Issue 51

C. Anselmi et alii, Frattura ed Integrità Strutturale, 51 (2020) 486-503; DOI: 10.3221/IGF-ESIS.51.37 492 on N was enclosed to take into account the limited compression strength. We note that the cross section of the two domains coincide at abscissa N=N 0 /2 (Fig. 9, referred to the (M 1 , M 2 , N) 3D space, being M 1 and M 2 the components of M in the section principal reference). The twelve planes are summarized by the following equations: 0 )k (kM)k (kMNd t t r r      i i i i (3) 0 4 Nd )k (kM)k (kM 0 t t r r      / i i i (4) 0 Nd )k (kM)k (kMN-d 0 t t r r       i i i i i (5) being i the generic side ( i =1, 2, 3, 4). domain in [4] domain proposed 3 M 2 M 1 in [4] (a) (a) M 1 M 2 N O Q (b) domain proposed domain in [5] a 18] Figure 9 : Yield domain for rocking in the 3D space (M 1 , M 2 , N). (a) Cross section at N=N0/2.; (b) 3D view (axonometric projection) of linearized yield domain proposed and the approximate non linear one proposed in [18]. If in the Eqns. (3) - (5) the sign (=) is replace with (≤), the conditions for N, M r and M t that define the linearized yield domain are obtained. Linear sliding yield domains As mentioned above, the twelve conditions (3)-(5) related to rocking domain are necessary for all the interfaces, while further conditions related to sliding domain (Fig.10) must be added about radial interfaces.        tgφ   tgφ φ φ O T t (or T r , or M n ) N Figure 10 : Yield domain for sliding. In particular, the yield domain normal force N – shear force T is defined by a cone (Fig.11a), with axis coinciding with the N- axis has been opportunely replaced, in this first approach, by a pyramid - circumscribed to the cone - having four faces. Therefore we impose four conditions making reference to the Cartesian components T t and T r of T shear force: