A numerical model for the analysis of masonry walls in-plane loaded and strengthened with steel bars

A novel macro-model for the analysis of masonry shear walls reinforced with steel bar grids is presented. The model is based on the so-called disturbed state concept (DSC), with a modified hierarchical single yield surface (HISS-CT) plasticity model accounting for a distinct behavior in tension and compression. The effect induced by the introduction of different reinforcement ratios is discussed, in terms of increase of both failure load and ductility. With reference to a quasi-square shear wall, an optimal reinforcement ratio is evaluated by means of the numerical model proposed and subsequently compared with recommendations provided by the Canadian masonry design standard. The comparison shows how minimum values proposed by Canadian standard are suboptimal and hence not totally suitable to obtain a proper increase of the seismic performance of shear walls in high seismicity region. A second example, relying into a shear panel with eccentric openings and subjected to horizontal loads, is analyzed in detail. It is assumed to strengthen the structure by means of a light and a heavy reinforcement, to deeply investigate the role played by steel bars in masonry seismic upgrading. A new explicit formula is finally presented, useful to provide a quick estimation of the load carrying capacity of reinforced masonry, to be eventually used in common design.