# Seismic Retrofit of Steel Truss Bridge Using Buckling Restrained Damper
## 4 Parametric Evaluation of the BRD
### Influence of the Length of the BRD Yielding Core on the Axial Stress of the Damaged Members  
The influence of the length of the BRD yielding core (L\({}_{\rm c}\)) on the axial stress of the damaged members is discussed in this section based on the model with the L-BRD. For this purpose, the ratio between the length of the yielding core and the total length of the BRD (L\({}_{\rm c}\)/Ltotal) is chosen approximately to be 0.85, 0.6, 0.3, and 0.15, and depending on these values, the variable lengths of L\({}_{\rm c}\) are given by 10.5, 7.0, 3.5 and 1.75 m, respectively. The numerical results are shown in Table 3. The hysteretic loops which correspond to each BRD parameters are shown in Figure 8a-d. For L\({}_{\rm c}\) is given by 10.5, 7.0, 3.5 and 1.75 m, the axial compressive stress is reduced by 17.9-68.0%, 23.3-72.1%, 24.5-76.6%, and 52.0-78.4%, respectively, and the axial tensile stress is also reduced by 5.1-13.8%, 5.2-21.3%, 5.6-33.7%, and 6.1-41.9%, respectively. It can be observed that the axial stress reduces as the length of the yielding core decreases. The damage may be occurred due to the length change of the members, and thus, the horizontal displacements at the moveable end of the damaged members are determined from each BRD model to verify the above observation. The horizontal displacement results are shown in Table 6.  
Table 6 compares the horizontal displacement results. For the initial model, the joint displacement in compressive direction and tensile direction due to the earthquake was determined by \(-\)8.468 and 67.525 mm, respectively. When the BRD core length, L\({}_{\rm c}\) is given by 10.5 to 1.75 m, the horizontal displacement in compressive direction is reduced by \(-\)7.4-59.3% while in the tensile direction it is reduced by 74.9-91.6%. It indicates that as the core length L\({}_{\rm c}\) reduces, the horizontal displacement at the moveable end of the damaged members is reduced. As a result, the axial stress can be significantly reduced, providing evidence that shortening the yielding part of the BRD is effective not only in reducing the horizontal displacement change at that joint but also in reducing the axial stress on the damaged members. Influence of the Length of the BRD yielding core on the horizontal displacement due to the earthquake. This section discusses the influence of the cross-sectional area of the BRD yielding core on the axial stress of the damaged members. The observation on the influence of the cross-sectional area of the yielding core of the BRD, A\({}_{\rm c}\), is made that as can be seen from the results that when L\({}_{\rm c}\) = 3.5 m and when its cross-sectional area, A\({}_{\rm c}\) is given by 5, 10, 20, 30 and 40 cm\({}^{2}\), the axial compressive stress is reduced by 24.5%, 44.5%, 72.2%, 74.7%, and 76.6%, respectively, and the axial tensile stress is decreased by 5.6%, 6.3%, 22.5%, 27.2%, and 33.7%, respectively as shown in Table 3. It indicates that as the \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\({}_{\rm c}\)** & **R\({}_{\rm t}\)** & **Min.** & **Reduction by BRD** & **Min.** & **Reduction by BRD** \\ \hline Initial model & 1.305 & 1.072 & \(-\)8.468 & - & 67.525 & - \\ L-10.5-20-0\({}^{\circ}\) & 0.853 & 1.011 & \(-\)9.097 & \(-\)7.4\% & 16.942 & 74.9\% \\ L-7.0 -20-0\({}^{\circ}\) & 0.515 & 1.006 & \(-\)8.909 & \(-\)5.2\% & 8.549 & 87.3\% \\ L-3.5 -20-0\({}^{\circ}\) & 0.363 & 0.830 & \(-\)5.865 & 30.7\% & 4.671 & 93.1\% \\ L-1.75-20-0\({}^{\circ}\) & 0.430 & 0.910 & \(-\)3.444 & 59.3\% & 5.644 & 91.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Influence of the length of the BRD yielding core on the horizontal displacement due to the earthquake. cross-sectional area of the yielding core increases, the axial stress can also be significantly reduced. Figure 8c shows the plastic behavior of each BRD.