A vertical response of a multiple degree of freedom system vibrating in axial modes at the instance of its maximum horizontal response vibrating in shear modes is analyzed by superposition of normal modes. The coincident vertical response acceleration at the instance of the maximum horizontal response acceleration between two independent single degree of freedom systems indicated probabilistic properties. It is of interest to extend concepts of the response coincidence in the response analysis of multi-story structures. Nevertheless, the distribution of the coincident vertical response along the building height may be the most important in connection with the seismic design. Its probable distribution and an approximate upper bound are investigated to determine an analysis constant. The analysis constant enables the computation of the coincident vertical response of multi-story structures at the instance of the maximum horizontal response by the modal analysis. The results of the proposed method and the direct numerical integration of governing equations of motion are compared, and conclusions are drawn about the use of the modal analysis to the coincident vertical response of multi-story structures.
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