# Seismic Retrofit of Steel Truss Bridge Using Buckling Restrained Damper
## 4 Parametric Evaluation of the BRD
### Influence of the Inclination of the BRD on the Axial Stress of the Damaged Members  
The effectiveness of the inclination of the BRD on the axial stress of the damaged member is evaluated in this section based on the model known as having an effective cross-sectional area and length. The R-BRDs are also considered so as to assess the inclination effect on the efficiency of R-BRDs. The analysis results are shown in Table 8.  
It can be observed that for the L-BRD, with the inclination of 0\({}^{\circ}\), 5\({}^{\circ}\), 10\({}^{\circ}\), and 15\({}^{\circ}\), the axial compressive stress of the damaged member is reduced by 72.2%, 73.6%, 45.0%, and 63.1%, respectively, whereas the axial tensile stress of the damaged member is decreased by 22.5%, 6.02%, 5.97%, and 6.46%, respectively, as shown in Table 8. For the R-BRD (attached near the roller support), the safety condition has not been satisfied even if the various inclination is introduced. The results indicate that the inclination is not effective on the axial stress of the damaged members for this truss bridge.  
The observation can be verified similarly to the parameters as mentioned earlier. For this purpose, the horizontal displacements at the moveable end of the damaged members, corresponding to each inclined BRD, are determined. The numerical results are compared in Table 9.  
\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}  & **R\({}_{\text{c}}\)** & **R\({}_{\text{t}}\)** & **Min.** & **Reduction by BRD** & **Min.** & **Reduction by BRD** \\ \hline Initial model & 1.305 & 1.072 & \(-\)8.468 & - & 67.525 & - \\ L-3.5-5-0\({}^{\circ}\) & 0.985 & 1.012 & \(-\)14.473 & \(-\)70.9\% & 19.177 & 71.6\% \\ L-3.5-10-0\({}^{\circ}\) & 0.724 & 1.004 & \(-\)7.867 & 7.1\% & 10.218 & 84.9\% \\ L-3.5-20-0\({}^{\circ}\) & 0.363 & 0.830 & \(-\)5.865 & 30.7\% & 4.671 & 93.1\% \\ L-3.5-30-0\({}^{\circ}\) & 0.331 & 0.780 & \(-\)3.463 & 59.1\% & 3.695 & 94.5\% \\ L-3.5-40-0\({}^{\circ}\) & 0.305 & 0.711 & \(-\)2.588 & 69.4\% & 2.827 & 95.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Influence of the cross-sectional area of the BRD yielding core on the horizontal displacement due to the earthquake.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Axial Stress, \(\sigma_{\text{idm}}\) (N/mm\({}^{2}\))**} & \multirow{2}{*}{**R\({}_{\text{c}}\)**} & **R\({}_{\text{t}}\)** \\ \cline{2-2} \cline{5-6}  & **Min.** & **Reduction by BRD** & **Max.** & **Reduction by BRD** & \\ \hline Initial model & \(-\)252.795 & - & 251.830 & - & 1.305 & 1.072 \\ L-3.5-20 - 0\({}^{\circ}\) & \(-\)70.343 & 72.2\% & 195.143 & 22.5\% & 0.363 & 0.830 \\ L-3.5-20 - 5\({}^{\circ}\) & \(-\)66.839 & 73.6\% & 236.677 & 6.02\% & 0.345 & 1.007 \\ L-3.5-20-10\({}^{\circ}\) & \(-\)139.010 & 45.0\% & 236.794 & 5.97\% & 0.718 & 1.008 \\ L-3.5-20-15\({}^{\circ}\) & \(-\)93.184 & 63.1\% & 235.561 & 6.46\% & 0.481 & 1.002 \\ \hline R-3.5-20 - 0\({}^{\circ}\) & \(-\)138.902 & 45.1\% & 237.070 & 5.9\% & 0.717 & 1.009 \\ R-3.5-20 - 5\({}^{\circ}\) & \(-\)162.732 & 35.6\% & 238.163 & 5.4\% & 0.840 & 1.013 \\ R-3.5-20-10\({}^{\circ}\) & \(-\)88.673 & 64.9\% & 235.228 & 6.6\% & 0.231 & 1.001 \\ R-3.5-20-15\({}^{\circ}\) & \(-\)66.839 & 73.6\% & 236.677 & 6.0\% & 0.345 & 1.007 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Axial stress reduction by the BRDs with an inclination.  
As can be seen from this comparison, the horizontal displacement at the moveable end of the damaged member has not been significantly decreased as the angle of inclination increases. This proves that any inclination for the design of BRDs is not effective for the retrofitting of this truss bridge.