## 3 Test Results and Analysis
### Horizontal Shear Performance  
Horizontal shear performance tests were carried out on the three bearings, in which the pressure was slowly and continuously loaded to 3400 kN and remained constant. The shear displacement corresponding to \(\gamma=100\%\) was applied horizontally at a low frequency of 0.01 Hz, and the whole loading process consisted of four cycles. The horizontal stiffness \(\mathrm{K_{h}}\) and equivalent damping ratio \(\mathrm{h_{eq}}\) of a bearing can be calculated according to Equations (8) and (9):  
\[\mathrm{K_{h}}=\frac{\mathrm{Q_{2}-Q_{1}}}{\mathrm{X_{2}-X_{1}}} \tag{8}\]  
\[\mathrm{h_{eq}(\gamma)}=\frac{1}{\pi}.\frac{\mathrm{W_{d}}}{2\mathrm{K_{H}( \gamma T_{r})2}} \tag{9}\]  
where \(\mathrm{Q_{1}}\) and \(\mathrm{Q_{2}}\) are the maximum and the minimum shear forces of the third cycle, respectively; \(\mathrm{X_{1}}\) and \(\mathrm{X_{2}}\) denote the positive and the negative maximum displacement of the third cycle, respectively, and \(\mathrm{X_{1}}=\mathrm{T_{r}\gamma}\), \(\mathrm{X_{2}}=\mathrm{T_{r}(-\gamma)}\); and \(\mathrm{T_{r}}\) is equal to the product of \(\mathrm{n_{r}}\) and \(\mathrm{t_{r}}\). \(\Delta\mathrm{W}\) represents the envelope area of the hysteresis curve. The horizontal hysteresis curves of the tested bearings are shown in Figure 11. It can be seen from the figure that the curves of the three bearings are respectively in crescent shape (HDRB-LSF) and spindle shape (TLRB and LRB). Among them, the hysteresis curves of HDRB-LSF are relatively less plump, that is, the energy dissipation capacity of which is surprisingly inferior to TLRB and LRB under the same shear deformation condition. The shape of hysteretic curves of each bearing is basically consistent with the specification requirements. Horizontal shear performances of the bearings are shown in Table 5. It shows that under the same vertical pressure and shear strain the horizontal equivalent stiffness of HDRB-LSF is smaller than those of TLRB and LRB, which indicates that under the premise of the equal total thickness of rubbers, the steel plates in HDRB-LSF have less binding force on rubbers than the bearings with lead core. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Bearings**} & **HDRB-LSF** & **TLRB** & **LRB** \\ \hline \multirow{2}{*}{Equivalent stiffness (kN/mm)} & Theoretical value & 1.09 & 1.35 & 1.35 \\  & Test value & 1.01 & 1.02 & 1.22 \\  & Error (\%) & \(-\)7.34 & \(-\)24.44 & \(-\)9.63 \\ \hline \multirow{2}{*}{Equivalent damping ratio (\%)} & Theoretical value & 8.06 & 23.56 & 28.69 \\  & Test value & 9.26 & 38.89 & 31.75 \\  & Error (\%) & 14.89 & 32.36 & 10.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Horizontal performance error between theoretical value and test value. The energy dissipation capacity of bearings is currently expressed by the equivalent damping ratio. The horizontal equivalent damping ratio of HDRB-LSF was approximately 9% in the third cyclic test (it was about 13% in the first cyclic test), expressing a better energy dissipation capacity than the NRB with a usual equivalent damping ratio of 3%. However, compared to TLRB and LRB with the lead core in the test, the energy dissipation capacity of HDRB-LSF designed in this paper is insufficient and needs improvement. When the vertical pressure is 3400 kN and the shear strain is 100%, the errors between the experimental values and the theoretical values of the horizontal performance of HDRB-LSF and LRB are both less than 15%. In contrast, the errors for TLRB are significant. In order to quantitatively evaluate the horizontal shear stiffness of the three bearings and studying its relationship with shear deformation, axial pressure, and loading frequency, the third cyclic results of horizontal hysteresis curves of the bearings subjected to various test cases were acquired. Then, the influences of different parameters on the horizontal stiffness and equivalent damping ratio of the three bearings were analyzed.