## 8 Incremental Dynamic Analysis (IDA)
However, for the case of Atkinson records as the number of records increased the predictions deviated from those obtained using the natural record sets. This is because for performing the analyses the records with the closest match to the target spectrum are selected, as discussed before. However, for the case of the Atkinson records the number of available records is limited and increasing the number of records will result in selecting records that are not sufficiently compatible with the target spectrum. For the case of natural records since a large pool of records was used, increasing the number of records only slightly changed the IDA predictions. Based on this information, 14 records were used for the case of artificial records and 44 records were used for the case of natural records. It is interesting to investigate if the use  
Figure 13: Incremental dynamic analysis (IDA) curves obtained for the irregular bridge using: (**a**) natural, and (**b**) Atkinson and (**c**) SIMQKE records and for the regular bridge using: (**d**) natural, and (**e**) Atkinson and (**f**) SIMQKE records. of a small number of artificial records can sufficiently predict the results obtained using a large number of natural records. The predictions obtained from IDA are summarized in Figure 15 for different record sets at different damage states and for the regular and irregular bridges studied. The results are compared in terms of IDA percentiles and variability of results at different damage states. The results indicate that the predictions of the median capacities from artificial records were in good agreement with those obtained using the natural records especially at collapse, as shown in Figure 15a,b. In Figure 16 the median IDA curves are shown and compared for the regular and irregular bridges predicted using the SIMQKE, as well as the Atkinson and natural records. For the case of the natural records, 44 records were used while, for the case of the artificial records, a smaller number of records were used, as discussed before. As shown in Figure 16. the predictions of the median collapse capacity using the artificial records are in good agreement with those using the natural records (e.g., around 5% difference is observed for the different cases studied). While the artificial records underestimated the 84% percentiles, the Atkinson records did better in predicting the 16% percentiles, as shown in Figure 15c-f). The variability of the results is presented in Figure 15g,h in terms of logarithmic standard deviation of the results obtained from a number of records. It is evident that the variability of the natural records is typically  
Figure 14: Effect of the number of records (indicated in parentheses) used on the IDA curves obtained for different record sets for the case of (**a**) natural records, (**b**) Atkinson records, and (**c**) SIMQKE records. larger, as expected, especially at ultimate damage states such as bar buckling and collapse. For the case of the Atkinson records applied to the irregular bridge, the dispersion of the results was higher at low damage states such as yielding and spalling, compared to the other record sets, as shown in Figure 15g. This can be attributed to the higher mode effects, complex dynamic behavior of the irregular bridge and the frequency contents of the Atkinson records. The record-to-record variability for the natural records was around 0.3 to 0.35 at collapse, as shown in Figure 15g,h. This is close to the value of 0.4 recommended by FEMA P695 [26]. Although general conclusions cannot be made without further research, the results show the possibility of using the median predictions from IDA, conducted using a smaller number of artificial records, along with appropriate values of record-to-record variability (e.g., value of 0.4) to predict the fragility curves with sufficient accuracy.