A P-Delta Discrete Macro-Element Model for Rocking Masonry Walls

This paper presents a robust and accurate P-Delta Discrete Macro-Element Method (DMEM) formulation to assess the out-of-plane (OOP) rocking behavior of masonry walls, allowing for both mechanical and geometric nonlin-earities with a limited computational cost. OOPs mechanisms are one of the main causes of failure or severe damage involving historical and monumental masonry constructions subjected to earthquake loading. These mechanisms can be activated at low-magnitude seismic actions mainly at the upper levels of masonry buildings due to the amplification of the dynamic response and wall displacements. In this paper, according to the DMEM, the wall is discretised in a number of shear-deformable macro-portions (macro-elements) interacting by interfaces allowing for flexural cracks and sliding at the joints. According to the proposed strategy, the equilibrium is imposed considering the system’s undeformed configuration, while the global load vector is computed at each step of the analysis according to the current position of loads. The model is validated against rigid-block numerical solutions accounting for large displacements and experimental tests. Finally, a real church façade is analysed, investigating the influence of the geometrical layout, boundary conditions, and masonry deformability on the structural response. The results confirmed the accuracy and efficiency of the model and its potential to be employed for real seismic assessments.