## 2 Seismic Design of Steel Chevron-Braced Frames in Literature  
### Conventional Approach with a Buckling-Brace/Yielding-Brace Plastic Mechanism  
The most common approach for the design of chevron-braced frames assumes that the inelastic response should be limited to the braces [16; 17; 18; 19]. Based on this concept, braces are designed to sustain the internal forces determined by the selected elastic method of analysis, so as to provide an almost uniform distribution of overstrength along the height of the building, whereas beams and columns are designed according to the capacity design principle. Design procedures suggested in the literature or seismic codes, however, differ because of the recommended behaviour factor, because of the definition of the lateral storey strength provided by the braces and because of the rules for the application of design capacity principles. Eurocode 8 (EC8) [16] requires that the axial forces determined by the design method of analysis in beams and columns be incremented by a scaling factor equal to \(1.1~{}\gamma_{\text{ov}}~{}\Omega_{\text{min}}\). This scaling factor takes into account the overstrength and the hardening of steel (\(1.1~{}\gamma_{\text{ov}}\)) and the minimum overstrength of the braces (\(\Omega_{\text{min}}\)). This latter overstrength is defined as the minimum ratio of the buckling resistance to the axial force of braces among all storeys of the building. In addition, the braced beam, i.e., the beam where the chevron braces meet, has to sustain the bending moment produced by the unbalanced vertical force transmitted at midspan by the braces when the brace in compression is in the post-buckling range of behaviour and the brace in tension has yielded. Since beams and columns are designed according to the capacity design, no specific requirement is provided to guarantee a ductile behaviour of these members. Unfortunately, research studies [20; 21] have proved that these simplified rules for the application of capacity design principles reported in Eurocode 8 are not effective in preventing the buckling of columns and yielding of the braced beams. To estimate the axial forces in columns more accurately, [PERSON] [22] proposed to evaluate these internal forces by equilibrium conditions based on two different design situations. In the first situation, axial forces in compressed braces are supposed to be equal to the buckling resistance, while the braces in tension have not yielded yet; in the second situation, braces in tension have yielded and are fully hardened, whereas braces in compression are in the post-buckling range of behaviour. According to [PERSON] et al. [18], the braces of the top storey should be designed to perform in the elastic range of behaviour. Owing to this, the top storey can act as an outrigger system, giving the building a \"shear type\" displacement profile. Columns are designed to resist the internal forces derived by two combinations of axial forces in braces. In the first combination, the axial forces are calculated according to EC8. However, differently from EC8, the minimum overstrength of the braces is calculated based on the plastic resistance of braces rather than on the buckling resistance. In the second combination, axial forces are calculated via equilibrium conditions, assuming that the braces in tension have yielded and the braces in compression are in their post-buckling range of behaviour. Moreover, in this latter combination, columns are assumed to be subjected to a bending moment equal to \(20\%\) of the plastic flexural resistance of the cross sections. Finally, to promote a more dissipative behaviour of braces, a beam stiffness requirement is proposed, suggesting that the beam-to-brace stiffness ratio should be greater than \(0.2\). [PERSON] et al. [19] showed that the lateral torsional buckling of columns was the predominant failure mode of concentrically braced frames designed by the abovementioned procedures because of the underestimation of the bending moment in columns.