# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 4 Structural Analysis
### Nonlinear Dynamic Analysis  
In the nonlinear dynamic analysis, ten earthquake records, consisting of five historical and five artificial earthquake records, were used for each SDC (Figure 15). The selected historical earthquakes are listed in Table 3. For artificial earthquakes, EqMaker [31] was used to generate the time histories for SDC B and D, with the relevant parameters specified in the KDS.  
The purpose of the nonlinear time history analyses is to capture the limit state of each structure and investigate the overstrength demand for the links. The link plastic rotation and story drift were chosen as the engineering demand parameters describing the state of the structure. In this study, a numerical technique based on the line search  
Figure 15: Spectral accelerations of the selected earthquakes: (**a**) SDC B; (**b**) SDC D.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SDC** & **Event** & **Station** & **Year** & **Magnitude** \\ \hline \multirow{6}{*}{B} & Superstition Hills & Poe Road (temp) & 1987 & 6.5 \\ \cline{2-5}  & Duzce, Turkey & Bolu & 1999 & 7.1 \\ \cline{2-5}  & San Fernando & LA—Hollywood Stor & 1971 & 6.6 \\ \cline{2-5}  & Imperial Valley & El Centro Array \#11 & 1979 & 6.5 \\ \cline{2-5}  & Manjil, Iran & Abbar & 1990 & 7.4 \\ \hline \multirow{6}{*}{D} & Landers & Yermo Fire Station & 1992 & 7.3 \\ \cline{2-5}  & Kocaeli, Turkey & Arcelik & 1999 & 7.5 \\ \cline{1-1} \cline{2-5}  & Kobe, Japan & Shin-Osaka & 1995 & 6.9 \\ \cline{1-1} \cline{2-5}  & Loma Prieta & Gilroy Array \#3 & 1989 & 6.9 \\ \cline{1-1} \cline{2-5}  & Northridge & Canyon Country-WLC & 1994 & 6.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: List of historical earthquakes.  
was used to minimize the number of nonlinear analyses required to reach the limit state. The nonlinear time history analysis was repeated with different scaling factors until the condition specified in Equation (9) was satisfied. In Equation (9), the first and second terms in the parentheses indicate the criteria for link rotation and inter-story drift, respectively.  
\[1.00<\text{Max}\left(\frac{\theta_{p,max}}{\theta_{pa}},\frac{\Delta_{max}}{ \Delta_{a}}\right)<1.01, \tag{9}\]  
where \(\theta_{p,max}\) is the maximum link plastic rotation angle in the response history and \(\theta_{pa}\) is the allowable plastic rotation specified in AISC 341 [1]. Similarly, \(\Delta_{max}\) is the maximum inter-story drift in the response histories and \(\Delta_{a}\) is the allowable inter-story drift corresponding to the collapse prevention level for braced frames as defined in FEMA 356 [32].  
Figure 16 illustrates the progress of iterations in the dynamic analysis using the line search method in the case of B-S15B2L1 as an example. An initial guess of 0.5 g was chosen for the maximum PGA (peak ground acceleration). After the first iteration, the PGA for the second iteration was determined based on the maximum link plastic rotation or the story drift recorded in the first iteration. As shown in Figure 16, the link plastic rotation was the dominant parameter rather than the inter-story drift, and the structure reached its limit state after six iterations.  
The overall procedure is similar to that of the incremental dynamic analysis (IDA), which is commonly used to assess the seismic performance of structures [33]. However, unlike IDA, the PGA value corresponding to collapse is not considered important in this study. The aim of the analyses is to capture the limit state of the structure for a given time history record and investigate the DCR distribution throughout the structure to determine the link overstrength demand, as described next.