Equivalent frame modelling of masonry walls based on plasticity and damage

This paper presents a force-based equivalent frame procedure applied to analyse masonry walls structural response under cyclic loadings. The presented macroelement formulation, consisting in the arrangement in series of a central elastic beam, two nonlinear flexural hinges at the ends and a nonlinear shear link, adopts a smooth hysteresis model for these latter, where a scalar damage variable is introduced to reproduce strength and stiffness degradation. Main points of the adopted force-based macroelement and hysteresis model are recalled, with emphasis on the capability to reproduce the typical in-plane cyclic response of masonry. Validation of the element is presented through various examples, comparing numerical and experimental results. The first validation set is composed by a group of four panels, characterized by different boundary conditions and pre-compression levels. The second validation case is a classical literature benchmark, in which the performance of the model is tested in case of a wall with openings composed of piers, spandrels and rigid links. Moreover, for this example, numerical results obtained with the presented equivalent frame approach are also compared with a more refined numerical model, showing limits and advantages of simplified procedures.