## 4 Results and Discussion
### Objective 1: Results in Terms of Displacements
However, for the case of the highest intensity of seismic record number 3 and the twenty-story model, PHs developed first on some beams located on the middle third of the building height and then on the exterior columns of the second floor. The results of the three-story model (Figure 6) indicate that, on an average basis and as observed from the plots of individual strong motions, the reduction in the drifts may be significant when deep columns are used; mean values of \(R_{D}\) greater than 1.6 can be seen in many cases for the first story. It is also noted that the values tend to monotonically decrease as the story number increases, but no trend is observed with the seismic intensity. The maximum \(R_{D}\) mean values are quite similar for the \(NS\) and \(EW\) directions. Figure 6: Mean values of \(\mathrm{R_{D}}\), 3-story building: (**a**) \(NS\) direction, (**b**) \(EW\) direction. Figure 7: Mean values of \(\mathrm{R_{D}}\), 9-story building: (**a**) \(NS\) direction, (**b**) \(EW\) direction. From the results of the nine- and twenty-story buildings (Figures 7 and 8), it is shown that the drift reductions, although smaller than those of the three-story building, may still be considerable; the maximum values are 1.4 and 1.2 for the nine- and twenty-story model, respectively. For the intermediate stories (8-12) of the twenty-story model, values very close to and even smaller than unity (implying an increment) can be observed; however, it does not correspond to the maximum structural demands in terms of drifts in most of these cases. It is worth mentioning that the mean values of \(R_{D}\) for the twenty-story building were also calculated by using hypothetical W44 columns (assuming that they were compact) instead of W40 sections in such a way that the ratios of the moments of inertia, or plastic moment, of the deep columns to those of the medium columns, were approximately the same for the three building models. It is important to say that the maximum observed mean values of \(R_{D}\) were only larger by about 4% with respect to those of Figure 8; the maximum observed mean values of \(R_{D}\) were about 1.25. Thus, the trend regarding the reduction in \(R_{D}\) as the height of the building increases remains unchanged. As stated earlier, for a given building, the mean values of \(R_{D}\) tend to decrease with the story number. In the same manner, the \(R_{D}\) mean values tend to also decrease as the building becomes taller. One of the reasons for this is that as medium columns are replaced by deep columns, the stiffness and the strength increase, which are lower in the tallest model. Another reason is that the effectiveness of deep columns in reducing the drifts becomes less significant for the stories away from the base since their stiffness relative to the base decreases. This is similar to the transversal stiffness associated to a point of a cantilever beam, which is inversely proportional to the distance from the fixed support (base) to the point under consideration. The MVs for the \(R_{DT}\) parameter are shown in Column (2) of Table 6 for the three models. The results are similar to those of \(R_{D}\) for the case of the three- and nine-story models in the sense that the reduction in the roof displacements is significant when deep columns are used and that no trend is observed with the seismic intensity. However, the maximum values of \(R_{DT}\) are smaller than those of \(R_{D}\). For the case of the twenty-story building, the reduction is negligible. As in the case of \(R_{D}\), the maximum mean values of \(R_{DT}\) tend to decrease with the building height: the maximum values are observed to be 1.38, 1.17, and 1.02 for the three-, nine-, and twenty-story models, respectively. These results indicate that the observed reduction in the response in terms of two parameters, which are considered to be similar and widely used to represent the maximum overall structural deformation, may be quite different when deep columns are used.