## 4 Results and Discussion
### Discussion  
In this study accidental torsion response of buildings subjected to earthquake ground motion is evaluated. A parametric investigation is carried out on different multi-story symmetrical buildings configurations having different ratio of uncoupled torsional to translation frequency and different floor  
Figure 17: [PERSON] [PERSON] and [PERSON]. [6] proposed method and dynamic analysis normalized edge displacement.  
Figure 18: [PERSON] [PERSON] and [PERSON]. [6] proposed design factor to calculate normalized edge displacement, (\(A_{t}\)).  
plan geometric aspect ratios. Accidental torsion response for the case study structures was determined using dynamic analysis as well as ASCE 7-16 static analysis.  
Dynamic analysis results of accidental torsion response showed that for all building translation periods, \(b\)/\(\tau\) ratios, the coupled frequency ratio, \(\Omega\), gives an indication of buildings torsional rigidity. Buildings with uncoupled torsional to translational uncoupled frequency ratio \(\Omega>1\) are torsionally stiff and exhibit high relative modal mass in horizontal \(Y\)-direction and little or zero rotation around the vertical \(Z\)-axis in the first or second fundamental mode. On the other hand, buildings with uncoupled torsional to translational uncoupled frequency ratio, \(\Omega<1\), are torsionally flexible and exhibit high relative modal mass rotation around the vertical \(Z\)-axis and little or zero relative modal mass in the horizontal \(Y\)-direction in the first or second fundamental mode.  
Accidental torsion response predicted using dynamic analysis procedures is different from response obtained using ASCE 7-16 static analysis. The buildings responses calculated using ASCE 7-16 static analysis are more conservative for flexible structures of torsional to translation frequency ratio \(\Omega<0.7\)-0.8, while for stiffer buildings results obtained using static analysis are less conservative. The response amplification factor, \(A_{x}\), that characterizes the static analysis method appears to target structures with frequency ratio \(\Omega<0.7\)-0.8, particularly to address amplification of torsionally irregular floor diaphragms, but the results as shown in Figures 5-14 are conservative compared to dynamic analysis. Static analysis provides unconservative prediction of accidental torsion response for stiffer structures with frequency ratios greater the range 0.7-0.8 as shown in Figures 5-13, compared to dynamic analysis. The actual frequency ratio in the range 0.70-0.8 at which static analysis changes from conservative to unconservative depends on the specific frequency ratio of the floor plan.  
The normalized edge displacements due accidental torsion for buildings that are rectangular in plan is higher than normalized edge displacement for square buildings regardless of translation period and uncoupled frequency ratio.  
The general trend in rectangular buildings response demonstrated by Figures 5-10 is that increase in torsional rigidity of the floor plan and its structural system decreases the accidental torsion response, except when the frequency ratio is \(\Omega=1.0\) where a consistent decrease in response predicted using dynamic response occurs regardless of the building period. The same drop in accidental torsion response for floors with \(\Omega=1\) is noted in square buildings as shown in Figures 11-13. Static analysis was not able to capture this response drop due to the consistent approach of using the amplification factor, \(Ax\), for all frequency ratios. The decrease in response captured by dynamic analysis was also noted in published literature [6; 14]. When the frequency ratio equal unity, the torsion radius described earlier in this article equals to the radius of gyration. Eurocode 8 uses the torsional radius to classify floors and their structural systems as torsionally rigid or flexible. Torsionally flexible buildings will have frequency \(\Omega<1.0\) or torsional radius less than the radius of gyration.