## 4 Results and Discussions
### Hysteretic Behavior  
Figure 10 shows the test load-displacement curves of the specimens. It can be seen from Figure 10 that specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\) showed quite different deformation characteristics, which demonstrated that stiffness and strength in the positive direction were significantly larger than those of specimens in the negative direction, indicating the bucking behaviors of specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\) in comparison to other specimens. These were because when the applied loads were in the positive direction, X-shaped metal plates with an oblique angle were mainly in tension and shear, as shown in Figure 4b. In the negative direction, X-shaped metal plates were mainly in compression, resulting in the occurrence of out-of-plane deformation. Subsequently, the tensile and shear behaviors of X-shaped metal plates eliminated the out-of-plane deformation. Therefore, the hysteretic curves of specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\) were obviously asymmetric. Additionally, the above buckling behaviors of specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\) could also be found in the obtained test results, as shown in Figure 7.  
In Section 5.1, an elastic stiffness calculation method for X-shaped metal dampers with an oblique angle is proposed. Additionally, [PERSON]'s critical stress for specimens in the negative position can be determined based on the following equation [38]: \(P_{\text{cr}}=\frac{\pi^{2}EI}{(\mu L)^{2}}\), where \(P_{\text{cr}}\) represents the critical buckling load of compressive components, \(EI\) represents the elastic stiffness of compressive components, \(\mu\) represents the length coefficient of compressive components, and \(L\) represents the length of compressive components. Therefore, the buckling behavior in the hysteretic curves for specimen W30-O30\({}^{\circ}\) was more obvious compared with that of specimen W30-O15\({}^{\circ}\) due to lesser Euler's stress. In addition, when the applied displacement was lower than 3.6 mm, the corresponding loads were lower than the critical buckling load; therefore, parallelogram hysteretic loops were observed in specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\), as shown in Figure 10a. After that, the hysteretic loops of specimens W30-O15\({}^{\circ}\) and W30-O30\({}^{\circ}\) showed obvious buckling characteristics.  
It can be seen from Figure 10b-e that relatively stable load-displacement curves were obtained in the other specimens, which indicated that cover plates and stiffening ribs can effectively restrict the buckling behavior of X-shaped metal dampers. Asymmetric hysteretic loops were also observed in specimens with an oblique angle of 15\({}^{\circ}\) or 30\({}^{\circ}\), as shown in Figure 10c,d. The hysteretic loops of specimens with stiffening ribs were slightly fatter than those of specimens with cover plates due to the contribution of stiffening ribs, as shown in Figure 10b-d. This implied that specimens with stiffening ribs can be used as an energy-dissipating device for shear walls with vertical joints. Additionally, the hysteretic curves of specimens W20-O0\({}^{\circ}\)-LS and W30-O0\({}^{\circ}\)-LS were asymmetric and specimen W30-O0\({}^{\circ}\)-LS showed fatter hysteretic loops, as shown in Figure 10e.  
Figure 9: Test deformation observations of specimens: (**a**) front view; (**b**) vertical view.