PSI - Issue 78

Beatrice Travasoni et al. / Procedia Structural Integrity 78 (2026) 1111–1118

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Finally, Fig. 5c illustrates the out-of-plane deformation of the façade wall, emphasizing the key interplay between diaphragm stiffness and connection effectiveness. In configurations with rigid diaphragms (plywood and concrete), the connection systems are more effectively mobilized, resulting in enhanced restraint and a more uniform deformation profile. Conversely, in the presence of flexible diaphragms (simple boards and timber boards), the limited in-plane stiffness reduces the relative displacement at the wall–diaphragm interface, diminishing the activation of the connections and leading to larger out-of-plane displacements. 3.1. Identification of a combined out-of-plane mechanism The deformed shapes obtained from the analyses indicate that the out-of-plane response of the façade wall does not correspond to a pure overturning mechanism restrained by connections, nor to a classical vertical bending mode, either limited to a single storey or involving both storeys of the wall. In the first case, a linear displacement profile along the wall height would be expected, with maximum displacement at the top; in the second, the presence of fully rigid connections would imply fixed points, which would significantly overestimate both the activation multiplier and the ultimate collapse capacity of the mechanism. Instead, the numerical results reveal a combined mechanism, characterized by an initial out-of-plane rotation followed by vertical bending around an intermediate section of the wall, approximately near the mid-height of the second floor. This configuration is schematically represented in Fig. 6(c), and differs from both the classical overturning model with nonlinear ties (Fig. 6a) and the idealized bending mechanism with fully rigid connections at the top (Fig. 6b). This response reflects the progressive failure of both connection levels, and highlights the need to explicitly consider the nonlinear tensile behavior of wall-to-diaphragm connections. In this regard, the kinematic approach proposed by Lagomarsino (2013) introduces the nonlinear behavior of tie elements directly within the collapse multiplier, enabling a realistic simulation of connection failure once their relative displacement capacity is exceeded. Conversely, standard nonlinear kinematic formulations—typically assuming infinitely rigid restraints—are unable to capture such progressive degradation, and may therefore significantly overestimate the out-of-plane capacity of the wall. This aspect is particularly relevant even in the case of rigid diaphragms, such as those with concrete slab. While the diaphragm itself may be considered stiff, the connection system often includes mechanical anchors embedded in the masonry, which constitutes the weakest part of the assembly. As a result, assuming infinitely rigid behavior of the wall–diaphragm connection is not justified, and the nonlinear tensile response of the connector, especially on the masonry side, should be carefully accounted for.

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Fig. 5. Global pushover analysis results for different diaphragm and connection configurations. (a) Pushover curves showing the global lateral force vs. displacement at the second floor (control node); (b) Horizontal displacement profiles along the façade at a global displacement of 4 mm; (c) Normalised vertical deformation along the mid-span of the façade wall. In (b) and (c) light blue and black lines are for first and second storey deformation, respectively.