# Seismic Retrofit of Steel Truss Bridge Using Buckling Restrained Damper
## 5 Conclusive Remarks  
Analytical studies on the effectiveness of the buckling restrained damper (BRD) on the seismic behavior of an existing steel truss bridge were carried out. Four design parameters of the BRD, i.e., location, length, cross-sectional area of the yielding core, and inclination, were studied. To this end, the safety of the existing truss bridge under a large earthquake was assessed by nonlinear finite element analyses. The seismic behavior only in the longitudinal direction of the bridge was considered. Through the safety evaluation, some members were damaged due to the large earthquake. To improve the seismic resistance of the bridge, two pairs of BRDs are individually attached between the bridge abutment and each bottom-end of vertical links that are rigidly connected to joints at the lower chord of the truss bridge. The vertical links were modeled to be absolute rigid bodies, and their properties are not taken into account in the scope of this study.  
Based on the safety condition of the model with BRD, the effectiveness of the four parameters for the design of the BRD was evaluated: (1) Location: near the roller support of the current truss bridge is not effective; (2) Length: shortening the yielding part of the BRD is more efficient; (3) Cross-sectional area: increasing the cross-section of the BRD yielding core is also effective; (4) Inclination: the inclination for the design of BRD is not effective.  
The performance-based verification proves that the BRD is applicable for the existing truss bridge to sustain its resistance against large earthquakes. Figure 9 indicates that the axial compressive and tensile stresses of damaged members could be reduced by BRDs with different design parameters that are shown to be effective.  
The results open a path for the use of BRD to provide high levels of seismic resistance to existing bridges.  
Figure 9: Effectiveness of the design parameters of the BRD.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**The safety condition**} & \multicolumn{2}{c}{**Horizontal Displacement at the Moveable End of the Damaged Members (mm)**} \\ \cline{2-7}  & \(\mathbf{R_{c}}\) & \(\mathbf{R_{t}}\) & \(\mathbf{Min.}\) & **Reduction by BRD** & **Min.** & **Reduction by BRD** \\ \hline Initial model & 1.305 & 1.072 & \(-\)8.468 & - & 67.525 & - \\ L-3-5-20 - 0\({}^{\circ}\) & 0.363 & 0.830 & \(-\)5.865 & 30.7\% & 4.671 & 93.1\% \\ L-3-5-20 - 5\({}^{\circ}\) & 0.345 & 1.007 & \(-\)6.106 & 27.9\% & 5.607 & 91.7\% \\ L-3-5-20-10\({}^{\circ}\) & 0.718 & 1.008 & \(-\)7.585 & 10.4\% & 8.919 & 86.8\% \\ L-3-5-20-15\({}^{\circ}\) & 0.481 & 1.002 & \(-\)9.595 & \(-\)13.3\% & 10.922 & 83.8\% \\ \hline R-3-5-20 - 0\({}^{\circ}\) & 0.717 & 1.009 & \(-\)3.787 & 55.3\% & 7.462 & 88.9\% \\ R-3-5-20 - 5\({}^{\circ}\) & 0.840 & 1.013 & \(-\)5.488 & 35.2\% & 4.370 & 93.5\% \\ R-3-5-20-10\({}^{\circ}\) & 0.231 & 1.001 & \(-\)6.900 & 18.5\% & 6.121 & 90.9\% \\ R-3-5-20-15\({}^{\circ}\) & 0.345 & 1.007 & \(-\)8.765 & \(-\)3.5\% & 8.978 & 86.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Influence of the inclination on the horizontal displacement due to the earthquake.  
**Author Contributions:** Analysis, investigation, and writing-original draft, P.S.; supervision and software, E.Y.  
**Funding:** This research received no external funding.  
**Acknowledgments:** P.S. thanks to Mongolia-Japan higher Engineering Education Development project (MJEED), the Government of Mongolia for the financial support.  
**Conflicts of Interest:** The authors declare that there is no conflict of interests.