Abstract
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. We assume that 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. An analytical solution to the problem is determined, including explicit expressions for the internal forces and interfacial stresses. As an application, we consider the standard IPE series for the steel beam and the Sika® CarboDur® system for the adhesive and laminate. For each considered cross section, we first carry out a preliminary design of the unstrengthened steel 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. KEYWORDS. Steel beam; FRP strengthening; Adhesive; Beam theory; Cohesive-zone model; Analytical solution; Pre-stressing; Ultimate limit state; Load bearing capacity.
Highlights
F ibre-reinforced polymers (FRP) are increasingly used in civil engineering for the strengthening of existing constructions
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
W e have presented the mechanical model of a supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed FRP laminate
Summary
F ibre-reinforced polymers (FRP) are increasingly used in civil engineering for the strengthening of existing constructions. The material properties, factored according to the Eurocodes [20, 21] and Italian regulations on FRP strengthening [22, 23], are the following: steel (grade S235): Young’s modulus, Es = 210 GPa; characteristic yield stress, fyk = 235 MPa; partial factor for material, s = 1.05; design yield stress, fyd = fyk / s = 223.81 MPa; adhesive (Sikadur®-30): shear modulus, Ga = 4.923 GPa; characteristic strength, k = 15 MPa; environmental conversion factor, a = 0.85; partial factor for material, a = 1.2; design strength, 0 = a k / a = 10.63 MPa; laminate (CarboDur® S): longitudinal Young’s modulus, Ef = 165 GPa; characteristic tensile strength, ffk = 3100 MPa; partial factor for material, f = 1.1; design tensile strength, ffd = a ffk / f = 2395.45 MPa. Concerning the geometry of structural elements, the geometric properties of the steel cross sections are listed in Tab. 1. We consider the elastic limit state of the beam To this aim, the normal stresses at the upper and lower surfaces of the mid-span cross section of the beam, 2 and 2 , respectively, are computed.
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