PSI - Issue 78

Tommaso Petrella et al. / Procedia Structural Integrity 78 (2026) 976–983

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1. Introduction Masonry buildings represent a significant portion of the existing building stock in many seismic-prone regions, especially in ones characterized by historic centres and older urban areas (Shabani et al. 2021). Despite their widespread use and historical value, masonry structures are highly vulnerable to seismic actions, with Out-Of-Plane collapse among the most frequent and hazardous failure modes. (Penna et al.,2014; Fiorentino et al., 2017; Tomassetti et al., 2018). Local OOP mechanisms are characterized by the loss of stability of individual wall portions subjected to lateral forces, perpendicular to the main-dimension wall plane. The absence of box-type behaviour frequently induces local mechanisms (Lourenco et al, 2011), derived from a non-effective connection between orthogonal walls, emphasized when panels do not bear vertical axial load (Magenes et al., 1997). To mitigate these risks, current seismic assessment standards, suggest specific checks for local mechanisms together with global evaluations. In this framework, kinematic limit analysis - which models wall portions as rigid blocks connected -is one of the most widely adopted approach to estimate the onset of collapse (Heyman, 1966). This method allows to determine the critical acceleration multiplier 0 and the ultimate rotation , providing a first-order insight for the failure behaviour. However, analytical kinematic models are inherently limited when dealing with complex boundary conditions, non inertial force contributions, or the evaluation of post-strengthening configurations. Such scenarios often require more refined approach to fully describe the structure ’ s behaviour. This study preliminary explores the use of Finite Element (FE) modelling as a complementary tool, focusing on the simulation of OOP mechanisms through non-linear static analysis. Through SAP2000 v25 (Computer and Structures, Inc, 2025), a frame idealization is used to discretize masonry walls into rigid macro-elements with plastic hinges, which parameters are calibrated using the results derived from the kinematic analysis. This hybrid strategy allows the transition from a purely analytical framework to a numerical model capable of capturing both the activation and evolution of local collapse mechanisms, even considering more complex phenomena in between. The effectiveness of the proposed approach is assessed by comparing analytical predictions with the results of non-linear static analyses, offering valuable insights into the seismic response of masonry walls and an alternative model schematization. 2. Kinematic analysis: local out-of-lane mechanisms Current seismic codes indicate both global and local assessments when working with masonry buildings, since seismic events often trigger OOP collapse mechanisms involving the loss of stability of wall portions subjected to lateral. A widely adopted method to study these phenomena is the kinematic approach based on rigid block models, as stated before. The masonry wall is typically reduced to a single-degree-of-freedom (SDOF) system, where the collapse is described by virtual displacements around the assumed point of rotation (i.e., pivot point). This modelling approach is valid if masonry integrity is preserved. Traditionally, in kinematic approach masonry ’ s hypothesis are: (i) no tensile strength; (ii) no sliding occurs between blocks; and (iii) compressive strength capacity is theoretically unlimited. However, this idealization was initially proposed for rigid-body rocking systems made by Housner, 1963, More advanced formulations incorporate additional effects, such as friction between blocks, weak interlocking, and limited compressive strength. These aspects may cause hinges to form away from the geometric edges (Casapulla & Argiento, 2017). Furthermore, numerical models have been developed to incorporate these aspects into non-linear analyses of masonry structures (Lourenço, 2002). Kinematic analysis can be performed either linearly, by determining the critical acceleration 0 that induce collapse, or non-linearly, by tracing the mechanism ’ s evolution through a force-displacement relationship. In both cases, the seismic action is modelled with horizontal forces proportional to the participating masses, scaled by the factor , which represents the ratio between the horizontal forces and the self-weight of the block. Typically, the first step is to identify the possible collapse mechanism and calculate the corresponding multiplier 0 . This is followed by the definition of the − curve, where is the displacement of the selected control point. After, this curve can be converted into a capacity curve and compared with seismic demand using Acceleration-Displacement Response Spectra (ADRS). The linear method leads to a direct comparison between the demand and capacity acceleration, while the non-linear method captures the progressive development of the mechanism up to its complete loss of load bearing capacity.