An application of multicomponent directional-cum-modal combination rule: routine seismic design and performance assessment

Abstract

A framework is proposed for incorporating the multi-component directional-cum-modal combination rule within the practice of seismic design/performance assessment. Target spectrum is assumed to be available in the seismic performance assessment practice for a given single component representation of the orthogonal pair of horizontal components. With this available information, first, a suite of ground motion is selected matching the horizontal target spectrum through amplitude scaling. Next, under the assumption of hazard consistency, the same amplitude scale factor is used for other components also in the respective seismic events. Average of the resulting spectra in the respective directions leads to the multicomponent target spectra consistent with the horizontal seismic hazard. Apart from these multicomponent target spectra, directional-cum-modal combination rule also requires additional inputs such as, (a) one-sided power spectral shape for all components of ground motion; and (b) cross-spectral density functions (normalized) for all directional pairs of ground motions. This paper also proposes the construction of each of these additional inputs using the same selected and scaled ground motion suite matching the target spectrum. A total of three examples are presented as sample illustrations of the proposed framework using a couple of buildings and different representative suites of ground motions. The framework performs reasonably well for all practical purposes when compared with the response history analysis. The proposed framework can also be extended to the seismic design practice given multicomponent target spectra as the available input but with a nominal modification in the selection and scaling of the suite.