## 4 Case Study  
The proposed design procedure has been applied to design a 4-storey and an 8-storey residential building endowed with braces in the chevron configuration. The plan layout of the buildings is shown in Figure 1. The length \(L\) of each bay is equal to 8.0 m, whereas the interstorey height \(h\) is equal to 4.0 m. The buildings stand on stiff soil (soil A according to EC8) and are located in a seismic area with a peak ground acceleration (\(a_{\text{g}}\)) equal to 0.15 g. Based on the values of \(a_{\text{g}}\) provided by the National Institute of Geophysics and Volcanology (IGNV [26]), this value is larger than that expected for seismic events with a probability of exceedance of 10% in 50 years in the 73.1% of the entire Italian territory. The seismic loads are entirely resisted by the braced bays that are located in the central span of the perimetric frames. Beams and columns denoted as G-B and G-C in Figure 1 are designed to sustain gravity loads only. Geometric and mass properties are assumed to be equal at all storeys. The characteristic values of gravity dead (\(g_{\text{k}}\)) and live (\(q_{\text{k}}\)) loads are equal to 4.4 kN/m\({}^{2}\) and 2.0 kN/m\({}^{2}\), respectively. Specifically, the dead load was derived assuming that the weight of the collaborating steel sheet is equal to 1.91 kN/m\({}^{2}\), the weight of the suspended ceilings is equal to 0.40 kN/m\({}^{2}\), the weight of screed is equal to 0.84 kN/m\({}^{2}\), the weight of the floor porcelain stoneware is equal to 0.44 kN/m\({}^{2}\) and the weight of the internal partitions is equal to 0.8 kN/m\({}^{2}\). The characteristic value of the live load is that given in Eurocode 1 [27] for category of use type A (areas for residential activities). Gravity loads in the seismic design situation (\(g_{\text{k}}+\psi_{2}q_{\text{k}}\)) are equal to 5.0 kN/m\({}^{2}\). Internal forces are determined by means of a modal response spectrum analysis. To optimize the design, an iterative procedure is adopted. HSS cross-sections with steel grade S355 (characteristic value of yield stress \(f_{y}\) equal to 355 MPa) are used for the braces and wide flange cross-sections are used for the braced beams (HEA with steel grade S235) and columns (HEB, HEM with steel grade S235, S275 or S355). IPE cross-sections are used for the beams designed to sustain gravity loads. The considered structures were designed according to the proposed design procedure assuming a value of \(k=\delta_{\text{b}}/\delta_{\text{u}}\) in the range from 0.2 (stiff beam) to 1.8 (flexible beam), in step of 0.4. The obtained structures are named k02, k06, k10, k14 and k18. For the sake of comparison, the same structures also were designed according to the design  
Figure 1: Layout of the considered structures. procedure stipulated in EC8 in accordance with the conventional approach of the buckling-brace/yielding-brace plastic mechanism (Q2.5 case study) or in accordance with the non-dissipative approach with all members in the elastic range of behaviour. In this latter case, a behaviour factor equal to 1.0 (Q1.0 case study) or to 1.5 (Q1.5 case study) was used. To evaluate the impact of the value of \(k\) on the designed structures, the structural costs of the braces, braced beams and braced columns were determined for the 4-storey and 8-storey structures and plotted in Figure 2a,b, respectively. In the same figures, the structural costs of the EC8 designed frames Q1.0, Q1.5 and Q2.5 are also reported. The Sicilia region's official price list [28] was taken as a reference to evaluate the unit prices. In particular, in the case of H-shaped cross-sections, the unit price is equal to 3.53 \(\upxi\)/kg for steel grade S235 or S275 and 3.73 \(\upxi\)/kg for S355; in case of hollow cross-sections, the unit price is equal to 6.43 \(\upxi\)/kg for steel S235 or S275 and 6.74 \(\upxi\)/kg for S355. Regarding the structures designed according to the proposed criterion, the figure shows that the smaller the value of \(k\), the greater the structural costs of the braced beams.