PSI - Issue 78

Antonella Ranaldo et al. / Procedia Structural Integrity 78 (2026) 552–559

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3. Finite Element Modelling To investigate the seismic response of the two churches considered as case studies, numerical models are implemented using the FEM within the MIDAS FEA NX software (MIDAS FEA NX, 2024). This paper reports preliminary results of NLPAs, focusing on two common architectural portions of the churches, named macro elements, that are the lateral façade and the triumphal arch. Numerical analyses are carried out in order to reproduce the lateral façade simple overturning and the in-plane failure mechanism of the triumphal arch, including the interaction with the surrounding vaulted elements. The FEM models implemented are shown in Fig. 4 for Saint Fransis of Assisi Church, and in Fig. 5 for Jesus Resurrection Church. To reduce the computational burden in the NLPAs, non-linear material behavior is assigned solely to the vertical walls and columns, whereas the vaults are only half-modelled and considered as elastic material. Walls and columns are fixed at the base, while the vaults are restrained such that only the vertical translation is restrained.

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Fig. 4. Macro-element FEM models of Saint Fransis of Assisi Church: (a) lateral façade; (b) triumphal arch; (c) triumphal arch with lateral walls.

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Fig. 5. Macro-element FEM models of Jesus Resurrection Church: (a) lateral façade; (b) triumphal arch; (c) triumphal arch with lateral walls.

The elements are analyzed using the smeared crack model, a technique that enables the simulation of both the initiation and subsequent propagation of cracks within the structural elements. The specific mechanical properties attributed to the masonry of Saint Fransis of Assisi and Jesus Resurrection Churches can be found in Table 1. NLPAs are performed by using a lateral forces distribution proportional to the static inertial nodal forces of the main translational vibration mode along the direction investigated. In particular: Mode n. 1 for NLPA along -X direction for lateral façade local simple overturning, and +Y direction for triumphal arch failure mechanism as for Saint Fransis of Assisi Church; Mode n. 1 for NLPA along +Y direction for lateral façade local simple overturning and triumphal arch failure mechanism as for Jesus Resurrection Church. These analyses are conducted under displacement node control, employing an iterative procedure with a modified Newton-Raphson method to calculate the non-linear solution. Each NLPA starts with the application of gravity loads, followed by increasing lateral loads until failure.