## 4 Results and Discussions  
### Failure Modes  
For ease of description, the hydraulic actuator pushing the tested specimen is defined as the positive direction, as shown in Figure 4b. Based on the observed phenomena of the test results, two types of deformation characteristics could be found in the tested specimens, that is, out-of-plane buckling deformation and in-plane deformation behaviors. Additionally, a steel plate fracture and weld fracture were the main failure modes of X-shaped metal dampers. Specimen W30-O15\({}^{\circ}\) was taken as an example to analyze the failure processes of X-shaped metal dampers without buckling-restrained devices. Before the applied displacement reached 4.8 mm, the deformation characteristics of specimen W30-O15\({}^{\circ}\) were in-plane  
Figure 4: Test setup: (**a**) photo; (**b**) schematic diagram. Figure 5: Loading procedure. deformation behavior, as shown in Figure 6a. When the applied displacement was 6.0 mm in the negative direction, the X-shaped metal damper was mainly in compression and shear, resulting in obvious buckling deformation, as shown in Figure 6b. At the applied displacement of 7.2 mm in the positive direction, the buckling deformations of steel plates were eliminated due to the shear and tensile behavior of specimen W30-O15\({}^{\circ}\), as shown in Figure 6c. With an increase in the applied displacement, the out-of-plane and in-plane deformation behaviors of X-shaped metal dampers alternated repeatedly. When the applied displacement was 14.4 mm in the positive direction, the buckling deformation of steel plates could not be recovered, as shown in Figure 6d. In addition, the out-of-plane deformations of steel plates in the negative direction were much larger than those of steel plates in the positive direction, as shown in Figure 6e. Finally, a weld fracture was found in specimen W30-O15\({}^{\circ}\) due to enormous buckling deformation, as shown in Figure 6f. For specimen W30-O30\({}^{\circ}\), third-order buckling behavior was also observed in the entire loading process, and a steel fracture at the center of the weakened segment was found in another specimen, as shown in Figure 7.  
Specimen W20-O0\({}^{\circ}\)-LS was taken as an example to analyze the failure processes of X-shaped metal dampers with stiffening ribs. In the early loading process, there was no out-of-plane deformation or obvious in-plane deformation observed in specimen W20-O0\({}^{\circ}\)-LS,  
Figure 7: Test deformation observations of specimen W30-O30\({}^{\circ}\): (**a**) buckling behavior; (**b**) steel fracture. as shown in Figure 8a. With the increase in applied displacement, in-plane deformation was gradually observed due to higher shear and tensile force. When the applied displacement reached 10.2 mm, S-shaped deformation behavior could be found in the stiffening ribs, as shown in Figure 8b. When the applied displacement increased continuously, in-plane deformation was obviously seen in the stiffening ribs, as shown in Figure 8c. The welding seams fractured and the test stopped when the applied displacement was 19.2 mm, as shown in Figure 8d. For the other specimens with stiffening ribs, welding fractures were the main failure modes due to higher in-plane stiffness. Specimens with an oblique angle of 15\({}^{\circ}\) were taken as examples to compare the influence of buckling-restrained devices on the hysteretic performance of X-shaped metal dampers. Figure 9 shows the final deformation characteristics of specimens W30-O15\({}^{\circ}\), W30-O15\({}^{\circ}\)-LP, and W30-O15\({}^{\circ}\)-LS. According to the test results, there was no obvious buckling behavior observed in specimen W30-O15\({}^{\circ}\)-LP, indicating that cover plates can effectively restrict the out-of-plane deformation of X-shaped metal dampers. However, because the length of cover plates was smaller than that of the X-shaped steel plates, out-of-plane deformations at the end of X-shaped metal dampers were observed in the late plastic stage.