Investigation of response to earthquake excitation: a statistical basis for spectrum superposition, 1983

In the response spectrum superposition methods to earthquake-resistant design, it is assumed that: (1) the structure remains linear or can be modeled by an equivalent linear system; and (2) that vibration can be described by the superposition techniques using the largest relative (or absolute) response amplitudes of each mode. For better understanding, the evaluation of the progressing damage, and remembering that the maximum amplitudes of responses for all modes of vibration do not occur at the same time, it us useful to determine other response characteristics which, for example, relate duration of strong shaking with all, not just the largest, relative response amplitude. A theory is presented here for evaluation of the expected and the most probable amplitudes of local response peaks for each level of multi-story structure in terms of: (1) root-mean-square amplitude; (2) a measure (E) of the frequency width of the response spectrum; and (3) total number of peaks of response at each level. The parameters root-mean-square, E, and the total number of peaks are derived using a discrete transfer function model of multi-degree-of-freedom system. Comparisons of the expected and most probable values with SRSS, SUM, and CQC have been presented.