Out-of-Plane Response of URM Façades Accounting for In-Plane Diaphragm and Wall-Diaphragm Connection Deformability: Application to Palazzo Renata di Francia in Ferrara, Italy

This study investigates the out-of-plane (OOP) seismic behaviour of unreinforced masonry (URM) walls with different diaphragm configurations and connection types, with particular emphasis on the nonlinear response of wall-to-diaphragm systems. A modal-driven approach based on the kinematic theorem of limit analysis is introduced, allowing the collapse mechanism to evolve as a combination of overturning and vertical bending, in line with the actual deformation modes of the fa & ccedil;ade. The approach is first applied to a benchmark URM model incorporating four types of diaphragms and three categories of wall-to-diaphragm connections, each characterised by experimentally derived force-displacement laws. Subsequently, a real case study involving Palazzo Renata di Francia, a historical building in Ferrara (Italy), is analysed to assess the effect of a 1960s retrofit on OOP vulnerability. Comparative analyses between pre- and post-retrofit conditions highlight the influence of diaphragm stiffness and anchorage deformability on failure mode activation, displacement capacity, and safety margin. Results demonstrate that simplified assumptions such as perfectly rigid or absent connections can lead to non-conservative or overly conservative assessments. The study confirms the need to incorporate nonlinear connection behaviour into seismic assessment models for heritage masonry buildings, as it directly affects the OOP stability and collapse mechanism of masonry walls.