Issue 47

E. Grande et alii, Frattura ed Integrità Strutturale, 47 (2019) 321-333; DOI: 10.3221/IGF-ESIS.47.24 325 On the basis of these assumptions it is evident that, after the attainment of the slip threshold value at the lower interface, two different parts characterize the behavior of the specimen: part “1” where the upper mortar and the interfaces are both in the pre-peak stage and part “2” where the upper mortar and the upper interface are both in the pre-peak stage while the lower interface is de-bonded for a length a , representing an unknown of the problem. Consequently, four differential equations govern the problem. The first two equations are derived by considering the equilibrium involving an infinitesimal portion of the strengthening system in the part “1”: 2 1 3 1 1 2 2 2 1 1 4 1 2 2 0 0 0 i e i i e e d s K s s dx x L a d s d s K s dx dx                            (7) where: 3 1 4 2 , , i e e e G K K G K K G G     . The other two equations are obtained through the equilibrium involving an infinitesimal portion of the strengthening system of the part “2”: 2 2 3 2 2 2 2 2 2 4 2 2 2 0 0 i e i e e d s K s dx L a x L d s d s K s dx dx                            (8) where i res e G    . The system of differential Eqns. (7) and (8) has an analytical solution that depends on eight constants of integration determined by introducing suitable boundary conditions. In particular, the following conditions are indeed enforced:                         1 1 2 1 2 1 2 1 2 1 2 1 1 0 0 0 0 0 P e e c c e e c c e e p p i i e e i L L a L a L a L a s L a s L a s L a s L a s L a s                         (9) The solution is graphically reported in Fig. 2 by considering a length value of the part “2” equal to a=50 mm , a residual value of shear strength equal to zero and the data reported in Tab. 1. Approach 2: nonlinear behavior of both the interfaces As shown in [11,17], the damage of the upper mortar generally occurs before the slipping of the reinforcement/mortar interfaces by particularly influencing the shear stress transfer mechanism. This phenomenon is here simple introduced by considering an elastic-fragile behavior also for the upper interface and assuming for this component of the strengthening system a bond strength equal to the shear stress corresponding to the attainment of the tensile strength of the upper mortar layer. In other words, the effect of the damage of the upper mortar is implicitly introduced into the behavior of the upper interface.