# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 6 Proposed Overstrength Factors for Column Design  
The overstrength demands for columns (\(\Omega_{\text{c}}\)) were relatively small in the lower stories because the probability of simultaneous yielding (actually developing their full capacity) of all links in the upper stories is low. However, the current AISC 341 [1] does not account for this phenomenon, which can lead to overdesign of columns in lower stories. Therefore, an equation representing the overstrength factor for column design is proposed based on the analysis results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Five-Story Building** & **Ten-Story Building** & **Fifteen-Story Building** \\ \hline
1F & 1.345 & 1.263 & 1.120 \\ \hline
2F & 1.400 & 1.262 & 1.133 \\ \hline
3F & 1.384 & 1.257 & 1.149 \\ \hline
4F & 1.464 & 1.259 & 1.173 \\ \hline
5F & 1.500 & 1.284 & 1.187 \\ \hline
6F & & 1.325 & 1.197 \\ \hline
7F & & 1.361 & 1.219 \\ \hline
8F & & 1.406 & 1.275 \\ \hline
9F & & 1.497 & 1.306 \\ \hline
10F & & 1.500 & 1.359 \\ \hline
11F & & & 1.407 \\ \hline
12F & & & 1.421 \\ \hline
13F & & & 1.453 \\ \hline
14F & & & 1.479 \\ \hline
15F & & & 1.500 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Maximum demands of \(\Omega_{\text{c}}\).  
Figure 18: \(\Omega_{\text{c}}\) factor from nonlinear dynamic analysis results: (**a**) five-story building; (**b**) ten-story building; (**c**) fifteen-story building.  
First, the effects of SDC, bay width, and link span ratio on the overstrength demands were investigated, and the results are shown in Figure 19. As can be seen, the maximum demand does not show significant differences despite differences in the design variables.  
From the regression analyses of the maximum overstrength demand shown in Figure 18 and Table 4, an equation for \(\Omega_{\mathrm{c}}\) was proposed as follows:  
\[\Omega_{c,i}=1.50-0.025\big{(}N_{story}-i\big{)}\geq 1.15, \tag{12}\]  
where \(N_{story}\) is the number of stories and \(i\) is the column location.  
Figure 20 compares the \(\Omega_{\mathrm{c}}\) factors from the proposed equation with the maximum demands from the analysis results. As can be seen, the \(\Omega_{\mathrm{c}}\) demands decrease almost linearly from the top to the bottom stories. As the slopes of the regression equation results for the five-, ten-, and fifteen-story frames were similar, a constant slope was used in the equation regardless of the number of stories. A lower bound, similar to the minimum value in Table 4, was set to prevent excessively small values in high-rise buildings.  
To validate the proposed equation, a new set of example buildings was generated. New \(\Omega_{\mathrm{c}}\) factors multiplied by \(R_{y}/\phi\) instead of the AISC factor were applied and similar nonlinear analyses as those described in Section 4 were performed. Figure 21a shows the structural quantities for the performance group of D-S15B  
Figure 19: Effects of the SDC, bay width, and link span ratio on \(\Omega_{\mathrm{c}}\): (**a**) SDC B and D; (**b**) bay width (6, 9, and 12 m); (**c**) link span ratio (10%, 30%, and 50%).  
designed using the proposed equation, the structural quantities averaged for 100 example buildings was 140.8 tons, which is 18.9% and 14.3% lower than those obtained using the AISC 341 [1] and Richards [11] equations, respectively. Figure 21b shows the DCR values of the EBF members designed using the proposed equation based on the dynamic analysis results. As shown in the figure, the DCRs of the members did not exceed unity, indicating that yielding of any non-dissipative members did not occur. Consequently, by using the proposed \(\Omega_{c}\) factors, the structural quantities of the EBF system were reduced while satisfying the capacity design principle.