Issue 51

C. Anselmi et alii, Frattura ed Integrità Strutturale, 51 (2020) 486-503; DOI: 10.3221/IGF-ESIS.51.37 491 t G r Figure 6 : Generic quadrilateral interface and local reference Linear rocking yield domains For the case of unlimited compression strength, a linear yield domain was proposed in [3, 4] with reference to the quadrilateral section of Fig. 7; within a coherent kinematic mechanism, the rotation axis has to coincide with one of the four section sides, so we imposed four limit conditions: 0 MNd   i i i (2) with d i (Fig.7a) distance between the G centroid and the generic side i ( i =1, 2, 3, 4), and i i kM   M , being t t r r M M k k M   the Cartesian expression of the bending moment M (Fig.7b). k 3 d 4           d 3 d 1 k 2 k 4 k 1 G d 2 (a) M r d i k  i M t G r M i M t (b) Figure 7 : The quadrilateral interface. (a) Geometric aspect; (b) Mechanical aspect. These conditions define four planes passing through the origin O of the 3D-reference (M t , M r , N), that form the pyramid of Fig. 8, having cross section homothetic to the quadrilateral interface (coincident with the linear domain proposed in [18] starting by a different formulation). M r O′ M t O M r M t N (a) M r O M t (b) Figure 8 : Yield domain. (a) The four planes through the origin O; (b) Cross section. As the present paper only consider vertical loads, here we have assumed a limited compression strength of the masonry; in order to include a limit to the compressive stress into domain of Fig. 8, we have added four planes parallel to N-axis of the 3D-reference (M t , M r , N), and four other planes forming an opposite pyramid passing through the Q point at abscissa N=N 0 , being N 0 the limit normal force applied in the G centroid which leads the entire section to the collapse. This linear yield domain results circumscribed to the approximate nonlinear one proposed in [18], where an additional quadratic term