## 2 Materials and Methods
Listed in Table 1, they are as follows:  
* \(\overline{E}_{f}\) is the normalized modulus of elasticity of the dry fiber (_E/ff_);
* \(\overline{E}_{1}\) is the normalized uncracked modulus of elasticity of the composite (_E_1/ff_);
* \(\overline{E}_{2}\) is the normalized post-cracking modulus of the composite (_E_2/ff_);
* \(\overline{\sigma}_{\sigma}\) is the normalized first cracking strength of the mortar matrix;
* \(\varepsilon_{uf}\) is the ultimate strain of composite. The outcomes of the research by [PERSON] et al. [23] allowed us to focus on typical ranges of material properties and, as an example, the properties of a commercial system are adopted and \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\bar{E}_{f}\) & \(\bar{E}_{1}\) & \(\bar{E}_{2}\) & \(\overline{\sigma}_{\sigma}\) & \(\varepsilon_{uf}\) \\ \hline [-] & [-] & [-] & [-] & [-] \\ \hline
16.67 & 500 & 12.61 & 0.25 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Normalized parameters adopted for the analyses. Figure 5: Equilibrium of the strengthened masonry section including the effect of the mortar matrix of the composite in compression–dimensionless form. normalized. In Table 1, the normalized parameters are derived from a material, with the mechanical properties outlined in Table 2:  
* \(E_{m}\) is the modulus of elasticity of the mortar matrix;
* \(\sigma_{\sigma}\) is the homogenized first cracking in tension of the mortar matrix [23];
* \(E_{f}\) is the modulus of elasticity of the dry fiber;
* \(E_{1}\) is the uncracked modulus of elasticity of the composite homogenized to dry fiber [23] (see Figure 3);
* \(E_{2}\) is the post-uncracked modulus of elasticity of the composite homogenized to the dry fiber [23] (see Figure 3);
* \(\varepsilon_{\sigma}\) is the strain corresponding to the stress \(\sigma_{\sigma}\). Figure 6 shows the linear and bilinear behavior according to the values listed in Table 1.  
In order to have a good variability of the results, the mechanical compressed mortar matrix reinforcement the ratio (\(\omega_{m}\)) and mechanical fiber reinforcement ratio (\(\omega\)), which varied to define several p-m interaction domains. In this way, the influence the constitutive relationship of other parameters, such as the mechanical reinforcement ratios, were analyzed. Figure 7 shows the numerical results in terms of p-m interaction domains from case 1 to case 4 as the dimensionless parameters \(\omega_{m}\) and \(\omega_{f}\) change. The diagrams were grouped to fix the mechanical fiber reinforcement ratio, where \(\omega_{f}\) was equal to 5%, 10%, and 20% (Figure 7a-c, respectively). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(E_{f}\) & \(f_{f}\) & \(E_{m}\) & \(\sigma_{\sigma}\) & \(t_{f}\) & \(t_{mor}\) & \(E_{1}\) & \(E_{2}\) \\ \hline [GPa] & [MPa] & [MPa] & [MPa] & [mm] & [mm] & [GPa] & [GPa] \\ \hline
36 & 2150 & 1041 & 538 & 0.02 & 20 & 1077 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensional parameters for the analyses. Figure 6: Stress–strain constitutive relationship of composite in tension, adopted for the analyses. Figure 7: _Cont._  
In Figure 7, the comparison between the p-m interaction domains at different mechanical ratios confirmed that the contribution of the mortar matrix played a non-negligible role, as its presence greatly enhanced the axial load capacity during compression and improved the bending capacity of the strengthened cross section. The increase in flexural capacity was mainly related to the mechanical fiber reinforcement ratio \(\omega_{f}\). When \(\omega_{f}\) was relatively low (for example the diagrams in Figure 7a), in the typical working range of masonry structures with a variable p from 0 to 0.4, the increase in flexural capacity was relatively moderate if compared to the case where \(\omega_{f}\) was higher.