# Seismic Performance of LRS-FRP-Concrete-Steel Tubular Double Coupling Beam
## 4 Seismic Performance
### Energy Dissipation  
Energy dissipation performance reflects the energy consumption capacity of components under earthquake action. Usually, the fuller the hysteretic curve is, the stronger the energy dissipation performance, and the better the seismic performance. Under repeated loading, the member absorbs external energy during loading and releases energy during unloading. The subtraction of the energy during the cycle is defined as energy dissipation, as shown in Figure 14, which is equal to the area surrounded by the hysteresis loop. The equivalent viscous damping coefficient, \(\xi_{eq}\) calculate with Equation (4), and the cumulative energy dissipation, \(\Sigma S\), can be used to evaluate the energy dissipation capacity of members in an earthquake.  
\[\zeta_{eq}=\frac{1}{2\pi}\cdot\frac{S_{(\text{ABC}+\text{CDA})}}{S_{(\text{ OBE}+\text{ODF})}} \tag{4}\]  
As shown in Figure 15a, the cumulative energy dissipation has shared similarities before yielding. The DCB specimen yields first resulting in cumulative energy dissipation, which increased faster than the others. The total cumulative energy dissipation of the LRS-DCB specimen and the DST-DCB coupling beams were improved significantly relative to the DCB control specimen. Compared to the control specimen, the cumulative energy dissipation of the LRS-DCB, DST-DCB-89, DST-DCB-76, and DST-DCB-89P specimens corresponding to \(\Delta_{u}\) improved by 2019%, 376%, 496%, and 500%, respectively. Moreover, the cumulative energy dissipation of the LRS-DCB, DST-CB-89, DST-CB-76, and DST-CB-89P specimens corresponding to \(\Delta_{u,\textit{ffp}}\) improved by 2352%, 2877%, 2345%, and 2660%, respectively, compared to the control specimen. This indicates that the energy dissipation performance of the coupling beam could be greatly improved by wrapping one PET-FRP sheet. The DST composite system also presents excellent energy dissipation. In addition, the results indicate that the tube's diameter has a slight positive effect on the energy dissipation behavior of the coupling beam.  
Figure 14: Sketch for the calculation of equivalent viscous damping coefficient.  
On the other hand, compared to the control specimen, the equivalent viscous damping coefficients of the other four specimens are similar to each other when the displacement is less than 10 mm. The strengthened PET-FRP sheet delays concrete damage and steel bar yielding, which results in the coefficient of the control specimen being larger than that of the other four specimens. Then, the concrete damage results in the coefficients of the DCB and LRS-DCB specimens increasing faster than the coefficient of the DST coupling beams. With the deformation increase, the constraint effect provided by the PET-FRP sheet controlled any further concrete damage, and the coefficient of the LRS-DCB specimen became stable. Relatively speaking, the coefficients of those DST coupling beams tend to attain a linear increase with the deformation increase. The main reason for this is that the constraint effect provided by the PET-FRP sheet and inner steel tube decreased the early damage of concrete.