## 4 Horizontal Mechanical Properties Tests of CBRBs
### Horizontal Compression-Shear Cyclic Test
#### 4.2.2 Mechanical Properties Analyses  
Figures 15-18 show the hysteretic curves of the rubber bearings at different pressure levels (2 MPa, 4 MPa and 6 MPa) and shear strains (\(\gamma\) equal to 25%, 50%, 75% and 100%).  
Figure 14: Bearing R2 under compression-shear test with shear strains: (**a**) 0; (**b**) 50%; (**c**) 75%; (**d**) 100%.  
Figure 15: Hysteretic curves of R1: (**a**) 2 MPa; (**b**) 4 MPa; (**c**) 6 MPa.  
From Figures 15-18, we can obtain the following results:  
1. The hysteretic curves of the four bearings at different pressure levels are relatively full, symmetrical and smooth, which proves the horizontal performance of the new bearing is stable.  
2. As the shear strain increases, the stiffness of the bearings gradually decreases and exhibits bilinear features, due to the rollover deformation.  
3. When the shear strain of the bearing is 100% and the vertical pressure is 2 MPa, the shear stress of the bearings' rubber layers (approximately \(\tau=G\gamma=1.85\) Mpa) is much greater than the friction stress (approximately \(\tau=\mu N=0.4\times 2=0.8\) Mpa, where \(\mu\) is the friction coefficient between the bearing and two steel plates, and \(\mu\) is assumed 0.4 [32]), causing the bearing to slip, which makes the area of the hysteresis curve of 2 MPa obviously greater than that of 4 MPa and 6 MPa.  
Figures 19 and 20 illustrate the effective horizontal stiffness and damping ratio of R1, R2 and R4 at different shear strains and pressure levels. In Figures 19 and 20, \"2 MPa\" represents the vertical pressure of 2 MPa, and \"R1\" represents the bearing label, other legends are similar.  
Figure 16: Hysteretic curves of R2: (a) 2 MPa; (b) 4 MPa; (c) 6 MPa.  
Figure 17: Hysteretic curves of R3: (a) 2 MPa; (b) 4 MPa; (c) 6 MPa.  
Figure 18: Hysteretic curves of R4: (a) 2 MPa; (b) 4 MPa; (c) 6 MPa.  
As can be seen from Figure 19, the effective horizontal stiffness of the bearings decreases with increasing shear strain. In addition, the curves under a constant vertical pressure of 2 MPa (marked by circle) further decrease significantly, due to sliding of the bearing after the shear strain exceeding 50%. However, the reduction is not noticeable for the pressure of 4 MPa or 6 MPa (marked by triangle and pentagram, respectively). The effective horizontal stiffness of R2 increases with the increase of vertical pressure. When the vertical pressure of 4 MPa is applied, as the number of fabric layer increases, the effective horizontal stiffness of bearings also increases. Under the other two pressure levels, the above-mentioned conclusions cannot be obtained, and we will further study the specific reasons in the future research. As can be seen from Figure 20, when the shear strain is within 50%, its equivalent damping ratio decreases with increasing shear strain; as the shear strain is greater than 50%, its equivalent damping ratio changes without obvious rules, but the fluctuation is not large. However, the sliding of the bearing causes the effective horizontal damping ratio increase with increasing shear strain. In general, the effective horizontal damping ratio of this new type of bearings is about 15% without considering the sliding of the bearing.  
Figures 21 and 22 show the horizontal equivalent stiffness and the effective damping ratio of R2 and R3 at different shear strains and pressure levels. The legends in Figures 21 and 22 have the same meaning as that in Figures 19 and 20.  
Figure 19: The effective horizontal stiffness of CBRB R1, R2 and R4.  
Figure 20: The effective horizontal damping ratio of CBRB R1, R2 and R4.  
Obviously, the effective horizontal stiffness and damping ratio of R3 are slightly larger than those of R2, but considering that the residual displacement of R3 during vertical compression is significantly larger, it is still not recommended for application in structures.