## 7 Predictions Using 2D Analysis  
For the 2D analyses the bridges were subjected to the horizontal components of the ground motions in the transverse and longitudinal directions separately. Due to different spectrum-matching procedures in the codes for 2D and 3D analyses, some modifications to the records selected for the 3D analysis were necessary to perform 2D analysis. The average displacements of the bridge columns in the transverse and longitudinal directions are summarized in Tables 5 and 6 for the regular and irregular bridges, respectively. The average displacements were determined using both the average of the maximum absolute displacements and the average of the maximum positive and negative displacements. The differences between the different averaging methods were smaller for the 2D analysis (Tables 5 and 6) compared with the 3D analysis (Tables 2 and 3). The results also indicate that the use of the 30% rule for the bridges studied resulted in very good predictions of the maximum radial displacements obtained from 3D analyses. For example, for the case of the natural records the displacements for the central columns of the regular and irregular bridges were predicted as 123 and 178 mm using 2D analysis (Tables 5 and 6), respectively, which are similar to the predictions of 123 and 166 mm from 3D analyses (Tables 2 and 3). Similar trends were observed for the case of the artificial records. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Average Maximum Absolute Values**} & \multicolumn{3}{c}{**Average in Different Directions**} \\ \cline{3-8}  & & **Natural** & **Atkinson** & **SIMQKE** & **Natural** & **Atkinson** & **SIMQKE** \\  & & **Records** & **Records** & **Records** & **Records** & **Records** & **Records** \\ \hline \multirow{2}{*}{Transverse} & C1 and 3 & 64 (1.7) & 64 (1.7) & 59 (1.6) & 58 (1.5) & 54 (1.4) & 54 (1.4) \\  & C2 & 94 (2.4) & 95 (2.4) & 87 (2.2) & 84 (2.2) & 82 (2.2) & 80 (2.1) \\ \hline \multirow{2}{*}{Longitudinal} & All & 96 (2.5) & 90 (2.4) & 78 (2.0) & 81 (2.1) & 83 (2.2) & 72 (1.9) \\ \hline
30\% Rule & C2 & 123 (3.2) & 122 (3.2) & 111 (2.9) & 109 (2.8) & 108 (2.8) & 102 (2.6) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of the mean maximum absolute displacements (mm) for columns C1, C2 and C3 using 2D analysis for the regular bridge with mean ductility demands given in brackets. Figure 9: Mean displacements for column C2 in different radial directions: (**a**) regular bridge; (**b**) irregular bridge. The predictions of the mean displacements obtained using the Atkinson records and the SIMQKE records are also presented in Tables 5 and 6. The predictions from the artificial records were obtained using 14 horizontal components, while the mean displacements for the case of the natural records were predicted using 44 horizontal components of the ground motion records. For the case of the irregular bridge the maximum differences between the predictions from the artificial SIMQKE records and the natural records for the transverse, longitudinal and radial directions (estimated by the 30% rule) were around \(-7\%\), \(-6\%\) and \(-6\%\), respectively. These differences for the case of the Atkinson records were \(4\%\), \(-10\%\) and \(-7\%\), respectively (for the critical column C2). The results for this case are in good agreement and the differences are typically smaller than \(10\%\). For the case of the regular bridge, the predictions from the SIMQKE records were somewhat smaller than those obtained from the natural records and the Atkinson records. For this case the maximum differences from the SIMQKE records for the transverse, longitudinal and radial directions were around \(-7\%\), \(-19\%\) and \(-10\%\) compared to the natural records. These differences were around \(1\%\), \(-6\%\) and \(-1\%\), respectively, for the case of the Atkinson records. Using the 30% rule and the SIMQKE records results in a \(-10\%\) difference compared with the overall radial displacement of the critical column, C2.