Peak Factor–Based Modal Combination Rule of Response-Spectrum Method for Peak Floor Accelerations

Abstract

The seismic safety of acceleration-sensitive secondary elements rigidly connected to the primary structure can be ensured in the case of ordinary structures by simply and accurately estimating the largest peaks in the floor accelerations consistent with a given seismic hazard. A new modal combination rule is developed in this study to estimate the peak floor accelerations in the case of lumped mass, classically damped, multistoried structures. The formulation is based on stationary random vibration theory and the use of nonstationary peak factors together with the amplitudes of the specified design spectra. The proposed formulation is supported by the development of (1) an expression for estimating the peak factor for floor acceleration from the peak factors for modal displacement responses and peak modal contributions to the peak floor response, wherein both floor acceleration and modal peak factors are normalized by the (nonstationary) peak factor for input ground acceleration, and (2) a two-parameter power function for estimating the normalized modal peak factors for relative velocity from the oscillator period, together with the scaling equations for the two parameters in terms of ground-motion characteristics. A numerical study using five example buildings and six example ground motions shows that the proposed modal combination rule works well, with the absolute error averaged over all floors of the structure being less than 10% for 90% of the cases. Also, the proposed rule works better compared to when various peak factors are taken to be identical.