# Experimental Evaluation of Rigidity Center
## 2 Materials and Methods
### Building Properties  
Story height of the buildings was one of the hard issues to determine because low height would result in small displacements in most of the buildings, and it may not be easy to see the clear difference between the displacements of the members to comment on. On the other hand, as balsa wood has low _modulus of elasticity_, displacements in the buildings with a reduced number of vertical members would be great when the story height was high, but vertical members might break under those displacement levels. From several tests and analyses, it was decided to keep story height as 100 mm in all buildings to have satisfactory displacement and easily interpret the results. A total of 20 buildings in 4 groups were built from balsa wood and MDF plates to experimentally determine their rigidity center. In the following tables, \(A_{c,EW}\) and \(A_{c,NS}\) are the column areas in east-west and north-south directions, respectively; \(A_{w,EW}\) and \(A_{w,NS}\) are the shear wall areas in east-west and north-south directions, respectively; and finally, \(A_{f}\) stands for the ground floor area. Having square sections, cross-sectional areas of the columns were counted both in E-W and N-S directions, but shear wall areas were counted only in the strong direction. In order to be compatible with the experimental results, south direction was placed in positive vertical direction. Figure 2: Three-point bending of the balsa wood. (**a**) Balsa stick, (**b**) balsa plate. Group A buildings had only four vertical load-carrying members (Figure 4). The aim of this group was first to reduce the number of vertical members and simplify the problem and then to see the displacement clearly and understand how rigidity center alters as asymmetry arouses. A1 had only four columns placed at the corner of the floor plan; A2 had one shear wall placed in N-S direction; A3 had two shear walls, one in E-W direction and the other one in N-S direction; A4 had three shear walls, two in E-W direction and one in N-S direction; and finally, in A5, all the columns were replaced by shear walls. Column and shear wall areas are presented in Table 1.  
Group B buildings had 6 \(\times\) 6 equally spaced axis, and at each conjunction, a vertical member was placed (Figure 5). Column and shear wall areas are presented in Table 2. This group was built to see the displacements in buildings with increased number of vertical members and understand the change in rigidity center with the introduction of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bldg.** & \(A_{\epsilon\text{EW}}\) **(cm\({}^{2}\))** & \(A_{\epsilon\text{N}}\) **(cm\({}^{2}\))** & \(A_{w\text{,}EW}\) **(cm\({}^{2}\))** & \(A_{w\text{,}NS}\) **(cm\({}^{2}\))** & \(A_{f}\) **(cm\({}^{2}\))** \\ \hline A1 & 1.44 & 1.44 & 0 & 0 & 900 \\ A2 & 1.08 & 1.08 & 0 & 3.0 & 900 \\ A3 & 0.72 & 0.72 & 3.0 & 3.0 & 900 \\ A4 & 0.36 & 0.36 & 6.0 & 3.0 & 900 \\ A5 & 0 & 0 & 6.0 & 6.0 & 900 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of Group A buildings. Figure 3: Construction process. shear walls. B1 having only the columns and B6 having both columns and shear wall were the symmetrical buildings. In B2, symmetry was ruined by introducing a shear wall at the south-east corner of the buildings. B3 was symmetrical in N-S direction, but in E-W direction, as shear wall was used only at the south side of the building, no symmetry existed in E-W direction. An additional shear wall was placed to ruin the symmetry in N-S direction of B3 to create B4. B5 was symmetrical in N-S and E-W directions separately, but from global point of view, the centroid of the shear walls was observed to be in N-W direction. Group C buildings were rectangular in plan; they all had shear walls either placed symmetrically or not (Figure 6). Areas of the vertical members are presented in Table 3. C1 was a symmetrical building whose shear walls were all at the corners. C2 had symmetry in both directions, but globally shear walls were seen to be in the south direction.