A cohesive-zone model for steel beams strengthened with pre-stressed laminates

We analyse the problem of a simply supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed fibre-reinforced polymer (FRP) laminate. According to the assumed application technology, the laminate is first put into tension, then bonded to the beam lower 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. An analytical solution to the problem is determined, including explicit expressions for the internal forces and interfacial stresses. For illustration, an IPE 600 steel beam strengthened with a Sika® Carbodur® FRP laminate is considered. First, the elastic limit state load of the unstrengthened beam is determined. Then, the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate for the strengthened beam are calculated. As a result, the increased elastic limit state load of the strengthened beam is obtained.