## 4 Discussion of Test Results
### Energy Dissipation and Equivalent Viscous Damping  
Related to the load-displacement curves, energy dissipation is another important index to evaluate the seismic performance of the specimens. It is generally accepted that the energy dissipation \(E_{s}\) can be measured by the area surrounded by the hysteretic curve in one loading cycle, as shown in the shadowed area of Figure 11. The approach adopted here is also suggested in the literature [12; 27; 28; 29]. Moreover, in order to evaluate the influence of the prestressing technology more directly, the load-displacement curves are divided into three phases: the ascending stage, max state and descending stage. The comparison displacements in the ascending stage and descending stage are chosen as the first displacement cycle and the displacement when the lateral resistance of the specimens dropped to 85% of the maximum lateral resistance, respectively. It should be noted that the displacement cycle of 10.0 mm is selected for BMFT to be consistent with that of BMFTP, although the negative maximum lateral resistance of the BMFT specimen reached the displacement of 17.5 mm. Table 5 summaries the calculated results of the energy dissipation of the specimens, and the energy dissipation of the specimens versus drift curve is plotted in Figure 12a. Figure 12a clearly shows that the dissipation energy of the specimens is influenced by the section type of the specimens. The \(E_{s}\) of the specimens with a rectangular section increases with the increment of the displacement, while the \(E_{s}\) of the specimens with a T-shape section increases at the initial stage but remains stable after a drift of 2.5%. For the BMF and BMFP, the comparison results show that the \(E_{s}\) of BMFP is lower than that of BMF at the ascending stage, but the \(E_{s}\) of BMFP is about 15% higher than that of BMF, with an increment of the displacement at the max state and descending stage. Figure 10: Stiffness degradation of the specimens. For the BMFT and BMFTP, the comparison results show that the \(E_{s}\) of BMFTP is higher than that of BMFT at the ascending stage and max state, but the \(E_{s}\) of BMFTP is lower than that of BMFT at the descending stage. This indicates that the prestressing technology also improved the energy dissipation of the specimens at the ascending stage. Overall, it demonstrates that the influence of the prestressing technology on the \(E_{s}\) of the specimens is related to the failure mode of the specimens, and it improves the energy dissipation of the specimens before they reach their maximum lateral resistance. Furthermore, a common and simple indicator to represent the damping of the specimens is the equivalent damping ratio. The equivalent damping ratio \(\xi_{eq}\) can be defined as the ratio of the energy dissipation of the specimens in one cycle to the total energy input by the actuator, as shown in Equation (2):  
\[\xi_{eq,i}=\frac{E_{s,i}}{2\pi K_{si}\Delta_{\max,i}^{2}}, \tag{2}\]  
where \(E_{s,i}\) represents the energy dissipation of the specimen in one cycle, \(K_{si}\) is the secant stiffness, and \(\Delta_{\max,i}\) is the maximum displacement in one cycle. Figure 12b shows the relationship between \(\xi_{eq}\) versus drift, and the average \(\xi_{eq}\) of each specimen is listed in Table 5. Figure 12b clearly shows that \(\xi_{eq}\)firstly decreases, but it then increases with the increment of the drift after a drift of 0.2%. Moreover, \(\xi_{eq}\)gradually remains constant after the drift reaches 1.0%. The final average values of \(\xi_{eq}\) of specimens BMF, BMFP, BMFT and BMFTP are 10.8%, 10.0%, 8.2% and 8.2%, respectively. The \(\xi_{eq}\) obtained in this study is similar to that provided in the literature [4]. However, it seems that the prestressing technology used in this study has no marked influence on the equivalent damping ratio of the specimens. Figure 11: Calculation method of energy dissipation.