## 5 Conclusions  
Because of the compactness of the webs and flanges of a vast number of deep steel sections of grade 50, and because of the necessity of higher bending and shear stiffness to reduce drifts, structural engineers often use deep columns in high seismic areas, which results in more economical designs. Yet this contradicts what is stated in some experimental investigations in the sense that even though deep columns satisfy current seismic provisions, they may suffer premature twisting. In other studies, however, which encourage the use of deep columns, it is stated that deep column twisting in the tests might have occurred primarily because there was no lateral bracing at the top flange of the beams, which is normally provided by the floors in actual buildings. This is an indication that much research needs to be developed in this area. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Direction**} & \multicolumn{1}{c}{**S\({}_{\text{a}}\)/g**} & \multicolumn{2}{c}{**EXT**} & \multicolumn{1}{c}{**R\({}_{\text{AM}}\)**} \\ \hline \multirow{8}{*}{1} & & 0.2 & 1.14 & 1.19 \\  & & 0.4 & 1.13 & 1.15 \\  & & 0.6 & 1.05 & 1.05 \\  & \(NS\) & 0.8 & 0.99 & 1.00 \\  & & 1.0 & 0.98 & 0.99 \\  & & 1.2 & 0.96 & 0.97 \\ \cline{2-5}  & & 0.2 & 1.17 & 1.23 \\  & & 0.4 & 1.06 & 1.10 \\  & \(EW\) & 0.6 & 1.01 & 1.02 \\  & & 0.8 & 0.97 & 0.98 \\  & & 1.0 & 0.96 & 0.97 \\  & & 1.2 & 0.95 & 0.96 \\ \hline \multirow{8}{*}{2} & & 0.1 & 1.24 & 1.31 \\  & & 0.2 & 1.24 & 1.31 \\  & \(NS\) & 0.3 & 1.19 & 1.24 \\  & & 0.4 & 1.13 & 1.19 \\  & & 0.5 & 1.10 & 1.14 \\ \cline{2-5}  & & 0.1 & 1.24 & 1.32 \\  & & 0.2 & 1.22 & 1.30 \\  & \(EW\) & 0.3 & 1.14 & 1.19 \\  & & 0.4 & 1.08 & 1.13 \\  & & 0.5 & 1.08 & 1.11 \\ \hline \multirow{8}{*}{3} & & 0.05 & 1.03 & 1.03 \\  & & 0.10 & 0.98 & 1.05 \\  & \(NS\) & 0.15 & 0.99 & 1.03 \\  & & 0.20 & 0.97 & 0.99 \\  & & 0.25 & 0.98 & 0.99 \\  & & 0.30 & 0.98 & 0.99 \\ \cline{2-5}  & & 0.05 & 1.07 & 1.10 \\  & \(EW\) & 0.10 & 1.00 & 1.06 \\  & \(EW\) & 0.15 & 1.01 & 1.02 \\  & & 0.20 & 1.00 & 1.01 \\  & & 0.25 & 0.99 & 0.99 \\  & & 0.30 & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: MVs for the \(R_{AM}\) parameter. In this study, the nonlinear seismic responses, in terms of several parameters, of steel buildings with perimeter moment-resisting frames and medium (W14) columns are numerically calculated and compared to those of similar steel buildings with equivalent deep columns in terms of cost (W27 and larger). Three building models and fifteen strong motions with different dynamic characteristics are used in the study. The main findings are as follows:  
(1) The interstory drifts may be significantly reduced when deep columns are used. For a given model, such reduction tends to decrease through the height of the model; similarly, such reduction becomes less relevant as the height of the building increases. The drifts of the models with medium columns may be up to 140%, 80%, and 60% larger than those of the models with deep columns, for the three-, nine-, and twenty-story models, respectively. (2) The corresponding percentages for top displacements are 38%, 25%, and 2%, indicating that the maximum reductions in terms of top displacements are smaller than those of drifts. The implication of this is that the observed reduction in the response when deep columns are used 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. (3) Significant reductions are also observed for normalized interstory shears. However, for the case of normalized combined axial loads and bending moments, the reduction, as for the case of top displacements, is significant only for the three- and nine-story models.