Issue 31

H.F.S.G. Pereira et alii, Frattura ed Integrità Strutturale, 31 (2015) 54-66; DOI: 10.3221/IGF-ESIS.31.05 57   2 2 0 s s d s D s dx E A     (1) where D is the diameter, A s is the cross sectional area, E s is the Young’s modulus of the reinforcing bars and s ( x ) is the slip between concrete and the embedded rebar’s length at the abscissa x . Using Eq. (1), important phenomena can be analysed such as: the anchorage length evaluation, the determination of the tension stiffening effect and crack spacing and opening. These problems can be solved once the boundary conditions of the specific problems are specified and this observation reinforces the importance of a consistent local bond-slip relationship. Relatively to the analytical expressions for the bond-slip relationships, several hypotheses have been proposed and used in the past. One simpler alternative is to define the bond stress – slip relationship with linear branches [15]. Nevertheless, alternatively, a more robust non-linear relationship between bond stress and slip can be used. The relationship established by Eligehausen [15] and afterwards adopted by the Model Code 2010 [27] is expressed by the following non-linear functions as follows:   max 1 1 ; 0 s s s s       (2) max 1 2 ; s s s      (3)       2 max max 2 3 3 2 ; f s s s s s s s             (4) 3 ; f s s     (5) Fig. 6 depicts the bond stress – slip relationship according to [27]. Tab. 1 includes the parameters of the bond-slip relationship proposed by Model Code 2010 [27] for distinct bond conditions. Figure 6 : Local bond stress-slip law according to [27]. Bond Conditions  max  f  [-] s 1 [mm] s 2 [mm] s 3 [mm] Good 2.5( fcm ) 0.5 0.4  max 0.4 1 3 Clear Rib spacing of rebar Table 1 : Parameters defining the bond-slip relationship [27]. In the present work two distinct local bond stress – slip laws were used. For the parametric study, the bond stress – slip relationship was modelled using the linear cohesive law provide by ABAQUS software, as depicted in Fig. 7. This constitutive model available in ABAQUS was originally developed for the delamination of composites, but it can also be used to model cohesion between steel rebar and concrete, assuming that the interaction between concrete and steel rebar can be collapsed to zero-thickness surface. This approach has been already previously adopted by Alfano and Serpieri [28,