## 4 Discussion of Test Results
### Stiffness Degradation  
Stiffness is an important index of the seismic analysis of structures. It is well known that the stiffness of a specimen decreases with the increase of the displacement [3; 4; 5; 6; 7]. With regard to the stiffness degradation, the secant stiffness \(K_{si}\) is adopted in this study and calculated by Equation (1). The \(V_{\text{max},i}\) and \(V_{\text{min},i}\) are the peak load resistance of specimen at the \(i\) cycle, while the \(\Delta_{\text{max},i}\) and \(\Delta_{\text{min},i}\) are the corresponding displacement at the \(i\) cycle, respectively. Moreover, the secant stiffness \(K_{si}\) is also normalized by the initial stiffness \(K_{0}\) at the first load cycle to estimate the stiffness degradation, and the relationship between the secant stiffness and drift were plotted in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Direction**} & \multicolumn{4}{c}{**Yield State**} & \multicolumn{4}{c}{**Ultimate State**} & \multicolumn{2}{c}{**Ductility**} \\ \cline{3-10}  & & **Q** & \(\Delta_{y}\) & **DR** & **Q** & \(\Delta_{u}\) & **DR** & \(\mu\) & \(\mu\) \\  & & **(\(\mathbf{\delta}\)\(\mathbf{N}\))** & **(\(\mathbf{mm}\))** & **(\(\mathbf{\%}\))** & **(\(\mathbf{k}\)\(\mathbf{N}\))** & **(\(\mathbf{mm}\))** & **(\(\mathbf{\%}\))** & **(\(\mathbf{\mu}\))** & \(\mu\) \\ \hline \multirow{2}{*}{**BMF**} & \(+\) & \(+143\) & \(+7.7\) & \(+0.43\) & \(+144\) & \(+37.0\) & \(+2.05\) & \(4.81\) & \multirow{2}{*}{\(4.63\)} \\  & \(-\) & \(-126\) & \(-6.3\) & \(-0.35\) & \(-131\) & \(-28.0\) & \(-1.55\) & \(4.44\) & \\ \hline \multirow{2}{*}{BMFP} & \(+\) & \(+147\) & \(+5.6\) & \(0.31\) & \(+154\) & \(+35.0\) & \(+1.94\) & \(6.25\) & \multirow{2}{*}{\(6.92\)} \\  & \(-\) & \(-147\) & \(-6.2\) & \(0.34\) & \(-151\) & \(-47.0\) & \(-2.61\) & \(7.58\) & \\ \multirow{2}{*}{BMFT} & \(+\) & \(+226\) & \(+6.7\) & \(+0.37\) & \(+222\) & \(+25.5\) & \(+1.42\) & \(3.79\) & \\  & \(-\) & \(-226\) & \(-8.3\) & \(-0.46\) & \(-212\) & \(-24.0\) & \(-1.33\) & \(2.88\) & \\ \multirow{2}{*}{BMFTP} & \(+\) & \(+234\) & \(+5.4\) & \(+0.30\) & \(+228\) & \(+28.0\) & \(+1.55\) & \(5.19\) & \\  & \(-\) & \(-195\) & \(-4.0\) & \(-0.22\) & \(-201\) & \(-21.0\) & \(-1.17\) & \(5.25\) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of calculation results of displacement ductility.  
Figure 9: Determination of yielding point.  
\[K_{si}=\frac{V_{\max,i}-V_{\min,i}}{\Delta_{\max,i}-\Delta_{\min,i}}, \tag{1}\]  
The initial stiffness of specimens BMF, BMFP, BMFT and BMFTP is calculated to be 67.3 kN/mm, 109.7 kN/mm, 107.1 kN/mm and 169.8 kN/mm, respectively. It can be observed that the prestressing technology had a significant influence on the initial stiffness of the specimens. An increase in the initial stiffness of 59% is found for the specimens with a rectangular section, while an increase in the initial stiffness of about 55% was found for the specimens with a T-shape section. As shown in Figure 10, it can be clearly observed that the normalized stiffness degradation versus drift curves divided into two categories: the specimens with and without prestressing technology. The specimens with prestressing technology experienced a greater fall in the degradation of the normalized stiffness than the specimens without this technology throughout the loading process. This demonstrates that the prestressing technology had a significant effect on the stiffness degradation of the specimens. On the other hand, the prestressing technology sped up the rate of the normalized stiffness degradation. A similar conclusion is also provided by [PERSON] et al. [17], who indicated that the posttension increases the initial stiffness but caused a rapid reduction in the secant stiffness. However, a greater amount of experimental data is needed to support this conclusion.