PSI - Issue 78

Emanuele Rizzi et al. / Procedia Structural Integrity 78 (2026) 1420–1427

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The OOP U mechanism (Fig. 4c) considers the simultaneous overturning of the column and the nave wall as a single unit rotating about the hinge O. In contrast, in the OOP R configuration (Fig. 4d), vertical bending is assumed, in order to account for the effect of the stiffened nave roof, modeled as an equivalent elastic springs k at the top (D). For both IP and OOP, two different scenarios are considered for the positions of hinges O and C: case 1 (C1), where hinges O and C are located at the outer edges of the cross section, and case 2 (C2), where hinges are retracted to account for toe crushing of the masonry. Specifically, hinge O is retracted by 250 mm in all mechanisms and hinge C is retracted by 307 mm for IP mechanisms, and 167 mm for the OOP R mechanism. These values are approximately consistent with those calculated using the method proposed by Boscotrecase and Piccarreta (2006), considering a masonry compressive strength of 4.6 N/mm² and taking into account the model’s mesh dimensi ons. 5. Numerical modeling The configurations illustrated in section 4 were modeled using Midas FEA NX v1.1 software (CSPFea 2024). The models (Fig. 5) consider a representative portion of the nave wall, consisting of one column and an overlaying wall portion extending half the span length on either side. The masonry was represented using hexahedral (8-node) and pentahedral (wedge, 6-node) elements. The mesh size ranges between 80 mm and 140 mm. Masonry was modeled as homogeneous, isotropic, elastic material: the corresponding mechanical properties, including self- weight, Young’s modulus, and Poisson’s ratio, are reported in Table 1. Nonlinearities were concentrated at the base and top of the column, where localized inelastic behavior is expected to occur, by introducing nonlinear spring elements. Specifically, rigid compression-only vertical springs are assigned at the base of the column, to simulate the ground support conditions, as well as the contact between the column and the arcade wall. Horizontal slip at the base and between the column and the arcade was avoided; however, it was verified that the horizontal load did not exceed the sliding resistance provided by the friction between the blocks, considering a friction coefficient equal to 0.4. The base nodes of the column were rigidly constrained in translation to a master node, which serves as the center of rotation and which varies depending on the position of hinges (as defined in cases C1 and C2 described in section 4). Rigid material properties were assigned to the elements at the top and bottom of the column and at the bottom of the nave wall, to avoid stress and strain concentration. Additionally, in the IP R model, a portion of the external wall and of the side aisle roof were included: Five truss elements, spaced at 1460 mm, represent the timber rafters, linking the nave wall with the external wall; four pairs of tension-only non-linear axial springs were used to simulate the roof bracing with tie rods. Th e springs’ stiffness (29.75 kN/mm) corresponds to that of a stainless steel tie rod (duplex 1.4462) with a diameter of 30 mm and a length of 4990 mm; the non-linear behavior was derived from a tensile test performed in the rolling direction (Gozzi and Olsson, 2003). The side aisle roof masses were applied to elements at an elevation of 9630 mm, while the central nave roof masses were applied to the top of the nave wall. The total weight of the column, nave wall, and the additional roof loads amount to 451.36 kN.

Table 1. Material properties assigned in the model.

Material

Self-weight kN/m 3

Elastic modulus N/mm 2

Poisson’s ratio -

Masonry

18 18

2000

0.49 0.49 0.40

Rigid

200000 10300

Timber

5.04

In the IP models, the top of the column and the nave wall were restrained against out-of-plane deflection and rotations, as well as torsion about their longitudinal axis. Additionally, the top of the nave wall was restrained against in-plane rotations. The external wall portion in IP R models was fixed at the base and restrained against torsion about