# Experimental Evaluation of Rigidity Center
## 3 Results and Discussion
### Results of Group A Buildings  
As previously mentioned, Group A buildings had only four vertical load-carrying members placed at each corner of the square floors. Figure 15 reveals the displacement profiles recorded after the tests. Although A1 was a symmetrical building, significant torsion was unexpectedly seen when it was loaded in the S-N direction. The degree of torsion was found to reduce when the building was loaded in the W-E direction. The reason can be attributed to the difference in the mechanical properties of the balsa sticks and the manufacturing quality of the model, as this model was the first one to be tested. Balsa contains many voids, and its mechanical properties change due to temperature changes and time. Although the mechanical properties were recorded before the tests, some undetermined situations may exist. A2 had a shear wall at the north-east corner, and clear torsion was seen when it was loaded in the S-N direction. When the building was rotated 90\({}^{\circ}\) and loaded in the W-E direction, with the decrease in the lateral stiffness of the shear wall, the degree of torsion reduced. Building A3 rotated clockwise when the load was applied in the S-N direction and counterclockwise when loaded in the W-E direction, depending on the location of the shear walls on the load direction. Having three shear walls, A4 rotated clockwise because of the one shear wall aligned parallel to the load. When the building was rotated 90\({}^{\circ}\), two strong shear walls resisted the load, and the deformations reduced significantly, and almost equal displacements were recorded on each floor. As for A1, A5 was also symmetrically planned, but torsion was observed when the building was loaded in either way. Therefore, it can be said that shear walls play an important role \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RC from ETABS**} & \multicolumn{2}{c}{**RC from Test**} & \multicolumn{2}{c}{**Difference, \%**} \\ \cline{2-7}  & \(x_{r}\)**, mm** & \(y_{r}\)**, mm** & \(x_{r}\)**, mm** & \(y_{r}\)**, mm** & \(\Delta x_{r}\) & \(\Delta y_{r}\) \\ \hline
2 nd floor & 26.2 & 106.3 & 26.9 & 102.1 & 0.23 & 1.40 \\
1 st floor & 25.6 & 105.3 & 27.0 & 102.7 & 0.46 & 0.87 \\ Ground floor & 25.2 & 102.3 & 27.2 & 106.7 & 0.68 & 1.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between the test results and ETABS. Figure 14: Rigidity center of A2. (**a**) Ground floor; (**b**) 1 st floor; (**c**) 2 nd floor. in reducing deformations and controlling torsion. If shear walls are planned reduce the torsion and to carry a significant amount of the lateral loads, they must be symmetrically placed in the plan or their load-carrying property balanced by another member in the same direction of loading. Otherwise, asymmetrical placement and differences in material properties and construction quality will affect the lateral behavior of buildings and may create serious torsion. From the recorded values of displacement and using the technique given in Equations (1)-(4), the rigidity centers of the buildings (shown as RCs) were calculated and given comparatively considering the results of the ETABS models (shown as E) in Figure 15, and the numerical values for only the second floor are summarized in Table 7. In the figure, the mass center is also illustrated to understand the distance between the MC and RC. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RC from ETABS**} & \multicolumn{2}{c}{**RC from Test**} & \multicolumn{2}{c}{**Difference, \%**} \\ \cline{2-7}  & \(\mathbf{x_{r}}\)**, mm** & \(\mathbf{y_{r}}\)**, mm** & \(\mathbf{x_{r}}\)**, mm** & \(\mathbf{y_{r}}\)**, mm** & \(\mathbf{\Delta x_{r}}\)**, mm** & \(\mathbf{\Delta y_{r}}\) \\ \hline A1 & 149.8 & 150.0 & 162.3 & 141.2 & 4.15 & 2.94 \\ A2 & 26.2 & 106.3 & 26.9 & 102.1 & 0.23 & 1.40 \\ A3 & 28.9 & 28.5 & 37.9 & 27.7 & 3.00 & 0.26 \\ A4 & 20.2 & 146.3 & 26.9 & 152.5 & 2.26 & 2.09 \\ A5 & 143.3 & 145.4 & 145.9 & 177.3 & 0.86 & 10.63 \\ \hline \hline \end{tabular}
\end{table}