# Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames
## 2 Overview of EBF Systems  
An EBF system comprises columns, braces, and beams, which are further divided into links and beams outside link. Figure 2 shows the plastic mechanism of a K-braced EBF, which is one of the most popular EBF systems. The design of an EBF system begins with the selection of link members, since the ultimate shear strength of the link affects the remaining non-dissipative members according to the capacity design concept. AISC 341 [1] specifies that the overstrength of links is basically 1.25 times the expected strength. However, for beams with floor slabs and columns in tall buildings, the overstrength factor can be reduced to 1.1 to account for the contribution of slabs to the yield strength and to account for the low possibility that all links above the story will yield simultaneously, respectively. The yielding behavior and deformation capacity of a link depend on its length. Shorter links tend to be governed by shear yielding, while longer links tend to be governed by flexural yielding. Thus, shorter links provide greater strength and a larger inelastic deformation capacity, whereas long links have the advantage of being able to freely place openings. In a K-braced frame, when the link is placed at the center of the bay, the moments at both ends of the link are identical. The relationship between shear force (\(V\)), end moment (\(M\)), and link length (\(e\)) can be represented by a simple equilibrium equation (see Figure 3), as follows:  
\[e=\frac{2M}{V}, \tag{2}\]  
Most design codes, including AISC 341 [1], SEAOC [13], and Eurocode 8 [14], classify links into three categories: \"Short links\" have a length ratio (\(\rho\)), as defined in Equation (3), of 1.6 or less; \"long links\" have a length ratio of 2.6 or more, as shown in Figure 4; and links in between are classified as \"intermediate links\", where the interaction between shear and moment is expected in the plastic range. In short links, energy dissipation occurs mainly  
Figure 2: Plastic mechanism of a K-braced EBF. through the inelastic shear behavior of the link web. However, in long links, energy is dissipated mainly via plastic hinge formation at both ends of the link flanges. \[\rho=\frac{e}{M_{p}/V_{p}}, \tag{3}\]  
where \(M_{p}\) and \(V_{p}\) are the link plastic moment and plastic shear strengths, respectively. AIGC 341 [1] states that when the ratio of axial force to the nominal yield strength (=\(P/P_{y}\)) is greater than 15%, the link length should be limited to prevent flange buckling; accordingly, the nominal strength is also reduced. However, for K-breaced EBF systems, the effect of the axial force on the link is negligible because the horizontal component of the trace force is completely transmitted to the beam outside link in the form of an axial force [15; 16]. The link's nominal shear strength (\(V_{n}\)), excluding the effect of axial forces, is defined as follows:  
\[V_{n}=\min\left(V_{p}\,\ \frac{2M_{p}}{e}\right), \tag{4a}\] \[V_{p}=0.6F_{y}A_{w},\] (4b) \[M_{p}=F_{y}Z, \tag{4c}\]  
where \(F_{y}\) denotes the specified minimum yield strength, \(Z\) is the plastic section modulus, and \(A_{w}\) is the web area of the link section. [PERSON] and [PERSON] [17] elucidated the correlation between \(\rho\) and the ultimate shear capacity of links using an M-V interaction curve. He suggested that the maximum shear and flexural strength were \(1.5V_{p}\) and \(1.5M_{p}\), respectively. A modification of [PERSON]'s M-V interaction model is represented in Equation (5), which is used to relate the link length and overstrength factor due to shear alone. The overstrength factor resulting from the shear behavior is designated as \(\Omega_{p}\) and plotted as a red line in Figure 5. Similarly, the M-V interaction model was modified in a different manner, as in Equation (6), to demonstrate the relationship between link length and the overstrength factor in terms of moment.