PSI - Issue 78

Elisabetta Bonaguro et al. / Procedia Structural Integrity 78 (2026) 1016–1023

1018

Three distinct configurations are modeled in DIANA (Figg. 1a,b,c) by juxtaposing the SUs to the western end unit: thislatter (Fig. 1c) isthemost investigated, as it ischosen as the reference model for setting up theanalyses on partial interventions. In the modeling framework, only the main structural elements (masonry walls, floor and roof slabs) are considered, neglecting internal partitions: all of them are shaped using bi-dimensional regular curved shell elements defined by three or four nodes, with a side of about 30 cm. Base boundary conditions arehinges, blocking only translations. Nonlinear static analyses (pushover) are carried out on these models obtaining the capacitycurves in terms of base shear versus top displacement using a uniform distribution of accelerations with the height of the UMCB. They are conducted along the positive X direction, aligned with themain façades, as thewalls in the Y direction do not exhibit relevant plastic behaviour as they do present no openings. A limit displacement of 6 cm, equivalent to 0.5% of the total building height, is considered. When considering configurations with two SUs and the full cluster, the displacement control point is always placed at the ridge of the tallest SU. For the unreinforced models, the capacity curves areinterrupted at points of bearing capacityloss, when severe tensile strains patterns occur (exceeding 0.2%), particularly affecting the transverse walls of the taller SUs.

a

b

c

Fig. 1. Models developed in DIANA environment: (a) full cluster; (b) two SUs; c) single SU. All these models can be unreinforced or strengthened by replacing the timber diaphragms with ribbed cast-in situ reinforced concrete slabs; only the model of the single unit (Fig. 1c) presents a wider range of strengthened configurations, as it serves as a reference model in a structural sensitivity analysis. The structural model adopted for masonry modelling isthe Total Strain Crack model, based on the fracture energyG (Lourenço & Gaetani, 2022), which it requires parameters about both the linear elastic and plastic behavior. The tensile behavior is assumed exponential and the compressive one parabolic. Masonrymechanical properties arethose of the coursed rubble type defined byMIT (2019) and identified bySaretta (2024) as the type best suiting the visual features of the masonry (Borri & De Maria, 2019). The chosen parameters (Table 1) consist in the average values of the ranges proposed by MIT (2019), reduced by a confidence factor CF=1.35, according to the minimum level of knowledge of the structure (MIT, 2018). This material and a constant average thickness of 60 cm are applied to the full cluster, in order to avoid local effects.

Table1. Mechanical propertiesassignedto coursedrubble masonry inDIANAenvironment. E [N/m 2 ] ν W [kg/m 3 ] f t [N/m 2 ] G ft [N/m] f c [N/m 2 ] G fc [N/m]

β

1.676·10 9

0.4

2100

93889

10

3.081·10 6

500

0.01

2.2. On the stiffness of diaphragms The shear modulus (G xy ) and the associated overall stiffness (K d ), which governs the in-plane stiffness of diaphragms, exhibits a significant variation when transitioning from flexible timber floors to rigid concrete slabs. The relation between G xy andK d is determined according to the equation (1) (Brignola et al., 2009; Federal Emergency Management Agency (FEMA), 2000), where χ=1.2 is the shape factor and t the thickness of the considered diaphragm.