Multicomponent directional-cum-modal combination rule for seismic analysis: Theory and illustrations

Since spectral representation of ground motion can capture the epistemic uncertainty and aleatory variability better than time series representation, direction-cum-modal combination rule plays the pivotal rule when incorporating the multicomponent excitations in seismic design and in assessing the seismic resilience. CQC is generally believed to be the best modal combination rule for unidirectional seismic excitation, but the directional combination rule is still at its infancy when six-component seismic excitations are considered. Though a few extensions have been reported to account for more than one component, six-component directional combination rule is still an open call. Directional-cum-modal combination rule is developed in this paper from the first principle to combine the modal responses of a structure subjected to six-component ground motion with spectral representation as the 5% damped acceleration response spectra. In addition, the framework requires the power spectral shape of each component of excitations, directional correlation function for each pair of excitations, and duration of the event. With linear time history analysis as the benchmark, the proposed combination rule is compared against CQC as the modal combination rule with SRSS for the directional combination. Two numerical examples are presented including a 30-storied building to emphasize the role of rotational (rocking) components. The proposed combination rule works much better if the recorded components of ground motion are used for structural analysis. However, the difference reduces if the recorded components of ground motion are rotated along-and-normal to the principal plane prior to analysis. This is verified against several suites of recorded ground motion.