Distribution of Peaks in Linear Earthquake Response

In the response spectrum approach to earthquake-resistant design, it is assumed that: (1)The structure remains linear or can be modeled by an equivalent linear system; and (2)vibrations can be described by the largest relative (or absolute) response amplitude. From the viewpoint of understanding the progressing damage, however, it is useful to determine other response characteristics which, for example, relate duration of strong shaking with all, not just the largest, relative response amplitude. A generalization of the theory of Cartwright and Longuet-Higgins is presented to describe the expected and the most probable amplitudes of local response peaks in terms of: (1)Root-mean-square amplitude of the response; (2)a measure, (ϵ), of the frequency width of the response spectrum; and (3) total number of peaks of response.