## 7 Analysis Results and Observations  
The 3D FE models for several recentering slit damper models (Figure 7) were loaded according to quasi-static displacement load history (Figure 13a) in order to simulate their inelastic behavior. After FE analyses, parametric studies are conducted to explore the size of steel slit dampers and the effect of superelastic SMA bars in the integrated system. The applied force _versus_ displacement hysteresis curves for six recentering slit damper models (SL1-SMA to SL6-SMA models) are presented in Figure 11. It can be shown that the recentering slit dampers proposed possess comparative advantages regarding ultimate strength and recentering capacity over the conventional steel slit dampers. Strength capacities are remarkably improved up to more than ten times. In particular, the superelastic SMA bending bars functioning as reinforcing restrainers avoid triggering strength degradation at the hysteretic curves, within the range of displacement loading. Most of all, these bars supplementally acting as recentering devices help to decrease permanent deformation to on average a 27% level of the conventional slit damper system. For instance, the SL1 model has approximately 15 mm permanent deformation at the last loading cycle (Figure 9) while the SL1-SMA model has only about 4 mm of permanent deformation. The response mechanism for the recentering slit damper can be constituted by deformable contributions obtained from four SMA bars and one steel slit damper (Figure 4). The simulated curves for the behavior of each component are presented in Figure 12, including the total behavior of the recentering slit damper. The lower limit for the level of recentering force is plotted as the dashed line in the figure. The quantities for specific points defined in this figure (_i.e._, \(P_{\text{SMA,max}}\), \(\Delta_{\text{SMA,max}}\)\(\Delta_{\text{SMA,p}}\), and six other points) are summarized in Table 3. In order to verify that individual components (_i.e._, four SMA bars and steel slit damper) shall be assembled in parallel to directly formulate the behavior of the recentering slit damper system, the ratio of force discrepancy between component assemblage and integrated system is presented in this table as follows:  
Figure 10: Applied force _vs._ displacement curves for fixed-end supported SMA bars under transverse end shear force, (**a**): \(\Delta_{\text{SMA,max}}=17.5\)mm Case; (**b**): \(\Delta_{\text{SMA,max}}=12.5\)mm Case. The superelastic SMA bending bars themselves completely recover from plastic deformation in that they have zero permanent deformation upon unloading (\(\Delta\)SMA\({}_{\rho}\) = 0 mm). The slit damper can only recover elastic deformation to the contrary, and thus exhibits a considerable amount of permanent deformation upon unloading as is presented in the table. Once the recentering force attributed to the contribution of superelastic SMA bending bars exceeds the maximum force of the slit damper, permanent displacement starts to decrease in the integrated system. The values of \(P_{\text{error}}\) are less than 1.0% at most, implying that the total behavior of the recentering slit damper can be equivalently formulated by combining the responses of two components in parallel. The recentering slit dampers have on average 8.5 times larger maximum forces than the conventional steel slit dampers within the range of displacement loading, but their permanent deformations decrease by about 74%, indicating on average \(\Delta\)\({}_{\rho,\text{ratio}}\) = 0.26. The recentering ratios (RRs) exceed 76% for all model cases. It can be thus concluded that the superelastic SMA bending bars lead the proposed damper systems in the betterment of structural performance in terms of strength and recentering capacity. For more observation of FE analysis results, both filed contours and history outputs are detected at the specific loading steps.