# Experimental Evaluation of Rigidity Center
## 3 Results and Discussion  
### Interpreting the Results and Details of the Comparisons  
Figure 12 shows an example regarding the interpretation of the test results. In the figure, the results for the A2 building are given. Tests were recorded using two video cameras, with one capturing the top floor behavior, while the other took pictures from the side view, as shown in the figure. As the building is rotated 90\({}^{\circ}\) and tests were performed considering only the _self-weight_ of the building, all the loads were through the gravitational direction. Therefore, in the figure, S-N indicates the load from the south to the north. The displacements of each floor were recorded using LVDTs, and displacement profiles were drawn for each floor considering each loading direction separately. As seen in Figure 12, the building was loaded in S-N and E-W directions separately. In the S-N direction, as the shear wall at the N-E corner had great lateral stiffness in the in-plane direction, the slabs at each floor level were rotated clockwise, resulting in higher displacements at the N-W corner. However, upon the reduced lateral stiffness of the shear wall in the out-of-plane direction, its effectiveness reduced, and the displacement difference was observed to be small when the building was loaded in the W-E direction. The floor rotation was counterclockwise in this case. In the figures, the O-O line indicates the reference line before loading. One example regarding the rigidity center calculation is given in Table 5 and details are given in Appendix A. In the table, the member name, including S-W, indicates the shear walls, and C stands for the columns. \(\mathrm{b_{x}}\) and \(\mathrm{b_{y}}\) are the sectional dimensions of the member in \(x\) (horizontal in-plane view) and \(y\) (vertical in-plane view) directions. \(I_{i}\) is the moment of inertia corresponding to the loading direction, \(E_{i}\) is the _modulus of elasticity_ of the member, and \(L_{i}\) is the story height. The other terms are described above. Using Equations (1)-(4), the rigidity center (RC) of the ground floor considering the S-N direction was calculated as 27.24 mm from the east side of the slab, whereas it was 193.35 mm from the south side. Similar calculations were also performed for the first and second floors. Figure 11: Displacement calculations of the vertical members of a typical building. It is known that there are several analytical approaches to calculate the rigidity center location. Some of them are given below [4; 19; 21; 22; 23]:  
* The resultant shear force location of the vertical load-carrying elements in a specific floor can be calculated. Calculations are performed separately for each main axis of the building;
* The resultant moment of inertia of the vertical load-carrying elements in a specific floor can be taken into account considering both the main axes separately;
* A unit horizontal load in x and y directions and a unit moment in z direction are applied to any point on the floor level, and the rigidity center is calculated by proportioning the rotations obtained as a result of these loadings. There is a moment of the inertia-based approach throughout the programs, and the load or displacement distributions are calculated using the stiffness matrices established for the system, and the rigidity center location is calculated as a result of the relationship between these forces and displacements. Although the logic behind the calculations is generally the same, the slightest assumption can affect the solution. Examples of these assumptions include:  
* The shear wall modeling (shell-type or single-frame element);
* The joint locations of the frame elements (as frame elements are connected from their centers, the beams or columns may be longer in the model, which reduces their stiffness);
* The modeling of the shear walls as a single-frame member for a quick solution, which further moves the joints away from the real joint locations;  
Figure 12: Test results of A2.