## 2 Investigated Buildings  
Three buildings were designed with the same plan layout but also varying the number of stories between 2, 4, and 8. The story height was set as a constant, and equal to 4 m. The number of bays in the X and Y directions is 3, each 8 m long (see Figure 1). Figure 1: _Cont._  
The lateral load-resisting frames in each direction are arranged to achieve independent structural behavior in the X and Y directions, as depicted in Figure 1.  
The moment-resisting frames and eccentrically braced frames were designed according to EN1998-1 [20] and EN1993-1-1 [21]. The design behavior factor (q) was assumed to be equal to 6, as this is the maximum recommended value for the EBFs systems. The dead and live vertical loads were assumed to be equal to 5 and 2 \(\mathrm{kN/m^{2}}\) at each story. A peak ground acceleration (PGA) equal to 0.2 g, considering soil type C, and a damping ratio equal to 2% were assumed. According to EN1998-1-1 [20], in the seismic design, the torsional effects were taken into account by magnifying the seismic demand through the factor \(\delta\), assumed to be equal to 1.3. Steel of S355 grade was selected for all elements. Figure 1: Plan, side, and 3d views of the investigated structures ((**a–c**), respectively). The EBFs were designed according to DCH concept [20], in order to enforce the dissipation of the seismic energy through shear plastic hinges in the links. According to [20], the formation of a global plastic mode of EBFs is guaranteed if the link overstrength ratios \(\Omega_{i}=1.5\ V_{p,link,i}/V_{E,d,i}\) (where \(V_{\text{p,link,i}}\) is the shear plastic strength of the i-th link, and \(V_{\text{E,d,i}}\) is the corresponding shear force demand) are sufficiently uniform along the building height; namely, the maximum ratio does not exceed 1.25 times the minimum value \(\Omega\). The MRFs of the dual configurations were designed in order to resist the complementary seismic effects corresponding to the full development of the plastic mode in the EBFs. In this regard, to estimate the design in dual frames, the two subsystems (MRF and EBF) were fictitiously decoupled. Indeed, as long as the EBFs are elastic, the MRFs can only take a minor amount of the seismic forces. In particular, the braced parts of both dual systems were designed to resist 75% of the design lateral forces, as indicated by AISC341-22 [22]. However, differently from the North American approach, the MRF zones were not designed to resist the complementary 25% of the design forces, but to resist at least 25% of the plastic lateral strength at each story \"i\", thus complying with \(V_{MRF,i}\geq 0.25V_{Dual,i}\), where \(V_{\text{Dual,i}}\) is the overall lateral strength, which was estimated as \(V_{Dual,i}=\frac{1}{0.75}V_{EBF,i}=\frac{1}{0.75}\ \frac{1.5V_{P,link,i}\cdot L}{B_{i}}\), where \(V_{EBF,i}\) is the lateral strength value of the EBF part, \(L\) is the span length of the ray containing the link, and \(h_{\text{i}}\) is the inter-story height. This approach leads to larger design forces for the MRF parts than those obtained using 25% of the design force from the reduced response spectrum. Each building was designed three times, changing the structural system as follows: (i) the first set was designed using only EBFs with short links as lateral load resisting systems, placed in the middle of the structures and identified hereinafter as GEG (i.e., gravity frames, eccentric frames, and gravity frames); (ii) the second set of structures was designed by placing the MRF in a single adjacent bay to the EBF, and it was named MEG (i.e., moment resisting frames, eccentric frames, and gravity frames); (iii) the third set of structures was designed by placing two MRFs adjacent to the EBF and was referred to as MEM (i.e., moment resisting frames, eccentric frames and moment resisting frames).