## 3 Material Testing of Window-Type NBSDs and the Results
### NBSD Material Test Results and Analysis  
(1) Load-displacement curves  
Load-displacement curves were obtained from NBSD-1 and NBSD-2, as shown in Figure 6, and images of the specimens after the maximum control displacement of 33 mm was reached are presented in Figure 7. These results are summarized in Table 2. The yield proof stress (\(Q_{dy}\)) and yield displacement (\(\delta_{dy}\)) results provided in Table 2 were determined as follows. First, a line with a slope one-third of the corresponding initial stiffness line was drawn, and a tangent line between this line and the corresponding load-displacement curve was determined. The intersection between the obtained tangent line and the initial stiffness line was then defined as referring to the yield displacement (\(\delta_{dy}\)) and yield proof stress (\(Q_{dy}\)) [38; 39]. Figure 5: Cyclic loading plan. Figure 6: Load-displacement curves: (**a**) NBSD-1 and (**b**) NBSD-2 specimens. For NBSD-1, the yield displacement \(\delta_{dy}\) was 1.49 mm, the yield proof stress \(Q_{dy}\) was 76.0 kN, and the maximum proof stress was \(Q_{d}\) =216.3 kN. For NBSD-2, the yield displacement \(\delta_{dy}\) was 1.56 mm, the yield proof stress was \(Q_{dy}\) =80.8 kN, and the maximum proof stress \(Q_{d}\) was 215.5 kN. As such, the two specimens showed very similar results. Equivalent damping ratios and energy dissipation The performance of seismic control systems can be determined by their ability to dissipate the seismic energy input, which is characterized by effective stiffness, energy dissipation capacity, and equivalent damping ratios. As shown in Figure 8b, the elastic potential energy (\(E_{So}\)) of a seismic control system can be calculated based on its effective stiffness (\(k_{d,eff}\)) illustrated in Figure 8a. Its cumulative energy dissipation (\(E_{D}\)) can also be calculated based on the concept described in Figure 8b. The equivalent damping ratio (\(\beta_{eq}\)) can be determined using the elastic potential energy (\(E_{So}\)) in Equation (5) and the cumulative energy dissipation (\(E_{D}\)) [17,40]. \[\beta_{eq}=\frac{1}{2\pi}\cdot\frac{E_{D}}{k_{d,eff}(i)\cdot\delta_{ave}^{2}}= \frac{1}{4\pi}\cdot\frac{E_{D}}{E_{So}} \tag{5}\]  
Here, \(E_{D}(i)\): total cumulative energy dissipation (\(i\): 11, 22, 33 mm), \(k_{d,eff}(i)\): effective stiffness of the seismic control system (\(i\): 11, 22, 33 mm), and \(\delta_{ave}\): average absolute value of displacements (\(\left|\delta_{d,min}+\delta_{d,max}\right|/2\)). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Specimen** \\ **Name** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Maximum Control** \\ **Displacement** \\ **(\(\delta_{d,max}\))** \\ \end{tabular} } & \multicolumn{2}{c}{**Yield**} & \multicolumn{2}{c}{**Positive Load**} & \multicolumn{2}{c}{**Negative Load**} & \multirow{2}{*}{
\begin{tabular}{c} \(k_{dy}\) \\ **(kN/mm2)** \\ \end{tabular} } \\ \cline{3-3} \cline{5-8}  & & \(\delta_{dy}\) & \(Q_{dy}\) & \(\delta_{d}\) & \(Q_{d}\) & \(\delta_{d}\) & \(Q_{d}\) & \(\delta_{d}\) \\  & & **(mm)** & **(kN)** & **(mm)** & **(kN)** & **(mm)** & **(kN)** \\ \hline NBSD-1 & \multirow{2}{*}{33} & 1.49 & 76.0 & 32.6 & 205.9 & 32.5 & 216.5 & 51.0 \\ NBSD-2 & & 1.56 & 80.8 & 32.3 & 201.6 & 32.6 & 215.5 & 51.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results obtained from the NBSD specimens. Figure 7: Images of the specimens at the maximum control displacement of 33 mm. The effective stiffnesses (\(k_{d,eff}\)) of the NBSD specimens are provided in Table 3, and the equivalent damping ratios (\(\beta_{eq}\)) and cumulative energy dissipation (\(E_{D}\)) were estimated based on the measured effective stiffnesses, as shown in Table 4. The average effective stiffnesses (\(k_{d,eff}\)) of the NBSD specimens were 11.6 kN/mm (11 mm), 7.3 kN/mm (22 mm), and 6.4 kN/mm (33 mm), respectively.