Issue 51

C. Anselmi et alii, Frattura ed Integrità Strutturale, 51 (2020) 486-503; DOI: 10.3221/IGF-ESIS.51.37 488 P RELIMINARY AND GEOMETRIC FEATURES ince only vertical loads are considered, a dome segment has been studied - corresponding to a sixteenth - between two contiguous meridian planes of symmetry, one passing through the center line of a sail, the other for a rib (Fig.1a). In the horizontal section of the dome, the angle between the two symmetry planes is π/8, and the segment can be studied - at least in this first approach - as fixed at the drum base and subject to dead loads due to their own weight and live loads corresponding to increasing overloads, as well as to the actions on the interfaces belonging to the symmetry planes, which are the redundant unknowns of the static problem. With regard to a dome segment of amplitude  =  /8 (Fig. 1b), a discretization in rigid blocks is made, each one bounded by two consecutive cross-sections i and i+ 1 defined by the angles θ i and θ i+ 1 respectively with the dome’s Z-axis (Fig. 1c). symmetry plane of a sail symmetry plane passing for a rib X Y π /8 (a) X Z Y (b) (c) φ=π/8 φ=π/8 O X Z θ i θ i+ 1 (c) Figure 1 : The dome segment. (a) the two contiguous meridian symmetry planes; (b) 3D view; (c) section in the X-Z plane. The generic block like this defined have six faces: two of them - named radial - lying on the aforesaid radial cross-sections i and i +1, two other - named meridian - lying on meridian symmetry planes, and finally two other again lying on the extrados and intrados surfaces of dome respectively (Fig. 2). j ce i+1 1 2 3 7 8 6 4 5 le i Meridian face j (1-2-4-3) Meridian face j +1 (5-6-8-7) Radial face i (1-2-6-5) Radial face i +1 (3-4-8-7) Extrados face (1-5-7-3) Intrados face (2-6-8-4) Figure 2 : The generic block Have been used two reference: the fixed one (O, X, Y, Z), to define the vertices coordinates of generic block (Fig.1), and a local one ( G f , n , r , t ) placed in G f centroid of each contact interface with a contiguous block (Fig.3a), to define the stress resultants interacting through this generic interface, as shown below. S