Flexural behaviour of calcarenite masonry walls reinforced with FRP sheets

The use of fiber-reinforced polymers (FRP) for structural strengthening has become increasingly popular in recent years. Several applications of FRP have been proposed and applied, depending on the target of the technique, kind and/or material of the structural member. In particular, because of their great tensile strength, FRP materials are commonly used to enhance the out-of-plane behaviour of masonry walls, allowing to increase their strength, ductility and improving safety against overturning. For these reasons, FRP laminates are often applied in vulnerable ancient buildings in seismic areas to reinforce façades and walls with poor structural features. However, some issues arise when adopting composites in historical constructions, the most related to the aesthetical impact of laminates and compatibility between FRP and masonry. Consequently, a correct evaluation of the reinforcement percentages for strength and ductility purposes is crucial, as well as the effective increase of structural performances. This paper presents a numerical-analytical approach able to reproduce the flexural behaviour of out-of-plane loaded masonry walls. The model is based on a simplified representation of the member, the latter modeled as a cantilever beam. Mechanical non-linearity is introduced by means of moment-curvature relationships, deduced with proper constitutive laws of masonry and by taking into account the ultimate debonding strain of FRP. Second order effects are considered by adopting an iterative step-by-step procedure. Comparisons are made in terms of moment-curvature and load-displacement curves with experimental data available in the literature and with non-linear finite element analyses, showing both good agreement. Finally, parametric considerations on the reinforcement percentages are made in terms of strength and ductility