# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 1 Introduction  
Eccentrically braced frames (EBFs) are lateral-force-resisting systems in which two braces are connected to a beam with an offset. The short segment of the beam between the connection points and braces, which is referred to as the link, is subjected to significant shear forces and moments. In EBFs, since yielding and energy dissipation are expected to occur only at the links, the links are the key members controlling the inelastic behavior of the system. Short links tend to yield due to shear, whereas long links tend to yield by flexure. The yield strength and deformation capacity of a link depend on whether it yields by shear or flexure. The remaining structural members, such as columns, beams outside the link, and braces, are referred to as non-dissipative members because they are expected to remain elastic even when the links reach their ultimate strength owing to material overstrength and strain-hardening effects. AISC 341 [1] requires that the design member force of non-dissipative members be determined by considering the capacity-limited seismic load effect, which is the member force that occurs when the links develop their ultimate strength. For this purpose, the link overstrength factor (or strain-hardening factor), \(\Omega\), is used, which is defined as the ratio of ultimate shear strength to expected yield strength of a link [2], as follows:  
\[\Omega=\frac{V_{u}}{R_{y}V_{u}}, \tag{1}\]  
where \(V_{u}\) is the ultimate shear strength, \(R_{y}\) is the material overstrength factor, and \(V_{u}\) is the nominal shear strength factor of a link. Several researchers have conducted studies to determine the \(\Omega\) factor of links. [PERSON] and [PERSON] [3] and [PERSON] et al. [4] conducted experimental studies using ASTM A992 wide flange sections (W-sections), obtaining \(\Omega\) factors of up to 1.4. They found that \(\Omega\) factor decreased as the link became slenderer. [PERSON] and [PERSON] [2] collected \(\Omega\) factors of W-section links from previous experimental studies, as shown in Figure 1. As shown in the figure, the \(\Omega\) factor of short links (\(\rho<1.0\)) was greater than 1.5, while that of intermediate links (\(\rho\approx 2\)) appears to be less than 1.5. For long links, \(\Omega\) = 1.5 can be considered a reasonable upper bound. [PERSON] and [PERSON] [5] and [PERSON] and [PERSON] [6] proposed an \(\Omega\) value of 1.5 for design purposes. The previous versions of the National Earthquake Hazards Reduction Program (NEHRP) [7] and AISC [8] used a value of 1.5 regardless of link length. Currently, AISC 341 [1] specifies a value of 1.25 for \(\Omega\) factor. As the nominal strength and resistance factor are used in structural design, the effective \(\Omega\) factor becomes 1.53 (\(1.25R_{y}/\phi\) = 1.25 \(\times\) 1.1/0.9), which is close to the experimentally obtained value of 1.5. The design member forces of beams outside links and braces were determined by the force developed when the adjacent links on the same floor reach their ultimate strength. For columns, the design axial force should be the sum of the axial forces resulting from the overstrength of all links above the floor. However, not all links in a multi-story EBF develop their ultimate overstrength simultaneously. In light of this, AISC 341 [1] allows for a reduced \(\Omega\) factor of 1.1 for column design in tall buildings. Previous experimental and analytical studies have investigated the degree of simultaneous yielding in links. [PERSON] et al. [9] performed shaking table tests on six-story EBF models and concluded that the possibility of the simultaneous yielding in all links was very low. [PERSON] and [PERSON] [10] performed time history analyses on eight- and sixteen-story K-braced EBFs, demonstrating that the links on upper stories frequently yielded simultaneously, and that using a factor of 1.25 for the \(\Omega\) factor would underestimate the axial forces of the upper floor columns.