainty, the worst-case analysis is needed for the earthquake resistant design of structures. The probabilistic critical excitation method proposes an input excitation with critical and largest responses in the structure. An optimization problem is introduced that is solved easier in frequency domain. In this research, a stationary input excitation is found for shear model of buildings in frequency domain to maximize drift as a design criterion. The input power (area of power spectral density function) and the intensity (magnitude of PSD function) are fixed and the optimal critical excitation is found under these constraints by solving an optimization problem using Simpson integration. This method is presented for structures with different natural frequencies. In addition, the effect of the first mode relative to higher modes is investigated.
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