Correlation of Seismic Responses of Structures

A practical analytical study is reported that leads to an improved definition of the correlation coefficient for seismic responses of structures. In contrast to definitions currently available, including the widely used expression developed for white-noise excitations by Der Kiureghian, the solution for the correlation coefficient reported in the present paper can efficiently account for the distribution of the frequency content of the excitation. The proposed expression for the coefficient is, in principle, applicable to excitations with narrow, intermediate, and wide frequency bandwidths. For the extreme wide-band case of a white-noise excitation, results of the proposed expression are shown to be in excellent agreement with those of that contributed by Der Kiureghian. Consequently, Der Kiureghian's correlation coefficient may be perceived basically as a special case of that introduced herein. Relevant analyses are made in both the time and frequency domains that contribute to enhance the appreciation for the factors that control the definition of response correlations. In particular, a time domain analysis is presented that leads to a simple, physically oriented interpretation of Der Kiureghian's coefficient. Furthermore, applications are reported for idealized excitations and the 1940 El Centro earthquake that elucidate the merits of the proposed correlation coefficient. The present study is of particular usefulness for estimates of peak seismic responses by using the complete quadratic combination rule, and for assessments of the potential for the pounding of structures during earthquakes.