Issue 22

S. Bennati et alii, Frattura ed Integrità Strutturale, 22 (2012) 39-55 ; DOI: 10.3221/IGF-ESIS.22.06 53 Figure 14 : Applied couple M as a function of the transverse displacement,  of the mid-span section. Considering the above, it is reasonable to conclude that the value of the applied couple, u M , corresponding to the end of stage 2 and the beginning of stage 3, represents a limit load for the FRP-strengthened beam. Although the model provides for the possibility of reaching equilibrium at higher load values, this comes at the cost of very large displacements and deformations, together with undesirable dynamic effects, which may not be compatible with the structure’s bearing capacity. Moreover, the fact that the stage 2 response may exhibit an only weakly non-linear trend represents a further hazard, as structural failure may come about suddenly without any warning signs. C ONCLUSIONS he problem of a simply supported beam strengthened with a strip of FRP glued to the intrados and subject to concentrated couples applied to its ends has been analysed. A mechanical model has been developed whereby the beam and reinforcement strip are modelled according to classical beam theory, while the adhesive and adjacent layers are modelled as a zero-thickness interface having a piecewise linear constitutive law defined over three distinct intervals (elastic response – softening response – debonding). The differential problem which describes the model has been solved analytically, and explicit expressions for the main variables of interest (displacements, internal forces, interfacial stresses) have been determined. For such a strengthened beam the model predicts an overall non-linear mechanical response divided into several stages: from a linearly elastic to a non-linear (damaged) response, up to complete detachment of the FRP reinforcement. The values of the applied couple corresponding to the beginning and end of each stage of behaviour have been determined. In particular, approximate, yet effective, analytical expressions for 0 M and u M have been given. These values correspond respectively to the end of the linearly elastic response (end of stage 1) and to incipient detachment of the FRP reinforcement (beginning of stage 3). u M has been recognised as a limit load for such an FRP-strengthened beam. In fact, higher values of the applied couple produce very large displacements and deformations, potentially incompatible with the structure’s bearing capacity. Moreover, it has been noted that these large displacements may occur suddenly, without warning, together with undesired dynamic effects, which could represent a further hazard in implementing strengthening operations of this type. A CKNOWLEDGEMENTS Financial support from MIUR (PRIN 2008 – Prot. N. 20089RJKYN_002) is gratefully acknowledged. T