Design Response Spectrum
The attenuation relationships described in Chapter 7 may be used to estimate the expected peak ground acceleration or peak ground velocity at a given site. For design purposes, however, the specifi cation of peak ground acceleration or velocity is not enough to determine the response of a structure to the expected ground motions. What is needed, instead, is the specifi cation of an acceleration time history or a response spectrum. Even more, for design purposes it is necessary to specify an ensemble of representative acceleration time histories or response spectra that averages or envelops the salient features of the response spectra of such an ensemble. The reason is that, as mentioned several times before, acceleration time histories and their response spectra vary signifi cantly from one earthquake to another and, thus, it is highly unlikely that the characteristics of future earthquakes at a site will be similar to those recorded in the past. Additionally, it is necessary to smooth such average response spectra to eliminate peaks and valleys. Peaks and valleys are not suitable for design given the uncertainties involved in the determination of a structure’s natural periods and the fact that these periods may change during and after an earthquake exposure. For engineering applications, therefore, response spectra from accelerograms that exhibit certain similarities are averaged and then smoothed before they are specifi ed for design. The smooth response spectrum that is used for the design of structures in a given seismic area is known as design response spectrum or simply design spectrum.