PSI - Issue 44

Carpanese Pietro et al. / Procedia Structural Integrity 44 (2023) 1752–1759 Carpanese Pietro et al./ Structural Integrity Procedia 00 (2022) 000–000

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Lastly, the interventions aimed at increasing the stiffness of horizontal diaphragms (i.e., of floors, FLR) have been differentiated according to the building typology, and show significant differences if performed on historical or more recent buildings. For wooden floors of historical buildings, the stiffening is provided by adding single or double wooden planks, orthogonally or at 45° over the existing ones (Valluzzi et al. 2010). In case of floors made of reinforced lattice joist and hollow tiles, the FLR intervention must be intended as the replacement or the addition of a reinforced slab and the insertion of adequate connections to the walls along the entire perimeter. 2.2. Implementation and analysis phase The interventions described at 2.1 have been studied individually (MSN1, MSN2, MSN, TR, CR, FLR) or in a combined way (MSN1+TR, MSN1+FLR, MSN2+TR, MSN2+FLR, MSN+CR, MSN+FLR), and were implemented on a database of 445 buildings, belonging to the 4 construction periods Pre-1919, 1919-1945, 1946-1960, and 1961 1980. The modeling process was carried out using the software Vulnus vb 4.0, developed at the University of Padova (Bernardini et al. 1990). Vulnus analyzes load-bearing masonry buildings based on limited information, such as geometry, material properties, construction details and other qualitative information (Valluzzi 2009). Specifically, Vulnus calculates three indices: I1, associated to in-plan mechanisms; I2, relating to the acceleration that triggers the main out-of-plan mechanisms; and I3, a qualitative index. Through the fuzzy set theory, these indices are used to elaborate three fragility curves: a central white probability curve, and two extreme probability curves (Upper- and Lower-Bound). These three curves are cumulative lognormal distributions and represent the probability of exceeding a moderate/severe damage state, associated with a DS2-3 with reference to the EMS98 damage scale (Grünthal 1998). Each building of the database was analyzed in Vulnus in its as-built state and in each of the retrofit configuration proposed. Some interventions could be directly modeled in Vulnus, while others had to be simulated, since the software does not allow detailed modeling. To simulate the intervention of masonry strengthening (i.e. MSN1, MSN2, MSN), the corrective coefficients available in table C8.5.II of the Italian Circular 2019/01/21 were applied to the mechanical characteristics of the materials composing the building. The coefficients depend on the type of intervention and on the construction material. In addition, since these interventions require addition of material, an average increase of masonry specific weight was estimated by 5% in case of stone masonry and 4% in case of solid and hollow brick masonry. Regarding connection interventions, Vulnus gave the possibility to insert the number of ties located in the two main direction of the building. So, tie-rods (TR) were directly implemented in Vulnus inserting two rods, one per side, placed parallel to the internal partitions, and one rod to the perimeter walls. On the other head, confining rings (CR) are simulated with the insertion of 2 tie-rods in each direction in correspondence of the horizontal diaphragms of the building. Lastly, floor interventions (FLR) were simulated by increasing the specific weight of the floor and placing diffuse chains and increasing the floor-to-wall friction coefficient to simulate the improved box-like behaviour when floors are stiffened.

As Built

MSN1

FLR

MSN1+FLR

Legend

Fig. 1. Fragility curves for as-built configuration and some interventions (Pre-1919).