Issue 51

C. Anselmi et alii, Frattura ed Integrità Strutturale, 51 (2020) 486-503; DOI: 10.3221/IGF-ESIS.51.37 495 R ESULTS he above described discrete model has been implemented by using Excel and its Solver. Although for the considered application cases has always been used a discretization in only eight macro-elements (six for the dome and two for the drum), the implemented program appears sufficiently versatile and, in addition to the mechanical characteristics, allows to define the intrados profile, the thickness variability, as well as to insert any window opening in the drum, the lantern at the top and the hoops at each level. Once the collapse loads multiplier has been found, through the introduction of appropriate matrices of directional cosines and taking advantage of the symmetry, the program provide the collapse mechanism of a quarter of a dome, represented through axonometric and zenithal views, and a section. In order to test the validity of the procedure, was considered a single dome with the same geometric and mechanical characteristics, and was analyzed the effect on the load-bearing capacity of the following features: (a) lack/presence of interlocking between the bricks at the ribs; (b) hoops in the case of possible failure at the ribs; (c) absence/presence of window openings in the drum; (d) drum width. The dome examined have the following geometric and mechanical characteristics: - the internal angular profile SA is a sixth of an acute fifth - horizontal internal semi diameter his = 11.5 m - thickness on top s0 = 1.5 m - thickness at base plane of dome sI = 1.5 m - thickness of drum sT = 1.5 ÷ 2.5 m - drum height hT= 8 m - height window opening hf= 6 m - half-width window opening Lf= 2 m - lantern radius RL = 2 m - lantern weight on a segment of dome PL= 100 kN - limit compressive strength σ 0 = -4000 kN/m 2 - friction coefficient fc= 0.75 - masonry density γ m = 18 kN/m 3 - density of covering material (as overload) γ c = 10 kN/m 3 - pre-tension force of a single hoop Nh = 200 kN The numeric results (multiplier α) are summarized in the Tab. 1 and compared in Tab. 2. Case Failure at ribs Lf (m) Nh (kN) sT (m) α 1 no 0 0 1,5 24.129 2 no 2 0 1,5 14.224 3 no 0 0 2,5 32.374 4 no 2 0 2,5 29.112 5 yes 0 0 1,5 7.567 6 yes 0 400 1,5 10.211 7 yes 2 0 1,5 3.168 8 yes 2 400 1,5 7.624 9 yes 0 0 2,5 17.621 10 yes 0 400 2,5 18.857 11 yes 2 0 2,5 13.046 12 yes 2 400 2,5 14.342 Table 1 : Examined cases. T