## 9 Conclusions  
In this paper, the behavior of a proposed damper was investigated experimentally and numerically. The results are summarized as follows:  
* Experimental results indicated that M_P had less strength and energy_dissipating capability than other models, as also confirmed by FE results in all types of main plate buckling. * Experimental and FE results indicated that connecting the cross plate to the web plate improved the strength and stiffness but reduced the ultimate displacement. Comparing the results of the specimen with (not connected to web plate) and without cross-flexural plates confirmed that the cross plate increased the ultimate strength by 2.65 and reduced the stiffness by 16%. The reduction in stiffness was due to the length of the web plate having a greater effect on stiffness than thickness. * Connecting the cross plate to the web plate improved the ultimate strength and stuffiness by 84% and 3.9, respectively. * In the main plate without a cross plate and with an unconnected cross plate, the yielding started at the bottom and top of the plate, whereas it started at the middle of the plate when the cross plate was connected to the main plate. For slender plates (elastic buckling, \(\lambda>1.4\sqrt{K}\)) without a cross plate, the dampers did not experience adequate nonlinear zones. Thus, dampers with \(\lambda>1.4\sqrt{K}\) without cross flexural plates are not appropriate for use as seismic dampers. * Upon adding the cross plate to the damper, the ratio of the normalized shear strength to plastic shear strength of the main plate exceeded 1. Hence, the cross plate not only changed the main plate behavior from flexural to shear but also contributed to resisting the applied loading. Therefore, the assumption in Section 2.2 was confirmed. * For a plate with plastic buckling (\(\lambda\leq 1.12\sqrt{K}\)), the cross_flexural plate increased the strength and stiffness by factors of 2 and 1.06, respectively, revealing a negligible effect on the stiffness for \(\lambda\leq 1.12\sqrt{K}\). For a plate with elastic buckling (\(\lambda>1.4\sqrt{K}\)), the strength and stiffness were increased by 1.2 and 2.64, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**FE Results**} & \multicolumn{2}{c}{**Proposed Relations**} & \multicolumn{2}{c}{**Error (\%)**} \\ \cline{2-7}  & \(V_{u}\) **(kN)** & \(K_{d}\) **(kN/mm)** & \(V_{u}\) **(kN)** & \(K_{d}\) **(kN/mm)** & **Equation (1)** & **Equation (2)** \\ \hline M\_P & 251.603 & 441.33 & 226.44 & 419.26 & 11.11 & 5.26 \\ M\_I & 268.273 & 583.47 & 225.35 & 548.46 & 19.05 & 6.38 \\ M\_E & 223 & 528.57 & 202.93 & 507.43 & 9.89 & 4.17 \\ M\_P\_St & 503.56 & 469.56 & 448.17 & 422.60 & 12.36 & 11.11 \\ M\_I\_St & 512.12 & 1081.75 & 466.10 & 973.57 & 9.89 & 11.11 \\ M\_E\_St & 267.6 & 1394.80 & 238.16 & 1255.32 & 12.36 & 11.11 \\ S\_P\_St & 604.681 & 1985.16 & 556.31 & 1925.61 & 8.70 & 3.09 \\ S\_I\_St & 660.454 & 918.60 & 601.01 & 881.86 & 9.89 & 4.17 \\ S\_E\_St & 630.256 & 938.71 & 579.84 & 882.39 & 8.70 & 6.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparing the FE results with the proposed relations. **Author Contributions:** Conceptualization, K-J.H. ; methodology, S.-H.J. ; formal analysis, A.G.; investigation, A.G.; resources, S.-H.J. and A.G.; data curation, A.G. and C.-h.K. ; writing--original draft preparation, A.G. and B.A. ; writing--review and editing, S.-H.J. ; visualization, B.A. and C.-h.K. ; supervision, K-J.H. ; project administration, K.-J.H. All authors read and agreed to the published version of the manuscript. This work was supported by a grant from the Korea Agency for Infrastructure Technology Advancement (KAIA), funded by the Ministry of Land, Infrastructure, and Transport ((Grant 21 SCIP-B146946-04)). Not applicable. **Data Availability Statement:** All research data used in this manuscript are available upon request.