## 4 Results and Discussion
### Calculation of the Normalized Edge Displacement Using Dynamic and Static Analysis  
Figures 5-13 depict the normalized edge displacements \(\hat{u}_{b/2}\) determined using static and dynamic analysis methods, for the three groups of buildings in the parametric study. It clear that static and dynamic analysis procedures predict different responses due to accidental torsion. The buildings' responses calculated using static analysis are more conservative for flexible structures with torsional to translation frequency ratio \(\Omega<\) 0.7-0.8, while for stiffer buildings results are less conservative. The conservative torsional response at \(\Omega<\) 0.7-0.80 is attributed to the ASCE 7-16 static analysis method that utilizes an amplification factor, \(Ax\), to increase accidental torsion response associated with the presence of torsional irregularity. Therefore, static analysis reliance on the amplification factor, \(Ax\), makes accidental torsion response more conservative for flexible structures compared to dynamic analysis. Figures 5c, 6c, 7c, 8c, 9c, 10c, 11c, 12c and 13c consistently show a decrease (dip) in accidental torsion amplification obtained through dynamic analysis for buildings with frequency ratio \(\Omega=1\) \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\Omega\) & **Mode** & **Period (Sec.)** & **UX** & **UY** & **UZ** & **RX** & **RY** & **RZ** \\ \hline \multirow{3}{*}{1.0} & 1 & 1.327 & 0.6616 & 0 & 0 & 0 & 0.3496 & 0 \\  & 2 & 1.281 & 0 & 0.6706 & 0 & 0.3417 & 0 & 0 \\  & 3 & 0.886 & 0 & 0 & 0 & 0 & 0 & 0.6639 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Modal Participating Mass Ratio Buildings (with \(b\)\(\
eq\) 3.16, 1 \(<T\)\(\overline{y}<\) 2 s, \(\Omega=\) 1.4). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\Omega\) & **Mode** & **Period (Sec.)** & **UX** & **UY** & **UZ** & **RX** & **RY** & **RZ** \\ \hline \multirow{3}{*}{0.7} & 1 & 1.491 & 0 & 0 & 0 & 0 & 0.6801 \\  & 2 & 1.214 & 0.6705 & 0 & 0 & 0 & 0.343 & 0 \\  & 3 & 1.152 & 0 & 0.6802 & 0 & 0.3344 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Modal Participating Mass Ratio Buildings (with \(b\)\(\
eq\) 3.16, 1 \(<T\)\(\overline{y}<\) 2 s, \(\Omega=\) 0.7). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\Omega\) & **Mode** & **Period (Sec.)** & **UX** & **UY** & **UZ** & **RX** & **RY** & **RZ** \\ \hline \multirow{3}{*}{1.3} & 1 & 1.354 & 0 & 0 & 0 & 0 & 0.6754 \\  & 2 & 1.255 & 0.6721 & 0 & 0 & 0 & 0.3402 & 0 \\  & 3 & 1.085 & 0 & 0.6873 & 0 & 0.3266 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Modal Participating Mass Ratio Buildings (with \(b\)\(\
eq\) 2.45, 1 \(<T\)\(\overline{y}<\) 2 s, \(\Omega=\) 0.8). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\Omega\) & **Mode** & **Period (Sec.)** & **UX** & **UY** & **UZ** & **RX** & **RY** & **RZ** \\ \hline \multirow{3}{*}{1.4} & 1 & 1.336 & 0.6661 & 0 & 0 & 0 & 0.346 & 0 \\  & 2 & 1.084 & 0 & 0.6874 & 0 & 0.3265 & 0 & 0 \\  & 3 & 1.067 & 0 & 0 & 0 & 0 & 0 & 0.6762 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Modal Participating Mass Ratio Buildings (with \(b\)\(\
eq\) 2.45, 1 \(<T\)\(\overline{y}<\) 2 s, \(\Omega=\) 1.0). regardless of vibration period or floor aspect ratio. Similar behavior was reported in the literature [6]. For buildings with large aspect ratio \(b/r=2.45\), the dynamic accidental torsion response curve exhibits a second peak (double hump), and as the vibration period increases to \(T_{y}>2.0\), a third peak appears for at large \(\Omega\) (Figure 13c). It is clear however, regardless of peaks and valleys of the dynamic response curve, the accidental torsion response generally trends to a decrease with increase in \(\Omega\). The results offer structural designers the potential to select suitable the lateral force resisting system stiffness within each range of \(\Omega\) in order to valley regions of the curves and hence minimize accidental torsion.