## 2 Materials and Methods
### Cross-Section Design
#### 2.8.3 Flexural Strength  
Considering the need to guarantee ductile failure, the minimum reinforcement \(\mathrm{A_{s,min}}\) was obtained according to Equation (9). The corresponding cracking flexural stresses (\(\mathrm{M_{cr}}\)) were computed by Equation (8). Table 6 shows the main equations and validation criteria related to the flexural behaviour of the cross-section for each structural system. Figure 9 shows the strains and stresses developed in both cross-section types assuming ULS and the simplified Bernoulli conditions for simple flexure. Figure 9: Schematics representing the simplified strains and stresses at ULS in flexure for (**a**) RC and (**b**) CS cross-sections. \begin{table}
\begin{tabular}{c c} \hline \hline \(V_{Rd}\) & \(V_{Rd,c}+V_{Rd,d}\) & (5) \\ \(V_{Rd,c}\) & \(\left[C_{Rd,c}\cdot k(100\cdot p_{l}\cdot f_{cd})\right]^{\frac{1}{2}}+k_{1}\cdot \sigma_{cp}\right]\cdot k_{w}\cdot d\) & (6) \\ \(V_{Rd,d}\) & \(A_{d}\cdot f_{yd}\) & (7) \\ \hline \hline \end{tabular} \(\mathbf{V_{Rd,c}}\)—design shear resistance of the member without shear reinforcement; \(\mathbf{V_{Rd,c}}\)—design ”shear” resistance of the longitudinal reinforcement, \(\mathbf{C_{Rd,c}}\)—coefficient of shear strength of concrete (\(0.18/\gamma_{c}\), with \(\gamma_{c}=1.5\)), \(\mathbf{r_{i}}\)—geometric ratio of longitudinal reinforcement (\(\mathrm{A_{d}}/\mathrm{b_{w}d}\)), \(\mathbf{b_{w}}\)—cross-section diameter, \(\mathbf{d}\)—effective section height, \(\mathbf{k_{i}}\)—shear behaviour coefficient, \(\mathbf{k}=1+\sqrt{(200/d)}\leq 2\), \(\sigma_{cp}\)—compressive stress of concrete due to normal forces (\(\mathrm{N_{Ed}}/\mathrm{A_{c}}<0.2f_{cd}\)), \(\mathbf{N_{Ed}}\)—axial force in the cross-section to loading, \(\mathbf{A_{c}}\)—area of concrete cross section. \(A_{st}\)—area of longitudinal steel reinforcement \(\mathbf{f_{ck}}\)—characteristic compressive strength, \(\mathbf{f_{cd}}\)—compressive failure stress of the concrete; \(\mathbf{f_{yd}}\)—design yield strength of the structural steel.  
\end{table} 
Table 5: Shear strength of the cross-section for both structural systems. The approach consisted of determining the equilibrium of the cross-section stresses that maximizes the flexural strength to verify the safety condition, \(\mathrm{M_{Rd}}>\mathrm{M_{Ed}}\). The problem was solved through the implementation of a flexural inverse analysis, which identified the critical cross-section as the one located in the proximity of the connection zone, since it shows simultaneously the minimum area and the maximum stress, as illustrated in Figure 7.  
The value of \(\mathcal{E}_{\mathrm{s}}\) was adopted to ensure the plastic regime and the optimal position of the neutral axis could be calculated. For that, the rectangular stress block for the distribution of stresses in the concrete and an elastic-perfectly plastic diagram for steel (\(\mathcal{E}_{\mathrm{cu3}}\), \(\mathcal{E}_{\mathrm{s=\infty}}\), 1 and h) were assumed. Subsequently, the required reinforcement to balance the tensile and compression forces in the cross-section was analysed, and the \(\mathrm{M_{Rd}}\) was calculated according to Equations (10) and (11). The phenomenon of cross-section steel saturation was considered, whereby an increase in \(\mathrm{A_{s}}\) does not necessarily result in a proportional increase in flexural strength due to cross-section limitations. The binary arms z, z\({}_{\mathrm{c}}\), and z\({}_{\mathrm{sc}}\) and the parameter that translates the geometric relationship between the concrete and steel cross sections and the position of the neutral axis \(\theta\) and \(\beta\) are shown in Table 6. Design assuming reinforcement in the elastic regime should be avoided, as it risks uneconomical solutions and brittle failure.