## 4 Modelling Assumptions  
The numerical models were developed using Seismostruct software [23], which is able to predict large displacement behavior in all elements using the fiber (i.e., infrmFB elements [23]) modeling technique, including geometric and material non-linearities.  
The fiber models of elements can accurately predict the axial and flexural responses of structural members but are not suitable for capturing the shear response. Hence, lumped shear springs were added at the ends of each link element to simulate both the elastic and plastic behavior of the short links.  
The stiffness of the shear springs is calculated as in Equation (1):  
\[K_{L1,0}=\frac{GA}{\chi\zeta} \tag{1}\]  
where \(G\) is the shear elastic modulus of the steel, \(A\) is the area of the cross-section, \(e\) is the link length, and the shear factor (\(\chi\)) used to calculate the shear area was determined in Equation (2):  
\[\chi=\frac{b\times\left(d-t_{f}\right)^{5}}{240 Ai^{4}}\times\left[15\frac{ \eta^{2}}{\zeta}+10\eta+5\eta\frac{b^{2}}{\left(d-t_{f}\right)^{2}}+2\zeta\right] \tag{2}\]  
where the following obtain:  
\(b\) is the width of the cross-section;  
\(d\) is the depth of the section;  
\(t_{f}\) is the flange thickness;  
\(i\) is the radius of gyration;  
\(\eta\) is the stiffness parameter, given by \(2\)\(t_{f}\)(\(d-t_{f}\));  
\(\zeta\) is the stiffness parameter, given by \(t_{w}\)/\(b\).  
Yield force limit was calculated as per Eurocode, taking only the shear capacity of the web, as summarized in Equation (3), while the ultimate shear capacity of the links was taken to be 50% higher than the yield force (see Equation (4)).  
\[V_{y}=0.577\times f_{y}\times A_{web} \tag{3}\]  
\[V_{u}=1.5\times V_{y} \tag{4}\]  
The post-yield stiffness was calculated such that the ultimate capacity would be reached at a plastic link rotation of 0.08 radians (see Equation (5)).  
\[K_{L1,1}=\frac{V_{u}-V_{p}}{0.08\times\frac{\epsilon}{2}\times K_{L1,0}+ \left(V_{u}-V_{p}\right)}K_{L1,0} \tag{5}\]  
The shear springs were modeled in Seismostruct using link elements as kinematic bilinear springs based on the following parameters (see Figure 3):  
(1) Initial stiffness (KL1,0).  
In addition, the reactions of the link springs drop to zero when the links reach their maximum expected shear resistance (i.e., 1.5 \(V_{p}\)).  
The Menegotto-Pinto material model, coupled with the hardening model proposed by [PERSON] et al. (2013), was used to simulate the steel's non-linear behavior. The braces were modeled with an out-of-plane camber equal to 1/1000 their working length to simulate their buckling.  
The boundary conditions of braces and beams of EBFs were assumed to be flexurally continuous. In addition, all columns were assumed to be fixed at the base.  
The diaphragm constraint was also modelled on each floor to simulate the in-plane rigidity of the slab and to connect the structure to the leaning column, where all masses and the gravity loads acting on the interior frames were applied. The leaning columns have no lateral stiffness and do not interact with the lateral stiffness of the frame.  
The static non-linear analyses were performed monitoring the link capacity; in particular, the numerical model accounts for the maximum resistance of the link in terms of both resistance and shear deformation, allowing the link element deletion, once the maximum capacity is reached during the analysis.