# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 3 Design of Example Buildings  
### Overview  
Figure 8 shows the plan and elevation views of the example building. The example building has a plan consisting of \(3\times 5\) modules, with each unit having a square shape of 6 m \(\times\) 6 m. All stories are 4 m in height. The K-braced EBF is located at the center of the exterior frame along the \(x\)-axis in all stories, as shown in Figure 8a. The beams, braces, and columns in the EBF are rigidly connected to one another. To ensure that the seismic load is resisted by the EBF only, the beams in the spans on either side of the EBF were hinge-connected to the columns. The effective seismic weight corresponding to 1.0 DL + 0.25 LL was considered in the analysis model. The red squares in Figure 8b represent the nodes where mass was assigned. In the \(y\)-axis direction, a moment-resisting frame was employed as the lateral-force-resisting system, which is not considered in this study. The example buildings were assumed to be located in Seoul, South Korea, where the effective ground acceleration, S, is 0.176 g. The seismic design coefficients of the EBF system according to the KDS (Korea Design Standard) [18] (\(R=8\); \(\Omega_{0}=2\); \(C_{d}=4\)) were applied. The design member forces of the link members were determined via response spectrum analysis. Various design conditions were considered, including the seismic design categories, height, width, and link length of the frames. Two site conditions of site classes A (hard rock) and D (stiff soil) were considered, resulting in two seismic design categories (SDCs), B and D, respectively. Furthermore, three building heights (5, 10, and 15 stories), three bay widths (6, 9, and 12 m), and three link span ratios (10%, 30%, and 50%) were considered. The variations in the design conditions are summarized into 54 performance groups and identified using the notation shown in Figure 9.  
Figure 6: Allowable rotation angle according to the link length ratio. Figure 7: Deformed shape of a K-braced EBF. SM355 steel with a yield strength of 355 MPa was used for the columns, beams, and braces. It was assumed that the links had a constant length throughout the building height and the same cross section as the adjacent beams outside the links. W-shaped sections from the KS D 3502 section table [19] were used, and the members were grouped as listed in Table 1. The example building design in each performance group was facilitated by a multi-objective optimization technique described in detail in the next section. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Stories**} & \multirow{2}{*}{**Member**} & \multicolumn{10}{c}{**Level (Floor)**} \\ \cline{2-13}  & & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline \multirow{3}{*}{5} & Column & \multicolumn{2}{c}{C1} & \multicolumn{2}{c}{C2} & \multicolumn{2}{c}{C3} & & & & & & & & & & \\ \cline{2-13}  & Beam & Bm1 & Bm2 & Bm3 & Bm4 & Bm5 & & & & & & & & & & \\ \cline{2-13}  & Brace & Br1 & \multicolumn{2}{c}{Br2} & \multicolumn{2}{c}{Br3} & & & & & & & & & & & \\ \hline \multirow{3}{*}{10} & Column & \multicolumn{2}{c}{C1} & \multicolumn{2}{c}{C2} & \multicolumn{2}{c}{C3} & \multicolumn{2}{c}{C4} & & & & & & & & & \\ \cline{2-13}  & Beam & Bm1 & Bm2 & Bm3 & Bm4 & Bm5 & & & & & & & & & & \\ \cline{2-13}  & Brace & Br1 & \multicolumn{2}{c}{Br2} & \multicolumn{2}{c}{Br3} & \multicolumn{2}{c}{Br4} & & & & & & & & & \\ \hline \multirow{3}{*}{15} & Column & \multicolumn{2}{c}{C1} & \multicolumn{2}{c}{C2} & \multicolumn{2}{c}{C3} & \multicolumn{2}{c}{C4} & \multicolumn{2}{c}{C5} \\ \cline{2-13}  & Beam & Bm1 & \multicolumn{2}{c}{Bm2} & \multicolumn{2}{c}{Bm3} & \multicolumn{2}{c}{Bm4} & & & & & & & & \\ \cline{2-13}  & Brace & Br1 & \multicolumn{2}{c}{Br2} & \multicolumn{2}{c}{Br3} & \multicolumn{2}{c}{Br4} & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Member grouping of the example buildings.