Issue 38

S. Bennati et alii, Frattura ed Integrità Strutturale, 38 (2016) 377-391; DOI: 10.3221/IGF-ESIS.38.47 378 element to be strengthened and the desired level of structural performance [1]. For the strengthening of steel structures, carbon fibre reinforced polymers (CFRP) are preferred because of their superior mechanical properties [2, 3]. Furthermore, CFRP laminates can be pre-stressed, which enables more effective use of the composite material, contribution of the strengthening in carrying out the dead load, closure of cracks in concrete [4, 5], and increased fatigue life in steel [6]. The existing structure and FRP laminate behave as a composite structure with a key role played by the adhesive layer, which transfers the stresses between the bonded elements. As a matter of fact, debonding of the FRP laminate due to high interfacial stresses is a relevant failure mode for this type of interventions. Therefore, a wide number of theoretical and experimental studies have been conducted to achieve reliable and accurate evaluation of such interfacial stresses. Smith and Teng [7] presented a review of the theoretical models for predicting the interfacial stresses and also developed a solution for strengthened beams in bending. Al-Emrani and Kliger [8] determined the interfacial shear stresses in beams strengthened with pre-stressed laminates subjected to mid-span concentrated loads. Benachour et al. [9] extended the previous solutions to distributed loads and multidirectional laminates used as strengthening. All the aforementioned models consider the adhesive layer as an elastic interface to obtain simple closed-form solutions. A more realistic modelling of the adhesive can be achieved by introducing a non-linear (or piecewise linear) cohesive law for the interface [10–12]. Bennati et al. [13] used a cohesive-zone model to determine the overall non-linear response of an FRP-strengthened beam in pure bending. In a preliminary version of the present paper [14], such model has been extended to account for the pre- stressing of the laminate. The beam is considered simply supported and subjected to uniformly distributed load. According to the assumed application technology, the laminate is first put into tension, then bonded to the beam bottom surface, and finally fixed at both its ends by suitable connections. The beam and laminate are modelled according to classical beam theory. The adhesive is modelled as a cohesive interface with 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 suitable boundary conditions. Here, we determine an analytical solution to the stated problem, including explicit expressions for the internal forces and interfacial stresses. As an application, we consider the standard IPE series [15] for the steel beam and the Sika ® CarboDur ® system [16] for the FRP strengthening. The latter consists of an epoxy resin adhesive (Sikadur-30 ® ) and pultruded carbon fibre-reinforced polymer laminates (CarboDur ® S). For each considered steel cross section, we first carry out a preliminary design to determine the length and permanent load of the “existing” unstrengthened beam. Then, we imagine to apply the FRP strengthening and calculate the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate. Lastly, we take into account the ultimate limit state corresponding to the plasticisation of the mid-span steel cross section and evaluate the increased load bearing capacity of the strengthened beam [17, 18]. Calculations are carried out according to the Eurocodes [19–21] and Italian regulations on FRP strengthening [22, 23]. Figure 1 : FRP-strengthened steel beam subjected to uniformly distributed load. M ECHANICAL MODEL et us consider an I-section steel beam AB of length 2 L , simply supported at its ends and subjected to a uniformly distributed load per unit length, p (Fig. 1). As better specified in the following, the load p will actually be a combination of the beam self-weight, g 1 , a permanent load due to non-structural elements, g 2 , and an imposed load, q . The beam is strengthened by an FRP laminate of length 2 l adhesively bonded to its bottom surface. As concerns the application technique, we assume that the laminate is first pre-stressed by a suitable axial force, P , then adhesively L