# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 7 Conclusions  
In EBFs, inelastic deformation owing to seismic loads is only permitted in the links. The remaining structural members, such as columns, beams outside link, and braces, are called non-dissipative members and are designed using the capacity design concept so that they remain elastic even when the links are fully yielded and strain-hardened. For this purpose, the link overstrength factor, \(\Omega\), is used in the design of non-dissipative members,  
Figure 21: Performance of the EBFs designed using the proposed equation (D-S15B9L1): (**a**) objective space of the design examples; (**b**) maximum DCRs of the member groups. Figure 20: Performance of the EBFs designed using the proposed equation (D-S15B9L1): (**a**) five-story building; (**b**) ten-story building; (**c**) fifteen-story building. and is defined as the ratio of the ultimate shear strength of a link to its expected strength. AISC 341 specifies a value of 1.1 for the \(\Omega\) factors of links for column design regardless of the number of stories. However, as the number of stories increases, the probability of simultaneous yielding decreases, and the axial force of columns in tall buildings may be overestimated. In this study, the relevance of the current \(\Omega\) factor for EBF systems was investigated through nonlinear analyses of example buildings. A sufficient number of example buildings was used to include the influence of variability owing to design conditions and designer preferences. Various design conditions were considered, including different seismic design categories (SDC B and D), building heights (5, 10, or 15 stories), bay widths (6, 9, or 12 m), and link lengths (10%, 30%, and 50% of the bay width), which resulted in 54 performance groups. Additionally, to account for the variability in member selection due to designer preferences, multiple design alternatives were included in the example buildings under the same performance group. An automated design algorithm based on a multi-objective optimization technique was applied to generate multiple design alternatives. A total of 471 example buildings were generated and used for nonlinear dynamic analysis to evaluate \(\Omega\) factors. In the nonlinear model, two types of zero-length spring elements were positioned at the link ends to simulate the inelastic behavior in shear and flexure. In the nonlinear time history analyses, an iterative method was used to accurately capture the limit state of the structure. The distribution of demand-to-capacity ratios (DCRs) throughout the structure was investigated to determine the link overstrength demand. The results indicated that it is reasonable to use the current \(\Omega\) factor for beam outside link and brace design; however, the current \(\Omega\) factor leads to an overestimation of axial force in columns, especially in the lower stories of tall buildings. Through regression analysis, a new \(\Omega\) factor equation for column design was proposed. It was demonstrated that the structural quantities of the 15-story frames designed using the proposed equation were reduced by an average of 19% compared to those designed using the current \(\Omega\) factor. Conceptualization, Y.H. and E.Y. ; methodology, Y.H. ; software, Y.H. ; validation, Y.H. ; formal analysis, Y.H. ; investigation, Y.H. and E.Y. ; resources, Y.H. ; data curation, Y.H. ; writing--original draft preparation, Y.H. ; writing--review and editing, E.Y. ; visualization, Y.H. ; supervision, E.Y. ; project administration, E.Y. ; funding acquisition, E.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by a grant (2022-MOIS63-003(RS-2022-ND641021)) of Cooperative Research Methods and Safety Management Technology in National Disasters funded by the Ministry of Interior and Safety (MOIS, Republic of Korea). Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.