# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 5 Analysis Results  
### Overstrength Demand  
As mentioned previously, the link overstrength factor is used to determine the design forces of non-dissipative members. The design forces of beams outside link and braces can be determined directly from the link shear force on the same story. The analysis results were used to calculate the overstrength demand by dividing the maximum link shear force by their expected shear strength, as follows:  
\[\Omega_{b,i}=\text{max}\bigg{[}\text{abs}\left(\begin{array}{c}V_{i}(t)\\ \hline R_{y}V_{n,i}\end{array}\right)\bigg{]}, \tag{10}\]  
Figure 16: Convergence process of the dynamic analysis (for B-S15B9L1): (**a**) link plastic rotation and inter-story drift; (**b**) PGA.  
where \(V_{i}\) is the shear force acting at the ends of the link (on the \(i\)th story), \(R_{y}\) is the material overstrength factor, and \(V_{n,i}\) is the nominal link shear strength (on the \(i\)th story).  
Figure 17 shows the link overstrength demand for the design of beams outside link and braces for the five-, ten-, and fifteen-story buildings. Each light-gray line depicts the overstrength demand in a single time history response; therefore, the value varies across stories. However, the maximum values in all time history responses (dark dots in Figure 17) reached 1.5 in all stories, which was expected, as the analytical link models (Figure 13) were established such that the maximum link strength was 1.5 times its yield strength. Therefore, a value of 1.5, which is equivalent to \(\Omega\) factor of 1.25 in AISC 341 [1] for the design of beams outside link and braces, is reasonable.  
However, the design axial forces of the columns should be the sum of the axial forces resulting from the overstrength of all links on the floors above. Therefore, the overstrength demands for column design, \(\Omega_{\rm c}\), were calculated based on the analysis results. The \(\Omega_{\rm c}\) value for the \(i\)th story is defined as the peak value obtained from the cumulated shear force of the upper links, normalized by the sum of their expected strengths, as follows:  
\[\Omega_{c,i}=\max\left[\text{abs}\left(\frac{\sum_{j=i}^{N_{story}}V_{j}(t)}{ R_{y}\sum_{j=i}^{N_{story}}V_{n,j}}\right)\right]. \tag{11}\]  
The results obtained using Equation (11) are shown in Figure 18, and their maximum values are listed in Table 4. The \(\Omega\) factors from AISC 341 [1] and Richards [11] are also shown as solid and dashed black lines, respectively, for comparison. It is worth noting that the \(\Omega\) factors from AISC 341 [1] and Richards [11] were scaled by multiplying them by the material overstrength factor (\(R_{y}=1.1\)) and divided by the resistance factor (\(\phi=0.9\)). Accordingly, the \(\Omega\) factor of 1.1 according to AISC 341 [1], which is typically used for tall buildings, was converted to approximately 1.34.  
As can be seen in Figure 18, the overstrength demands for column design are greater than the AISC 341 factor (\(\Omega=1.1\)) in all stories for the five-story frame and in the upper stories for the ten- and fifteen-story frames. The \(\Omega\) factors from [PERSON] [11] have a value of 1.25 for the top four stories, which appears to be reasonable compared with the analysis results. However, in the 10 th and 11 th stories of the 15-story building, the \(\Omega_{\rm c}\) demands exceeded [PERSON]'s factor. In the lower stories of the 10- and 15-story frames, the  
Figure 17: Link overstrength demands for design of beams outside link and braces: (**a**) five-story building; (**b**) ten-story building; (**c**) fifteen-story building.  
demands became significantly smaller, making the \(\Omega\) factors of both AISC 341 [1] and [PERSON] [11] appear overly conservative.