## 5 Comparison of the Pseudo-Dynamic Test Results and Nonlinear Dynamic Analysis Results
### Nonlinear Dynamic Analysis Results before and after Seismic Reinforcement  
Nonlinear dynamic analysis before and after seismic reinforcement was conducted based on the analytical models described in Section 6.1. On the first floor of the test building with no reinforcement applied, shear cracks occurred at its column members at 2.1 s (3.9 mm) when the input seismic ground motion was 200 cm/s\({}^{2}\). Subsequently, the  
Figure 28: Analytical models and simulated frames of the target RC school building before and after reinforcement: (**a**) analytical model before seismic reinforcement, (**b**) analytical model after seismic reinforcement, and (**c**) simulated frame after seismic reinforcement. maximum seismic response occurred at 3584.2 kN at 3.3 s (49.1 mm), at which the test building finally collapsed. In the test building retrofitted with NBSD-WSCS, shear cracks occurred at its column members at 2.3 s (5.4 mm) when the input seismic ground motion was 200 cm/s\({}^{2}\). Following the maximum seismic response at 3.6 s (17 mm), however, seismic responses remained lower than the maximum level, leading to limited seismic damage. The floor-specific load-displacement curves and time-displacement hysteresis loops of both the test building with no reinforcement applied and the test building retrofitted with NBSD-WSCS were obtained and compared, as shown in Figures 29 and 30. Among these analytical results, the maximum response stress and displacement of the two test buildings at 200 cm/s\({}^{2}\), which are important parameters for seismic performance evaluation, were compared, as summarized in Table 15. As can be seen in the figures and table above, at 200 cm/s\({}^{2}\), the maximum seismic response displacement of the test building retrofitted with NBSD-WSCS was about 0.35 times on the first floor, 0.37 times on the second floor, and 0.42 times on the third floor that of the test building with no reinforcement applied, respectively. These results confirmed the effectiveness of the seismic retrofitting design and NBSD-based seismic reinforcement method proposed in the present study. Figure 31 shows the seismic load-displacement response relationship obtained from the first floor of the test building retrofitted with NBSD-WSCS, and Table 16 summarizes the contributions of NBSD to energy dissipation with respect to the earthquake input. This clearly indicated that NBSD-WSCS with excellent energy dissipation capacity was able to accommodate about 42% of the total energy exerted on the test building. Figure 31: Seismic response load–displacement relationship of NBSD. Figure 30: Time-displacement hysteresis loops of the reference building and the building retrofitted with NBSD (firsts floor). The shear ductility (\(\mu_{s}\)) of the column members on each floor of both the test building with no reinforcement applied and the test building retrofitted with NBSD-WSCS is presented in Figures 32 and 33. Here, the shear ductility (\(\mu_{s}\)) was defined as the ratio of the maximum seismic response shear displacement (\(\delta_{max}\)) to the displacement when shear cracks occur (\(\delta_{c}\)), i.e., \(\mu_{s}=\delta_{max}/\delta_{c}\). \(\mu_{s}=5_{\text{s}}=5\) refers to the moment when a shear failure occurs. As shown in Figure 32, on the first floor of the reference building with non-seismic details, 15 out of the 24 columns were subject to shear failure. On the second floor, shear failure occurred at three columns. In contrast, on the first floor of the test building retrofitted with NBSD-WSCS, only shear cracks with \(\mu_{s}=3\) or less occurred at the columns, and it was found that no column members exceeded the criteria for shear failure. According to previous studies [47,48], the degree of seismic damage observed in the reference building was considered to correspond to _Collapse_, while that observed in the building retrofitted with NBSD-WSCS was considered to be _Small_.