PSI - Issue 78

Tommaso Petrella et al. / Procedia Structural Integrity 78 (2026) 976–983 = + + − + + + = + If the term is negligible compared to B, can be approximated as written in Eq. (6): ≅ 0 (1− ) (6) This result clearly shows that non-inertial horizontal forces reduce the ultimate displacement capacity, leading in values lower than the critical acceleration factor 0 . From literature many studies have compared the kinematic approach with advanced numerical models, including experimental validation that supports these models (Graziotti et al., 2016; Sharma et al., 2021). Numerical methods have the advantage of automatically detecting the prevailing failure mechanism which is neglected when simplified models are adopted. For this reason, combining kinematic and numerical approaches is recommended (Lourenço 2002). Kinematic analysis still represents a valuable tool guiding both the interpretation of results and the design of more detailed simulations. 3. Finite element modelling: out-of-plane mechanisms in SAP2000 3.1. Macro-Element modelling approach in SAP2000 The previous chapter presented the kinematic limit analysis, where the critical acceleration multiplier 0 and the corresponding ultimate rotation of the rigid block were introduced through analytical formulations. This section describes a Finite Element modelling strategy implemented in SAP2000 to simulate OOP local collapse mechanisms via non-linear static (pushover) analysis. In the case of a SDOF OOP collapse mechanism, where the wall is free at the top, a plastic hinge is placed at the wall base to simulate the overturning rotation. For multi-story walls, two potential collapse mechanisms are considered: the overturning of the entire wall as a single rigid block, or the partial overturning of the upper portion alone. In both cases, the ensemble of blocks and rotational hinges forms a kinematic chain characterized by a SDOF. The wall is discretized into vertical frame elements representing rigid masonry blocks. Each element is assigned equivalent geometrical properties to reproduce the actual mass. Loads and boundary conditions are applied directly to the frame elements. For each overturning mechanism, a lumped plasticity hinge is placed at the assumed rotation point, with a moment-rotation ( − ) law derived from the kinematic analysis. As illustrated in Figure 2a, these hinges are calibrated to mimic the rocking behaviour of masonry blocks: the wall initially remains nearly undeformed until the resisting moment reaches its ultimate value, after which the hinge allows (5) 979

T tie

M ult

 ult

 tie

F [kN]

M [kNm]

(a)

(b)

 [m]

 [-]

Fig. 2. (a) Moment – rotation (M- θ) law defined for the plastic hinge representing the wall rocking mechanism; (b) Force – displacement (F- δ) law defined for the link element modelling the steel tie.