Issue 51

C. Anselmi et alii, Frattura ed Integrità Strutturale, 51 (2020) 486-503; DOI: 10.3221/IGF-ESIS.51.37 489 (a) (b) X Y Z O r j n j r i G j G i G j+1 G i+1 r i+1 n j+1 n i+1 n i t j r j+1 t i+1 t i t j+1 n j N nj M rj G j G i G P t j n i t i M tj N ni M ni M ri T ri T ti M ti r i r j X Y Z O Figure 3 : (a) Fixed and local references; (b) Own weight P acting in the G centroid of block and stress resultants applied on the i radial face and on j meridian face. F ORCES ACTING ON THE SINGLE BLOCK ith reference to Fig. 3b, the generic block is subjected to the own weight P applied on its center of gravity G , and to the stress resultants applied on the centroid of each contact interface with a contiguous block, referred to the local reference n , r and t . The resultants on the radial interfaces are six, named normal force N n (or simply N), shear forces T t and T r , twist moment M n , bending moments M t and M r , respectively applied on the interfaces i and i+ 1. Whereas, on the meridian interfaces j and j+ 1, lying on symmetry planes, the resultants are only three: the normal force N n and the two bending moments M t and M r . With reference to i and j interfaces, all these forces can be expressed in matrix form by the S i and S j vector respectively:                                   i i i i i i x i x i x i r t n r t n )13( )13( )16( M M M T T N M R S                           j j j )x( j )x( j )x( j r t n 12 11 13 M M N M R S Besides, must be consider the overload acting on the dome - named OL - understood as a covering load applied in the centroid of extrados face (see Fig. 2), that in the present formulation increases through a collapse multiplier α  (Fig. 4a). If a lantern is present at the top of dome, also a force PL corresponding to one sixteenth of the lantern own weight will act on the block top (Fig. 4b), together with the OLL overload related to the small dome of the lantern (also increasing through the α multiplier). (a) (b) X Y Z O G e  ∙ OL PL  OLL Figure 4 : (a) The overload acting on the dome, increasing through an α multiplier  (b) The force on the block on top corresponding to one sixteenth of the lantern own weight, together with the overload (which also increases through α  acting to the small dome of the lantern. W