Response of Structures to Bidirectional Seismic Excitation Using Spectrum Compatible Records: Evolution of a Pair of Spectra from Newmark’s Sliding Block

Abstract

Bidirectional analyses covering a range of incidence angles for several records are essential yet challenging for routine design. Recent studies have shown that the response to bidirectional shaking may be estimated per straightforward unidirectional analysis in the most preferred orientation in conjunction with suitable combination rules, and this can also eliminate the need for various incidence angles. Further, it is well known that the mean response can be estimated with reduced dispersion using fewer spectrum-compatible records. The present investigation aims to combine the advantages of (1) the most preferred orientation; and (2) spectral matching within the context of bidirectional excitation. To this end, with the motivation derived from the Newmark’s sliding block theory, a pair of interrelated spectra directly connected to the most preferred orientation is proposed. Since the concept of these spectra is introduced for the first time, to our best knowledge, the mathematical basis of is discussed in rigor. The spectra are then illustrated and compared to other existing alternatives such as GMRotDpp, GMRotIpp, RotDpp, and MaxRotD50. The spectra evolved herein are orientation and period independent, implicitly account for directionality, and bear a clear physical meaning, which was obscured in earlier options. The proposed spectra are interpreted in the context of energy-based design and can be conveniently expressed in both force-based and displacement-based design formats. The proposed spectra help spectrally match two horizontal components independently and can specify bidirectional seismic loading. Response statistics of a simple multistory building demonstrate that, by using fewer spectrum-compatible records, the seismic demand can be estimated with reduced dispersion per bidirectional analyses as well as by unidirectional analyses.