## 6 Predictions Using 3D Analysis
\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{2}{*}{Transverse} & C1 and 3 & 77 (2.0) & 75 (2.0) & 69 (1.8) & 64 (1.7) & 68 (1.8) & 64 (1.7) \\ \cline{2-8}  & C2 & 109 (2.8) & 109 (2.8) & 99 (2.6) & 93 (2.4) & 97 (2.5) & 91 (2.4) \\ \hline \multirow{2}{*}{Longitudinal} & All & 86 (2.2) & 101 (2.6) & 92 (2.4) & 74 (1.9) & 89 (2.3) & 80 (2.1) \\ \cline{2-8}  & C1 and 3 & 101 (2.6) & 113 (2.9) & 100 (2.6) & 69 (1.8) & 86 (2.2) & 78 (2.0) \\ \cline{2-8}  & C2 & 123 (3.2) & 131 (3.4) & 115 (3.0) & 84 (2.2) & 93 (2.4) & 90 (2.3) \\ \hline \multicolumn{8}{l}{30\% Rule} & C2 & 135 (3.5) & 139 (3.6) & 127 (3.3) & 116 (3.0) & 124 (3.2) & 115 (3.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the mean displacements (mm) of columns using 3D analysis for the regular bridge with mean ductility demands given in brackets. \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{2}{*}{Transverse} & C1 & 95 (0.7) & 93 (0.7) & 84 (0.6) & 82 (0.6) & 86 (0.6) & 77 (0.6) \\ \cline{2-8}  & C2 & 131 (3.2) & 130 (3.2) & 118 (2.9) & 112 (2.8) & 120 (3.0) & 106 (2.7) \\ \cline{2-8}  & C3 & 101 (0.3) & 100 (0.3) & 91 (0.3) & 88 (0.3) & 92 (0.3 small (i.e., around 0.05 to 0.1). The minimum predictions from different record sets were around 10% to 15% smaller than the mean values. The mean values predicted from 20 different record subsets were used in Tables 2 and 3 to compare the predictions from the artificial and natural record sets. The mean predictions in different radial directions from 20 different subsets are shown in Figure 8 for the central column, C2, of the irregular bridge. The predictions obtained from the artificial records, as presented in Tables 2 and 3, were in good agreement with those obtained from the natural records. The differences in predicting the radial displacements for the critical column C2 in the regular bridge were around +6% and \(-6\%\) for the Atkinson and SIMQKE records, respectively. These differences for the case of the irregular bridge were \(-1\%\) and \(-5\%\), respectively. The differences were slightly larger when the displacements in the transverse and longitudinal directions are compared (around 10%). However, when these displacements were combined using the 30% rule the differences were around 5%. The mean displacement envelopes for the central columns of the bridges obtained using the averaging procedure in different directions are presented in Figure 9 for three different record sets considered. The results indicate that the mean predictions from the different sets are in good agreement. The results obtained using the 30% rule (Tables 2 and 3) provide slightly conservative values compared with the mean radial displacements obtained from the 3D analyses for all record types considered. However, when the averaging procedure in different directions is adopted, the predictions using the 30% rule were much larger than the radial displacements obtained using this procedure (see Tables 2 and 3).