PSI - Issue 44

Marialaura Malena et al. / Procedia Structural Integrity 44 (2023) 2052–2057 M. Malena et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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2.1. FE model and numerical analyses A three-dimensional finite element model of the whole church was provided adopting shell elements to model the mid-plane masonry walls. About mechanical characteristics, according to the Italian Standard (2), the unit weight and the Young Modulus were assumed equal to 21 kN/m 3 and 1740 N/mm 2 , respectively. The non-linear behaviour of masonry was described by mean of the model proposed in de Felice & Malena (2019) and Malena et al. (2019).

Fig. 2. Finite element model of the church. An elastic dynamic analysis was carried out on the whole three-dimensional model of the church. The first four modal shapes are showed in Fig. 3. Looking at the results of the modal analysis, the two macro-elements identified in the structure are: the bell tower with the walls of the vestry (macro-element A) involved in modes 1 and 2, and the nave (macro-element B) involved in modes 3 and 4 (Fig. 4). The nodes belonging to each macro-element are those characterised by a non-zero displacement for the selected modal form. Two models of the church were made: the first one characterized by non-linear behaviour for the finite elements belonging to the macro-element A and the second one characterized by non-linear behaviour for the finite elements belonging to the macro-element B. In both the cases the remaining part of the structure is characterized by elastic behaviour. The two models were pushed with horizontal forces. The analyses were carried out under conditions of constant gravitational loads and monotonically increasing horizontal loads. The adopted horizontal load distributions were consistent with the modal shapes of the three-dimensional structure. The first model was horizontally pushed with a load profile defined fitting the first modal shape (analysis number 1), while the second model was pushed with a load profile proportional to the third modal shape (analysis number 2).