PSI - Issue 11

Massimiliano Lucchesi et al. / Procedia Structural Integrity 11 (2018) 177–184 M. Lucchesi, B. Pintucchi, N. Zani/ Structural Integrity Procedia 00 (2018) 000–000

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At this stage of the study, only some limited in situ investigations have been conducted and consisted of visual inspections of the lower vaults, where they have partially collapsed (see Fig. 7). Such inspection reveals that they are made of lime mortar with full bricks laid on edge and a thickness of 14cm. Given the lack of specific information, the vaults of the upper level have been presumed to have the same characteristics.

(a)

(b)

(c)

Fig. 7. View of a section (a) and infill (b) of the lower vaults; c) vault’s sections and slab packages (dimensions in cm).

Due to the limited in situ investigations, according to the NTC, a structural knowledge level of LC1 has been selected, with a consequent confidence factor (CF) equal to 1.35. Hence, the strength values have been set equal to the minimum values specified in the code’s reference table for such a type of masonry, while the Young’s modulus, E, has been set equal to the median value given for the same type. Thus, assuming CF = 1.35 and a material safety factor γ m = 3, the following values have been obtained: Young’s modulus E = 1.5 GPa, Poisson’s coefficient ν = 0.1, compressive strength σ o =2.4/(3*1.35) = 0.59 MPa. Considering the current use of the building, two static analyses have been conducted under vertical loads. Firstly, a safety assessment was carried out for the ultimate limit state (ULS), as defined NTC. Then, a structural analysis was performed with reference to the serviceability limit state (SLS), with the aim of investigating the vault’s actual behavior in terms of deformations and stress state trends. The vaults’ mass density has been assumed equal to 1800 kg/m 3 for all analyses. Moreover, referring to Fig. 7c), non-structural permanent loads (infill, mortar bed, floor) have been evaluated assuming the value of 1600 kg/m 3 for the infill and screed density, and a value of 2000 kg/m 3 for the flooring. Given the building’s current state, the service loads have been set equal to 2 kN/m 2 on both floors, and snow loads have also been considered. Finally, the various loads -appropriately amplified as needed- have been combined according to the NTC. Once the needed information was obtained, a numerical model was created ex novo in order to study the response of a sub-system of the entire cellar structure: two levels of vaults with four spans. Interactions with the rest of the structure have been accounted for via boundary conditions. Conservatively, the stabilizing effects of the infill present have been neglected. The structure has been discretized by means of 9216 thick shell elements for a total of 46850 degrees of freedom. The constitutive model used is that of a masonry-like material, generalized by also limiting the shear stress on each plane proportionally to the normal stress acting (Lucchesi et al., 2017c). The material is considered non-linear elastic, characterized by the tensor C of the elastic modulus, a closed convex subset, K, of the space of all symmetric tensors. The stress, T, corresponding to an assigned strain, E, is the projection of CE on K, with respect to the energy inner product. In this way, the strain E is naturally decomposed into the sum of an elastic part, E e , and an inelastic part, E a , and T = CE e . The anelastic strain E a can represent the occurrence of fractures. 4.1. Nonlinear model used