## 4 Summary of FE Analyses
### Strengthened Walls  
The analyses on in-plane strengthened walls were aimed to check the effectiveness of three types of FRCM systems (basalt and glass grids, steel cords) as the mechanical properties of the masonry substrates change (i.e., tensile and compressive strength, fracture energy in tension). In all the cases, a balanced grid was assumed embedded in a cement-based mortar with thickness of 10 mm at each side of the masonry wall. The FRCM reinforcement was, indeed, modeled by shell elements as a simplified homogeneous material considering both the contribution of the fibers and of the inorganic mortar in the constitutive behavior in tension. The real geometrical \"grid\" configuration of the reinforcement was not modeled ([PERSON] et al., 2019 [15]), and it was considered perfectly bonded to the masonry substrate, since several experimental bond tests ([PERSON] et al., 2017a [7], [PERSON] et al., 2017b [8]) evidenced that debonding from the substrate rarely occurs for such materials. Figure 2 shows the experimental constitutive laws in tension of the three types of FRCM systems, i.e., a two-directional mesh made of basalt or glass fibers and a fabric made of unidirectional stainless-steel cords, used in the numerical simulations. The relations refer to the tensile stresses calculated in the whole composite cross section (grout + fibers) and are the average experimental ones obtained in tensile tests carried out on FRCM coupons (10 for each type of FRCM system) adopting the clamping-grip method by [PERSON] et al., 2017a [7]. Note that the average curves are stopped at the minimum tensile strain attained within the 10 tests. Moreover, bond tests on the same FRCM systems applied over specimens made of clay bricks evidenced that, in most cases, the maximum tensile stress attained in the bond tests, i.e., the conventional value suggested by the Italian Guidelines, was higher than the one obtained in the tensile test. This result, which seems anomalous, in reality, is related to the fact that, in the bond test, the presence of the masonry support works as a constraint to prevent \"in plane\" displacement of the FRCM reinforcement. Such a constraint is not present in tensile tests, which have, indeed, highlighted a significant sensitivity  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Masonry**} & \multirow{2}{*}{**Analysis ID**} & \multirow{2}{*}{\(E\)} & \multirow{2}{*}{\(f_{c}\)} & \multirow{2}{*}{\(G_{t}\)} & \multirow{2}{*}{\(f_{t}\)} & \multirow{2}{*}{\(V_{t,\text{EB}}\)} & \multirow{2}{*}{\(P_{FEM}\)} & \multirow{2}{*}{\(P_{FEM}\)} & \multirow{2}{*}{\(P_{FEM}\)} \\ \cline{5-11} \cline{6-11}  & & & **[MPa]** & **[MPa]** & **[N/mm]** & **[MPa]** & **[RN]** & **[RN]** & **[RN]** & **[RN]** & **[RN]** \\ \hline \multirow{3}{*}{Tuff} & 2,T-W & \multirow{3}{*}{1100} & \multirow{3}{*}{1.1} & \multirow{3}{*}{0.0120} & 0.06 & 15.0 & 80.0 & 56.57 & 70.40 & 40 & 26.67 \\  
of the specimens to misalignment with respect to the axis of the applied load during the test ([PERSON] et al., 2017a [7], [PERSON] et al., 2017b [8], [PERSON] et al., 2017 [49], [PERSON] et al., 2017 [50], [PERSON] et al., 2017 [51], [PERSON] et al., 2017 [52]). These observations mean that the ultimate strains of the constitutive laws plotted in Figure 2 are, in many cases, safe, with respect to the conventional values related to bond tests. This is further true if the conventional strain is amplified by the factor \(\alpha=1.5\) for checks far from the anchorage, according to CNR indications (CNR DT 215 2018 [26]). Finally, the use of the constitutive laws in tension for the FRCM materials plotted in Figure 2 means that the progressive damage in the mortar due to cracking and the eventual slippage of the fibers from the mortar are intrinsically taken into account in the numerical model, since they correspond to the real experimental behavior observed in tensile tests on coupons made of both fibers and mortar ([PERSON] et al., 2017a [6]).