## 7 Predictions Using 2D Analysis
However, the predicted mean displacement in the longitudinal direction for the SIMQKE records is around \(19\%\) smaller than that obtained from the natural records. However, this difference is most likely due to the overestimation of the displacement demands obtained from the natural records rather than an underestimation of the response by the SIMQKE records. This is because the mean response spectrum of the natural records is inevitably more loosely matched to the target spectrum, as presented in Figure 6a,b. Therefore, depending on the period range controlling the maximum response of the structure the results obtained from loosely matched records can either be overestimated if the mean response spectrum of the records is somewhat larger than the target spectrum in a certain period range or underestimated if the mean spectrum falls below the target spectrum in a particular period range. For example, for the regular bridge the longitudinal period is \(0.90\) s. The controlling period range can be approximately estimated by multiplying the period by the square root of the maximum ductility demand. Therefore, given a ductility demand of \(2.0\) (Table 5) for the SIMQKE records, the controlling period range in the longitudinal direction is approximately between \(0.90\) to \(1.27\) s (i.e., \(0.9\times\sqrt{2.0}\)). From Figure 6b it is clear that in this period range the mean spectrum of the natural records and the Atkinson records are larger than the spectral values of the target spectrum. However, the mean spectrum of the SIMQKE records is very close to the target spectrum (Figure 6b). Therefore, it is expected that the displacements are somewhat overestimated, for this case, when the natural or the Atkinson records, that have larger dispersion, are used. For the case of the irregular bridge the period of the bridge is \(1.28\) s in the longitudinal direction. For this case only the central column yields and the other columns remain elastic. The total stiffness of the columns at the maximum displacement was determined as \(0.41\) times the initial stiffness of the bridge. Therefore, the effective period range is  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Average Maximum Absolute Values**} & \multicolumn{3}{c}{**Average in Different Directions**} \\ \cline{3-8}  & & **Natural Records** & **Atkinson Records** & **SIMQKE Records** & **Natural Records** & **Atkinson Records** & **SIMQKE Records** \\ \hline \multirow{3}{*}{Transverse} & C1 & 78 (0.6) & 81 (0.6) & 74 (0.6) & 69 (0.5) & 74 (0.6) & 65 (0.5) \\  & C2 & 110 (2.7) & 115 (2.8) & 102 (2.5) & 96 (2.4) & 105 (2.6) & 90 (2.2) \\  & C3 & 86 (0.3) & 88 (0.3) & 80 (0.3) & 76 (0.2) & 81 (0.2) & 7 approximately between 1.28 to 2.0 s (i.e., \(1.28/\sqrt{0.41}\)). As shown in Figure 6b, in this period range the mean spectrum of the natural records is closely matched to the target spectrum, while the mean spectrum of the Atkinson records is somewhat below the target spectrum (which resulted in \(-10\%\) difference). The mean spectrum of the SIMQKE records is only slightly lower than the target spectrum in this period range that resulted in around \(-5\%\) differences. These differences are reasonably small and negligible. In Figure 10, displacement envelopes obtained from inelastic time history analysis using different record types are compared for the case of the regular and irregular bridge. The predictions shown in this figure were obtained using averaging in different directions. In this figure the predictions obtained using the multi-mode elastic analysis are also provided. For the case of the irregular bridge (Figure 10a) the differences in predictions obtained using different record sets are larger compared to the case of the regular bridge shown in Figure 10b.