Homogenized limit analysis of FRP-reinforced masonry walls out-of-plane loaded

A three-dimensional (3D) homogenized limit analysis model for the determination of collapse loads of out-of-plane loaded FRP reinforced masonry walls is presented. Homogenization is performed on unreinforced masonry, whereas strips are applied at a structural level on the already homogenized material. Unreinforced masonry strength domain is obtained by means of a compatible approach in which bricks are supposed infinitely resistant and joints are reduced to interfaces with frictional-cohesive behavior and associated flow rule. A sub-class of elementary deformation modes is a-priori chosen in the representative volume element (RVE), mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating power dissipated in the heterogeneous model with power dissipated in a fictitious homogeneous macroscopic plate. Afterwards, an upper bound FE limit analysis code is implemented to study entire unreinforced and FRP reinforced walls out-of-plane loaded. For unreinforced masonry, rigid infinitely resistant wedge-shaped 3D elements are used. The utilization of 3D elements is necessary to simulate the flexural strength increase induced by the introduction of FRP strips with negligible thickness, which are modeled by means of triangular rigid elements. FRP strips contribution is taken into account assuming that masonry and FRP layers interact by means of interfacial tangential actions. Internal power dissipation is possible at the interfaces between wedge adjoining elements (masonry failure), at the interfaces between triangular FRP and wedge masonry elements (delamination) and between triangular FRP adjoining elements (FRP failure). Two different structural examples are presented to validate the numerical model, namely a FRP reinforced masonry wall in cylindrical flexion and a set of masonry walls with openings in two-way bending. Results obtained with the model proposed fit well both experimental and numerical data available for all the cases analyzed, meaning that the procedure proposed can be used in building practice.