Issue 22

S. Bennati et alii, Frattura ed Integrità Strutturale, 22 (2012) 39-55 ; DOI: 10.3221/IGF-ESIS.22.06 39 A mechanical model for FRP-strengthened beams in bending S. Bennati, N. Dardano, P. S. Valvo Università di Pisa, Dipartimento di Ingegneria Civile – Strutture, Largo Lucio Lazzarino, 56126 Pisa s.bennati@ing.unipi.it, p.valvo@ing.unipi.it A BSTRACT . We analyse the problem of a simply supported beam, strengthened with a fibre-reinforced polymer ( FRP) strip bonded to its intrados and subjected to bending couples applied to its end sections. A mechanical model is proposed, whereby the beam and FRP strip are modelled according to classical beam theory, while the adhesive and its neighbouring layers are modelled as an interface having a piecewise linear constitutive law defined over three intervals (elastic response – softening response – debonding). The model is described by a set of differential equations with appropriate boundary conditions. An analytical solution to the problem is determined, including explicit expressions for the internal forces, displacements and interfacial stresses. The model predicts an overall non-linear mechanical response for the strengthened beam, ranging over several stages: from linearly elastic behaviour to damage, until the complete detachment of the FRP reinforcement. S OMMARIO . Nel presente lavoro affrontiamo il problema di una trave semplicemente appoggiata, rinforzata con una striscia di materiale fibro-rinforzato a matrice polimerica (FRP) incollata all’intradosso, e soggetta a coppie flettenti applicate alle sue estremità. Nel modello meccanico proposto, la trave e la striscia di rinforzo sono modellate secondo la teoria delle travi classica, mentre l’adesivo e gli strati adiacenti sono modellati come un’interfaccia avente una legge costitutiva lineare a tratti definita su tre intervalli (risposta elastica – risposta softening – debonding). Il modello è descritto da un sistema di equazioni differenziali, completato da opportune condizioni al contorno, che viene risolto analiticamente ricavando espressioni esplicite per le principali grandezze di interesse (spostamenti, caratteristiche della sollecitazione, sforzi d’interfaccia). Il modello prevede per la trave rinforzata una risposta meccanica complessiva non lineare, articolata in più fasi: da quella elastica lineare a quella danneggiata, fino ad arrivare al completo distacco del rinforzo di FRP. K EYWORDS . FRP strengthening; Adhesive; Beam theory; Interface. I NTRODUCTION ibre-reinforced polymers (FRP) are currently used in civil engineering to carry out strengthening and repair operations on existing constructions. The pre-existing structural elements (made of traditional materials such as, for instance, masonry, wood, concrete, steel etc.) are strengthened by gluing FRP reinforcement sheets or strips on their external surface. The shape and thickness of the external reinforcement obviously vary according to the type of element and the level of structural performance desired [1–4]. In order to evaluate the effectiveness of such operations, however, it is necessary to take in account the possible emergence of phenomena of delamination or detachment of the FRP reinforcement, which can seriously jeopardize the outcome of the strengthening operations. Moreover, delamination and detachment phenomena may manifest themselves in various and complex ways. In the case of concrete structures, for instance, delamination may occur at different levels involving the FRP strips themselves, the adhesive and/or the superficial layers of the concrete. Delamination is caused F