## 5 Measurement Equipment and Testing Setup
### The Building Strengthening and Upgrading Stages  
The building strengthening and upgrading process was divided into the following 11 stages:  
- Stage 0--the existing building before beginning the work at the site: the building was modeled according to its state (as is) following the guidelines of the modern code [1];  
- Stage 1--after completing the excavation for strengthening the foundations: the model was similar to that in stage 0, considering the excavation work required for strengthening the foundation that opened the ground floor columns by about 1 m (see Figure 2b);  
- Stage 2--after completing the ground floor columns, walls, and ceilings: the model was based on that used in stage 1, when walls and stiffening cores were added on the ground floor of the building;  
- Stages 3--after completing the columns, walls, and ceiling of the first to seventh floors, respectively;  
- Stage 10--structure in the service condition after completing all non-structural elements (the model based on that used in step 9 and full-service loads). The view of the building in stage 0 is shown in Figure 2. Stages 1-10 are shown in Figure 4.  
Figure 4: _Cont._  
Figure 4: The investigated building’s views and corresponding models for each strengthening/upgrading stage. Comparing and Discussing the Dynamic Characteristics of the Building at Each Strengthening/Upgrading Stage (1-10)  
As mentioned above, the dynamic parameters of the building were obtained both numerically and experimentally at each strengthening/upgrading stage. As the building was designed according to the requirements of the modern code [1] that is based on the linear elastic response spectrum, a linear elastic numerical model was used for numerical analysis. The following design parameters of the building were used according to [1]:  
* Peak ground acceleration (PGA), Z = 0.06;
* Horizontal spectral acceleration coefficient for the low natural vibration period, S\({}_{\text{v}}\) = 0.14;
* Horizontal spectral acceleration coefficient for the natural vibration period of 1 s, S\({}_{\text{I}}\) = 0.04;
* Site soil class--type D;
* Site coefficient for short vibration periods, F\({}_{\text{a}}\) = 1.6;
* Site coefficient for long vibration periods, F\({}_{\text{v}}\) = 2.4;
* Seismic force reduction coefficient that considers nonlinear deformations in the building, K = 1.5;
* Importance coefficient of the building, I = 1. Following the above-mentioned design parameters of the building, the design spectrum of the code [1] was updated similarly to the procedure described in [5], and the design spectrum was obtained, as shown in Figure 5.  
Numerical values of the building's natural vibration periods corresponding to the first 10 eigen modes are presented in Table 2. The table shows that the numerical values (Table 2) of the dominant natural vibration period for all eigen modes increase from stage 0 to stage 1 and decrease from stage 1 to stage 5 (when the stiffness of the building increases), which corresponds to the building strengthening stages without adding floors. In those stages, the contribution of additional stiffness is dominant relative to the mass of the walls. In stage 6, the dominant natural vibration period remains practically without significant change. Starting in stage 7, when new floors are added, the tendency changes, and the dominant natural vibration period begins to increase. The numerical value of the dominant vibration period after completing the work (stage 10, T = 0.432 s) is lower compared with that of the building before strengthening and upgrading (stage 0, T = 0.574 s), which means that the building was strengthened. However, the experimental values of the dominant vibration period decrease with the progress of strengthening (T = 0.315 s in stage 0 to T = 0.279 s in stage 5), which proves that the building was strengthened. Starting in stage 6,  
Figure 5: Design spectrum for the investigated building [1]. the dominant vibration period slightly increases (from T = 0.299 s in stage 6 to T = 0.399 s in stage 10).