Issue 38

S. Bennati et alii, Frattura ed Integrità Strutturale, 38 (2016) 377-391; DOI: 10.3221/IGF-ESIS.38.47 379 bonded to the beam, and finally fixed at both its end sections, C and D . We denote with a = L – l the distance of the anchor points from the end sections of the beam. We denote with b b and h b respectively the width and height of the steel cross section and with h f the thickness of the flange (Fig. 2). Furthermore, we indicate with A b , I b , W b , and Z b respectively the area, moment of inertia, elastic modulus, and plastic modulus of the cross section of the beam. Besides, we denote with b f and t f respectively the width and thickness of the laminate and with t a the thickness of the adhesive layer. Lastly, we indicate with A f = b f t f the area of the cross section of the laminate. Figure 2 : Cross section of the strengthened beam. Thanks to symmetry, the model can be limited to the left-hand half system (Fig. 3). The generic cross section of the beam is identified by a curvilinear abscissa, s , measured from the anchor point of the laminate, C . Similarly, the generic cross section of the laminate is identified by a curvilinear abscissa, s *, also measured from point C . We denote with w b ( s ) the axial displacements of points at the beam bottom surface and with w f ( s *) the axial displacements of the laminate cross sections. Figure 3 : Mechanical model of the strengthened beam. In the proposed mechanical model, the steel beam is considered as a flexible beam, while the FRP laminate is modelled as an extensible strip. An elastic-perfectly plastic behaviour is assumed for steel with Young’s modulus E s and design yield stress f yd (Fig. 4a). The behaviour of FRP is assumed elastic-brittle with Young’s modulus E f and design tensile strength f fd (Fig. 4b). The adhesive layer is represented by a zero-thickness cohesive interface, which transfers shear stresses,  , and no normal stresses. The interfacial stresses depend on the relative displacements,  w = w f – w b , between the laminate and the bottom surface of the beam. The interface behaviour is assumed linearly elastic for shear stresses up to a limit value,   ; then, a linear softening stage, corresponding to progressive damage, follows; lastly, debonding occurs. For  w ≥ 0, the cohesive interface law is given by the following piecewise linear relationship (Fig. 4c): s u u u k w w w w k w w w w w w w 0 0 , 0 (elastic response) ( ) ( ), (softening response) 0, (debonding)                         (1)