PSI - Issue 44

P. Sorrentino et al. / Procedia Structural Integrity 44 (2023) 1656–1663 P. Sorrentino et al./ Structural Integrity Procedia 00 (2022) 000 – 000

1658

3

= ∑ =1

(3)

m is the number of storey; F tot is the resultant of applied forces; F i is the generic horizontal force; H i is the height of application of the force. W tot is the total weight of the walls; B is the pier width. 3. The case of San Carlo all’Arena Convent

In this section, walls of San Carlo all’Arena Convent has been considered to test and discuss the formula. San Carlo all’Arena Convent (Figure 1) is located in the historical center of Naples. Its construction dates back to 1600, when the central part was realized. In 1681 the friars to enlarge it began the construction of a second part which was completed in 1715. In 1755 the third part of the cloister was built and at the same time the façade of the adjacent church was completed. With the restoration of 1800, a third level of the convent was built (Maio et al., 2016).

(a)

(b)

(c)

Figure 1. San Carlo all’Arena Convent in Naples: (a) 3D view, (b) plan and (c) section .

The building is a four-storey masonry building characterized by rectangular plan of dimensions 82x65m. The overall height is variable as the building is located close to the hill: the maximum height is equal to 28.25m and the minimum is 23.75m. The thickness of the main walls varies from 155cm, at the first level, to 30cm at the last one. The structure is made of tuff masonry. The floors consist of vaults and roof composed of steel beams. 3.1. Limit Analysis: application of simplified formula In this section the application of proposed formula to chosen masonry walls is given. In Figure 2 the analyzed walls are reported. The walls are characterized by irregular arrangement of openings in vertical and horizontal direction and consequently by variable width of piers in vertical direction; in particular, the walls 3x, 4x, 12x, 14x, 15x and 16x haven’t opening (or only one) at ground level. In the Table 1 the widths of piers and the weighted averages of widths are listed for each wall; the minimum widths are given in bold and the maximum in italic. In the case of variable width in vertical direction, the minimum value has been considered. In Table 2 the weights of each floor of the walls are listed; starting from these values, the equivalent heights have been evaluated. The equivalent height can be also defined as ; takin g into account this definition, for every wall α