Abstract：For the selection and scaling of ground motions in time-history analysis of long-period structures, a wide-band matching and weighted scaling method was proposed. In calculating the matching errors (SSE) and scaling factors (SF), the weighted least-squares method was applied. The weight coefficients of the first several modes of structures were introduced and determined by normalized modal participation factors, so that different contributions of higher modes to structural dynamic responses can be fully taken into account. The 20-story steel moment resisting frame structure designed for the American SAC Steel Project was used as an actual example. The average response spectra of the three ground motion sets developed in the project representing three exceedance probabilities (that is, 50%, 10%, and 2% probabilities of being exceeded in 50 years, respectively) were used as the target spectra. And the average values of the structural maximum inter-story drift angles calculated from the three ground motion sets (two-way records from 10 stations for each set, that is, 20 records) were taken as the benchmark seismic responses of each exceedance probability. The small-size database of seismic waves (total 40 records) established by simple geophysical parameters was used for selection and scaling. Six groups with 3 or 7 or 10 records and in different sequence were selected. The selection and scaling method with weighting was compared with that without weighting for predicting the mean structural response. The weighted and unweighted scaling methods have almost the same accuracies for estimating the mean structural responses (such as the maximum inter-story drift angle), but the weighted scaling method is superior to the unweighted method in reducing the variability of the structural responses. Moreover, if the ground motions are selected randomly, the weighted scaling method can also reduce the variability of the structural responses to some extent.
