Comparison of Scaling Ground Motions Using Arithmetic with Logarithm Values for Spectral Matching Procedure

In recent studies, spectral matching is the most commonly proposed method for selecting earthquake records for time-history analysis of structures. However, until now, there have been no serious investigations of the effects of coordinate values on the scaling of ground motions. This paper investigated the influence of using arithmetic and logarithmic values of response spectra in spectral matching procedures (i.e., ASM and LSM methods) on the results of nonlinear structural time-history analysis. Steel moment resisting frame structures of the 3-, 9-, and 20-stories, which represent low-, medium-, and high-rise buildings, respectively, were used as examples. Structural benchmark responses were determined by calculating the arithmetic mean and median of peak interstory drift ratio (PIDR) demands based on the three record sets developed by the American SAC Steel Project. The three record sets represent seismic hazard levels with 50%, 10%, and 2% probabilities exceeded in 50 years, and their average acceleration spectra were also taken as the target spectrum. Moreover, another 40 record components for selection were scaled both by ASM and LSM methods. The seven components whose spectra were best compatible with the target spectra were selected for the structural time-history analysis. The scale factors obtained by the LSM method are nearly larger than that of the ASM method, and their ranking and selection of records are different. The estimation accuracies of structural mean (median) responses by both methods can be controlled within an engineering acceptable range (±20%), but the LSM method may cause larger structural responses than the ASM method. The LSM method has a better capacity for reducing the variability of structural responses than the ASM method, and this advantage is more significant for longer-period structures (e.g., 20-story structure) with more severe nonlinear responses