# Seismic Performance of LRS-FRP-Concrete-Steel Tubular Double Coupling Beam
## 3 Results and Discussion
### Hysteretic Curve  
The load-displacement curves of all coupling beams under low-cyclic reversed loading, namely hysteretic curves, which could reflect the seismic performance of members, such as the ductility, energy dissipation, and stiffness degeneration. Usually, the plumper the hysteretic curve is, the better the energy dissipation and the better the seismic performance. As illustrated in Figure 8, those curves of specimens with a double coupling beam (DCB) wrapped with LRS-FRP or consisting of double skin tubular (DST) beams, which are wider and have better ductility than the control DCB specimen. Since there is no obvious yielding point in the envelope curves of all specimens, the yielding point of these members is determined by the method reported by [PERSON] [30]. As illustrated in Figure 9, which shows the point set corresponding to the 75% peak strength at point B. Then, point A is the intersection of the OB extension line and the horizontal line corresponding to the peak strength. Finally, we can define the interaction of the load-displacement curve and the perpendicular line passing through point A near the displacement axial as the yielding point (point Y in Figure 9). The calculated yield strength and corresponding deformation of the specimens are listed in Table 4.  
Figure 7: Failure modes of specimens: (**a**) reinforced-concrete double coupling beam (RC-DCB); (**b**) LRS-DCB; (**c**) DST-DCB-89. Figure 8: Hysteretic curves of all specimens: (**a**) RC-DCB; (**b**) LRS-DCB; (**c**) DST-DCB-89; (**d**) DST-DCB-76; (**e**) DST-DCB-89P. Figure 9: [PERSON]’s method for the yielding point. For the control specimen RC-DCB, as shown in Figure 8a, the force increases elastically before a crack generates. With the deformation increase, the cumulative damage expands and the stiffness degrades gradually. The specimen reaches the yielding stage when the longitudinal reinforcement yields. Then the load bearing capacity of the specimen can hardly be further improved. With the shear cracks generating and developing, the stiffness of the specimen is further reduced. Before the occurrence of shear failure, the load dropped suddenly, which also resulted in the ultimate lateral deformation being very small relative to the other strengthened specimens. Compared to the control RC-DCB, as illustrated in Figures 8-10, and Table 4, the ductility of the specimen LRS-DCB improved significantly. The ultimate lateral deformation increased 284% although its peak bearing capacity was similar to that of the RC-DCB specimen. Figure 10 shows that the pre-peak stage of LRS-DCB is almost the same as that of RC-DCB. This means that according to a lower Young's modulus of the PET-FRP material, a constraining stiffness develops but is not able to further improve the core RC beam's bearing capability in the initial stage. However, the bearing capacity presents a relatively stable state after a slight reduction. This indicates that with the deformation increase the constraint effect provided by the LRS-FRP composite jacket makes a great contribution toward maintaining the bearing capacity and improving the ductility of the coupling beam. For the cycling behavior of LRS-DCB, it presents an obvious pinching phenomenon, i.e., the LRS-DCB specimen needs only a small lateral force to restore its original position after the force unloads to zero. Notably, the well-known ultra-high rupture strain of the PET-FRP material could provide relatively high constraint stress to the core concrete in the stage of large deformation. In this case, even its Young's modulus is relatively much lower than that of traditional CFRP. Meanwhile, the existing experiments and theories [31] indicate that the compressive and shear strength of concrete could be improved due to its effective multi-axial constraining stress. This makes it possible to maintain its bearing capacity even under large deformation. However, the large lateral deformation is also accompanied by concrete damage. This damage also results in the reduction of tension and shear strength.