## 5 Equal Yielding Strength Analysis  
According to the above analysis, designing by using one-variable analysis is relatively simple, but the yielding strengths of the YSDs at each location are often unequal, which means various specifications of YSDs are needed. Meanwhile, the system switch actually demonstrates the effectiveness of the YSDs is according to the delay of the period of the post-yielding dominant transversal mode, which restrains the girder displacement after yielding. Therefore, an equal yielding strength, which means \(\mathrm{F_{ya}}=\mathrm{F_{yp}}=\mathrm{F_{yt}}\) may be reasonable for engineering practice. Additionally, the calculated cases were greatly reduced from 441 to 5. Figure 24 and Table 6 show that the RCD can be large and uniform when the yielding strength is 3000 kN, and the RD can be small and uniform when the yielding strength is 2000 kN. Compared with Table 3, the equal yielding strength can also achieve a significant effect in terms of reducing the seismic responses of the bridge in terms of RCD or RD. RD values are reduced by 59% \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bridge** & **YSD Layout** & **RCD of** & **RCD of** & **RCD of** & **RD of** & **RD of** & **RD of** & **Tower** & **Mid-Span** \\
**System** & **Plan** & **Tower** & **TP** & **AP** & **Tower** & **TP** & **AP** & **TD** & **Lateral Drift** \\ \hline \multirow{3}{*}{A} & Without & \multirow{3}{*}{0.59} & \multirow{3}{*}{2.04} & \multirow{3}{*}{1.99} & \multirow{3}{*}{0} & \multirow{3}{*}{417} & \multirow{3}{*}{235} & \multirow{3}{*}{173} & \multirow{3}{*}{515} \\  & YSDs & & & & & & & & & \\ \cline{1-1} \cline{6-10}  & Designed & \multirow{3}{*}{1.24} & \multirow{3}{*}{1.30} & \multirow{3}{*}{1.44} & \multirow{3}{*}{124} & \multirow{3}{*}{130} & \multirow{3}{*}{80} & \multirow{3}{*}{164} & \multirow{3}{*}{198} \\ B & layout 5 & & & & & & & & \\ \cline{1-1} \cline{6-10}  & Designed & \multirow{3}{*}{1.28} & \multirow{3}{*}{1.70} & \multirow{3}{*}{1.66} & \multirow{3}{*}{189} & \multirow{3}{*}{170} & \multirow{3}{*}{152} & \multirow{3}{*}{165} & \multirow{3}{*}{245} \\  & layout 6 & & & & & & & & & \\ \hline \hline \end{tabular} Note: TP means the transition pier, AP means the auxiliary pier, and TD means top drift. Designed layout 5: \(\mathrm{F_{ya}}=3000\) kN, \(\mathrm{F_{yp}}=3000\) kN and \(\mathrm{F_{yt}}=3000\) kN (designed for a large and uniform RCD), designed layout 6: \(\mathrm{F_{ya}}=2000\) kN, \(\mathrm{F_{yp}}=2000\) kN and \(\mathrm{F_{yt}}=2000\) kN (designed for a small and uniform RD).  
\end{table} 
Table 6: Key response comparison (Units: mm). Figure 24: Seismic responses with varying \(\mathrm{F_{y}}\). (**a**) Relative displacement; (**b**) ratio of capacity to demand. and 35% at the transition pier and auxiliary pier for layout 6, respectively, whereas they are reduced by 68% and 44% for layout 4. Meanwhile, the RCD of the tower column increases to around 1.25 from 0.59 for both layouts 5 and 6, which agrees well with the results of the layouts 1 and 3 by comprehensive multi-variable and one-variable analysis in Table 3. Remembering layout 3 in Table 3, \(\text{Fy}_{\text{t}}=2000\) kN is also the designed result by single-variable analysis in terms of RCD at the tower-girder location, and so layout 6 is preferable. In fact, the yielding strength of YSDs is closely related to the mass of the superstructure, so the approximate yielding strength can be quickly determined according to the mass of the superstructure. The results (Figure 25 and Table 7) show that there is an approximately constant ratio relationship between the total yielding strength of YSDs and the weight of the superstructure, at around 10%. Therefore, in the preliminary analysis, the yielding strength of YSD can be determined by the weight of the superstructure, and the RCD is large and uniform or the RD is small and uniform. At this time, the calculated cases were greatly reduced from 5 to 1, which greatly improves the efficiency of bridge design.