## 5 Comparisons between Numerical Analyses and Theoretical Formulations
### Strengthened Walls
Clearly, the current exploiting ratio of the fibers of FRCM reinforcement should be better assessed based on a wider database of experimental and numerical results and differentiated for FRCM typologies. As discussed in Section 1, the conventional tensile strain suggested by the Italian guidelines (CNR DT 215 2018 [26]) should be assessed by means of bond tests and by using the Young's modulus of the dry fibers. This procedure has to be applied carefully since: (1) the maximum tensile stress in a bond test is not always lower than the maximum tensile stress attained in a tensile test ([PERSON] et al., 2017 [49], [PERSON] et al., 2017 [50], [PERSON] et al., 2017 [51], [PERSON] et al., 2017 [52]), as already discussed previously, and, however, if it is lower, when it is increased by 1.5 in case of checks far from anchorage, it should never become higher; (2) the values of strain calculated by dividing the tensile stress to the Young's modulus of the dry fibers are not the same that can be read in the constitutive law of the FRCM composite material, which is markedly nonlinear due to the mortar matrix tension stiffening. Therefore, in Figure 5, the lines corresponding to the behavior of the dry fibers, i.e., depending only on their Young's modulus, are also plotted with dashed lines in order to evidence the differences in the evaluation of the strains, when the full section of the composite FRCM material, i.e., fibers + mortar, or only the section of the dry fibers is considered. Note that crossing of lines for the FRCM system made of steel cords is probably due to experimental slippage of the fibers in the mortar matrix ([PERSON] et al., 2017b [8]). Since the experimental constitutive laws of the FRCM are introduced in the FE model (Figure 2), the real behavior of the composite material (fibers + mortar) is automatically taken into account in the FE model. Based on the previous results, the shear strengths of the strengthened walls were re-evaluated using Equations (1) and (3) by updating the design values in the fibers with their effective values given by the FE analysis. Considering the graphs of Figure 5, two further cases were considered for calculating the stresses corresponding to the effective strains. Firstly, in accordance with the formulation of the Italian Guidelines, in Equation (1), the stresses were calculated by multiplying the effective strains provided by the FE analysis to the Young's modulus of the dry fibers (i.e., the stresses were read on the dashed lines of Figure 5). This procedure completely neglects the tension stiffening contribution of the mortar matrix, and the shear capacities provided in this way are indicated in Figure 6 with letter \"A\", i.e., \"Basalt A\", \"Glass A\", and \"Steel A\". Moreover, in order to have a more realistic comparison with the FE model, which considers the effective constitutive law of the FRCM materials during the numerical simulation, the total stresses in the composite were considered by including the mortar matrix contribution. Thus, in this second case, the term \(\varepsilon_{\textit{ff}}\):\(E_{\textit{f}}\) in Equation (1) was directly substituted by the tensile stress read in the constitutive laws of the FRCM systems (continuous lines in Figure 5) in correspondence of the strain attained by the in the fibers at the peak load. The shear capacities calculated according to this procedure are indicated in Figure 6 with letter \"B\", i.e., \"Basalt B\", \"Glass B\", and \"Steel B\". For both procedures, in Equation (1), the safety factor 2 was neglected, as done previously, while the coefficient \(\alpha_{\rm t}\) was assumed equal to 1, since the effective strains in the fibers were directly assessed by means of the FEM analyses.