Issue 47

E. Grande et alii, Frattura ed Integrità Strutturale, 47 (2019) 321-333; DOI: 10.3221/IGF-ESIS.47.24 324 Figure 1 : Schematic of an infinitesimal portion of the strengthening system and the upper mortar component used for performing the equilibrium of the involved forces. Considering a linear-elastic behavior for both the reinforcement and the mortar: i p p p p e i e e c c c c du ds E E dx dx du ds ds E E dx dx dx              (3) the system of differential Eqns. (1) becomes:       2 1 2 2 2 2 2 2 0 0 i e e i i i e e e d s K s s dx d s d s K s dx dx                           (4) where 1 K and 2 K are two constants equal to: 1 2 1 1 , e p p c c K K E t E t   (5) Considering the system (4), the explicit solution is here derived by introducing different shear stress-slip laws characterizing the behavior of the reinforcement/mortar interface. Approach 1: nonlinear behavior of the lower interface A preliminary approach is based on the assumption of a linear-fragile behavior with a residual shear strength in the post- peak stage only for the lower interface: 1 ( ) ( ) otherwise i i i i i i i i res s G s s s s           (6) where i res  is the residual value of the shear strength in the post-peak stage, and i G is the shear stiffness of the lower interface in the pre-peak stage. Differently, a linear-elastic behavior is assumed for the upper interface ( ) e e e e s G s   , where e G is the shear stiffness of the upper interface. P p p d    p  c c d    c  e  e  i  support lower interface strengthening upper interface upper mortar lower mortar x