## 6 Predictions Using 3D Analysis  
Structural analysis results are typically available only for the two perpendicular principal directions of the structure (i.e., X and Y directions) and, therefore, the peak displacements only in the X and Y directions are obtained. Since the peak displacements in the X and Y directions occur at different times, it is not possible to estimate the maximum radial (vectorial) displacement of the columns. In this study the radial displacements were determined at each time interval using the component of displacements in X and Y directions. The mean displacements obtained for the bridge columns using different natural and artificial record sets are presented in Tables 2 and 3 for the regular and irregular bridges, respectively. The results are shown using two different averaging methods: using maximum absolute values; and using averaging procedure in different radial directions. The average displacements and corresponding displacement ductility demands are determined for the longitudinal, transverse and radial directions. It is noted that to predict the displacement ductility demands, \(\mu\), the displacement demands, \(\Delta_{u}\) are divided by the yield displacements, \(\Delta_{y}\) as defined by the equations provided by [PERSON] et al. [7] (i.e., \(\mu=\Delta_{u}/\Delta_{y}\)). Further details regarding the predictions of ductility demands is available by [PERSON] and [PERSON] [1]. To estimate the maximum radial displacement of the columns using the analysis results in the principal directions of the bridges, typically 100% of the absolute displacement in each principal direction is combined with 30% of the absolute displacement in the perpendicular direction (referred to as the 30% combination rule used in codes). The results obtained using the 30% combination rule are also given in the tables. As presented in the tables, the predictions obtained using the absolute maximum displacements were significantly larger than those obtained by taking into account the direction of the displacement vectors for the radial displacements (around 30% to 40% difference). However, these differences were smaller when only the transverse and longitudinal displacements were considered (around 15%). The predictions of the mean displacements obtained from different record sets are compared in Tables 2 and 3. While for the natural records the two horizontal components are available as recorded from the real earthquakes, for the artificial records the horizontal components may be simulated separately. This can result in a very large number of possible record pairs that can be selected from a number of available horizontal components. Therefore, it is necessary to investigate if the predictions obtained using the artificial records that are randomly selected as pairs are sensitive to the selection of the record pairs. To investigate this issue, 20 different record subsets were selected for each type of artificial record. Each subset included 7 pairs of records which were randomly selected from 14 artificial horizontal components. The mean responses of the bridges were determined for each subset (i.e., the average responses from 7 pairs of records in each set). This resulted in 20 different predictions of the mean response for each artificial record set. The maximum and minimum predictions of the mean displacements obtained from these 20 subsets of records are presented in Table 4 for the critical column C2. The mean and coefficient of variation (i.e., standard deviation divided by mean) of the predicted mean values from 20 different subsets are also presented in Table 4 for the Atkinson and SIMQKE artificial records. The results indicate that on average the coefficients of variation were relatively