## 5 Global Structural Response of the Case Study
Overall, this distribution of modal mass and frequencies suggests that the structure is more susceptible to lateral vibrations in the X and Y directions in the lower modes with torsional effects becoming more significant in the third mode. Figure 12 illustrates the structural response through various analyses, focusing on top displacement and total base shear. The capacity curves from nonlinear static (pushover) analysis are compared with results from nonlinear dynamic analysis using 14 ground motions for each limit state. For each ground motion, the maximum base shear and top displacement values are plotted in Figure 12 for both the X and Y directions. Additionally, the linear analysis results are provided for two \(q\)-values: 3.0 (ductile mechanism) and 1.5 (brittle mechanism). As mentioned earlier, for asymmetric buildings, inelastic torsional effects can cause significant differences in displacement between the stiff and flexible sides. It is, therefore, a critical choice to be made in the target displacement within the pushover analysis. Although the centre of mass of the roof is usually adopted, taking into consideration only this may lead to the underestimation of seismic capacity because of the fact that the approach may not well represent the torsional behaviour. It also, hence, suggests that for such effects to be accounted for, displacement should be monitored at more than just the centre of mass reference points if a correct capacity of a structure is to be determined. The variation between the TH and pushover results in the X direction, compared to the consistent behaviour seen in the Y direction, can be attributed to factors like structural asymmetry, stiffness distribution, behaviour of infill walls, and higher mode effects. In the Y direction, the structure could be much stiffer and its response more uniform, which would explain the better agreement between the static and dynamic results of analysis. On the contrary, in the X direction, it was much more flexible or dominated by important higher mode contributions which showed differences between the two kinds of analysis. The Torsional Drift Ratio (TDR) is a measure of the torsional deformation of a building floor under lateral forces such as wind or seismic loads. It gives the quantification of relative lateral displacement at the edges of the floor with respect to its centre and denotes the extent of torsional response. In this study, the TDR is determined as \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & **Modal Mass** & **Modal Mass** & **Modal Mass** & **Natural** \\  & **Ratio (X** & **Ratio (Y** & **Ratio (About Z** & **Frequency** \\  & **Direction)** & **Direction)** & **Axis)** & **(Hz)** \\ \hline
1 & 53.66\% & 3.97\% & 19.19\% & 4.67 \\
2 & 13.54\% & 43.07\% & 10.8\% & 5.71 \\
3 & 5.7\% & 19.58\% & 38.27\% & 6.59 \\
4 & 0.007\% & 0.57\% & 0.016\% & 13.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Natural frequencies from numerical model and corresponding modal mass ratios. \[TDR=\frac{\delta_{\text{max}}-\delta_{\text{avg}}}{\delta_{\text{avg}}} \tag{3}\]  
where \(\delta_{\text{max}}\) represents the maximum lateral displacement at the floor's edge, and \(\delta_{\text{avg}}\) is the average lateral displacement, which is typically measured at the centre of mass of the floor. To thoroughly assess the torsional response of the structure under seismic activity, we implemented two distinct scenarios for applying ground motion (GM) components. In the first instance, seismic records were applied in their natural orientation, which means that the principal components applied along the X and Y axes of the building were labelled as XY. In the second one, these components were rotated 90 degrees with their application direction, thus their effective interchange to the Y and X axes, which was labelled as YX. This will ensure that the possible variation in torsional response due to different orientations of seismic input will be captured in the analysis in order to better understand seismic behaviour.