PSI - Issue 44

P. Sorrentino et al. / Procedia Structural Integrity 44 (2023) 1648–1655 P. Sorrentino et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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given: the ratios assume values between 12% and 33% for the part A and values between 17% and 40% for the part B; these values are in compliance with the rules of the art reported in the treatise of Rondelet which some examples are given: Baths of Diocletian (17%), the Basilica of S. Maria del Fiore (20%), the Pantheon (23%). In Figures 4b and 4c the histograms with values of the ratio for each level of the parts A, B and A+B in longitudinal and transversal direction are shown. The ratios assume values between 6% and 21% in longitudinal direction and between 7% and 19% in transversal direction for the part A, values between 10% and 30% in longitudinal direction and between 8% and 18% in transversal direction for the part B and values between 7% and 23% in longitudinal direction and between 7% and 18% in transversal direction for the parts A+B. These values are higher than the minimum prescribed by the current Italian Building Code NTC 18 (3.5%) and suggested by Lourenco (10%).

7%

13% 13%

6%

PART A PART B PART A+B

PART A PART B PART A+B

PART A PART B PART A+B

III IV V

III IV V

II I I V V

8% 8%

10% 10%

17% 17%

7% 7% 7%

7%

8%

14% 14% 14%

8%

7%

8%

10%

12%

20%

8%

8% 8%

15%

11% 11%

12%

18% 0% 10% 20% 30% 40% I II 18% 15% 19%

23% 0% 10% 20% 30% 40% I II 10% 30% 15% 21%

34% 0% 10% 20% 30% 40% I II 14% 24% 33%

40%

A wx /A TOT

A wy /A TOT

A w /A TOT

(a)

(c)

(b)

Figure 4. (a) A w /A tot ratios and A w /A tot ratios in (b) x direction and (c) y direction for part A, B and A+B.

4. Analysis – First hypothesis: no interaction In this section nonlinear static analysis of the central part (part A) and the connecting parts (part B) are given, considering the buildings as isolated structures and neglecting the interaction between the parts. To this aim, the equivalent frame approach has been considered, in compliance with current Italian Building Code (NTC 18). This approach consists of considering the masonry wall as composed of piers, spandrel beams and joint elements, in which the piers are modelled as columns, spandrels as beams and joint elements as rigid offsets at the end of the pier and spandrel as they are supposed infinitely resistant and stiff (Magenes, G., 2000). In particular, the spandrel is modeled as a weak spandrel (pendulum), because of the lack of any tensile resistant element. The pushover analysis has been performed adopting a load pattern of forces proportional to the mass. In Figure 5 the pushover curves in terms of base shear vs displacement (F-d) and the ratio between base shear and weight vs the ratio between displacement and height (F/w-d/H) in longitudinal and transversal direction are shown. The pushover curves of the part A exhibit maximum base shears V b,max of 207t and 303t and ultimate displacements of 69mm and 47mm, respectively in longitudinal and transversal direction, the pushover curves of the part B show maximum base shears V b,max of 303t and 165t and ultimate displacements of 112mm and 95mm, respectively in longitudinal and transversal direction. In terms of F/w and d/H, the curves of part A are characterized by F/w values of 3.63% and 5% and d/H values of 0.36% and 0.26%, respectively in longitudinal and transversal direction; the curves of part B show F/w values equal to 11.94% and 6.50% and d/H values equal to 0.60% and 0.50%, respectively in longitudinal and transversal direction.