Seismic Floor Spectra by Mode Acceleration Approach

Abstract

The truncation of the high frequency modes, so commonly used in dynamic structural analysis, sometimes can cause significant errors in the calculated response; this is caused by the so‐called missing mass effect. Such mode truncations can also affect the accuracy of floor spectra generated for stiff structural systems, and also for floors close to the base in even not so stiff structural systems, especially if the mode displacement methods are employed in the analysis. However, this problem due to mode truncation can be alleviated and virtually removed by employing the mode acceleration formulation in the analysis. Here, a direct response spectrum approach for generation of floor response spectra has been developed on the basis of the mode acceleration formulation and random vibration principles. As seismic input, this approach requires the relative acceleration spectra in lieu of the pseudo‐acceleration spectra—so commonly used with the mode displacement approaches. Because the relative spectrum values become very small for frequencies higher than the highest frequency component in the design ground motion, such high structural frequencies need not be considered in the analysis. Numerical results demonstrating the effectiveness of the proposed new approach are presented.