## 4 Results and Discussion  
### Objective 1: Results in Terms of Displacements  
In this part of the paper, the seismic responses of the building models with medium columns, in terms of drifts and roof displacements, are compared to those of the models with deep columns. To make the comparison, the following ratios (_R\({}_{D}\)_ and _R\({}_{DT}\)_) are used:  
\[R_{D}=\frac{D_{M}}{D_{L}} \tag{1}\]  
\[R_{DT}=\frac{DT_{M}}{DT_{L}} \tag{2}\]  
where the symbols \(R\), \(D\), _DT_, represent the words ratio, drift, top displacement, respectively. Similarly, \(M\) and \(L\), represent the words medium and large, which in turn stand for medium and deep columns, respectively. Hence, for a direction and a story of a given model, _D\({}_{M}\)_ and _D\({}_{L}\)_ represent the maximum drifts when medium and deep columns are used, respectively. _DT\({}_{M}\)_ and _DT\({}_{L}\)_ have a similar meaning except that top displacements are used instead. A value of _R\({}_{D}\)_, or _R\({}_{DT}\)_, greater than unity will indicate a reduction in the drift, or in the top displacement, when deep columns are used in the buildings. On the other hand, values of _R\({}_{D}\)_ or _R\({}_{DT}\)_ smaller than unity will indicate an increment in the above-mentioned response parameters. Results for drifts are discussed first. Some values of the _R\({}_{D}\)_ parameter for the _NS_ direction of the three-story model are presented in Figure 5a,c,e for seismic intensities of 0.4 g, 0.8 g, and 1.2 g, respectively; the corresponding results for the _EW_ direction are shown in Figure 5b,d,f. In these graphs, the term _ST_ stands for the number of stories. A significant variation in the _R\({}_{D}\)_ parameter can be observed from one strong motion to another without showing any trend, indicating a significant effect of the frequency content of the strong motions and the higher modes of vibration on the drifts of the buildings with medium and deep columns. The values are greater than unity in most cases. For a few cases, however, the values are smaller than unity. These results illustrate the significant differences that exist between the responses of buildings subjected to seismic loading and to static or cyclic loading. If static lateral loading were applied, the structural drifts would decrease in all stories for all cases. It is also observed that the closer the story is to the base, the greater the \(R_{D}\) values will be; however, no clear trend is observed for \(R_{D}\) as the seismic intensity increases. The most important observation that can be made so far is that the \(R_{D}\) parameter takes values of up to 2.4, which represents a considerable reduction in the structural drifts when deep columns are used. In addition to the six graphs given in Figure 5, another six were generated for \(R_{D}\) considering the other seismic intensities (S\({}_{\text{a}}\) = 0.2 g, 0.6 g, and 1.0 g) and both directions of the three-story model. Twelve graphs were also developed for roof displacements (\(R_{DT}\)). Similar sets of plots were also developed for the nine-story and twenty-story models. However, the total results are presented and discussed in all cases only in terms of the mean values (MVs) of the \(R_{D}\) and \(R_{DT}\) ratios. The MVs of \(R_{D}\) for the three-story model are shown in Figure 6a,b for the \(NS\) and \(EW\) directions, respectively. The corresponding values for the nine-story and the twenty-story models can be seen in Figure 7a,b and Figure 8a,b, respectively. It is worth mentioning that the formation pattern of plastic hinges (PHs) can vary significantly from one seismic record to another and from one model to another. For example, for the highest intensity of seismic record number 9 and the three-story model, PHs developed first on the beams of the first floor and then on the exterior columns of the ground level.