Estudio del inciso cuarto del artículo 42 de la Ley General de Seguros

Steel concrete interaction influences the crack behaviour of the beam and therefore the performance of the FRP concrete interface and eventually of

the entire retrofitted structural element. The mechanism by which forces are transferred between concrete and reinforcement has been widely inves- tigated since reinforced concrete was introduced as a construction material and a detailed discussion of this topic is outside the scope of this work. How- ever, the bond slip behaviour of steel reinforcement is briefly described for completeness and to give the relations used in the FEM models.

The interaction between concrete and rebars is characterized by four dif- ferent stages Figure 4.5.

Stage I (uncracked concrete): in this stage the bond action is due mainly to chemical adhesion. The bond stresses are characterized by low value, but highly localized stresses may arise close to lug tips (Figure 4.5, 4.7).

Stage II (first cracking): in this stage the chemical adhesion breaks down and the stress transfer is due to mechanical interlocking of the lugs in the surrounding concrete. Large bearing stresses are generated in the concrete at the lugs figure(4.7). Due to these bearing stresses micro cracks originate at the tips of the lugs allowing the bar to slip as the bond stresses increase. Stage III (conical struts action): for higher bond stress values, longitu- dinal cracks start to form originating from initial micro cracks, generating conical struts, Figure 4.5, 4.7. The outward component of the strut action Figure 4.7 is resisted by the hoop stresses in the surrounding concrete. The surrounding concrete will exert therefore a confinement action on the bar. Thus, the bond strength and the stiffness are due mostly to the interlocking among the lugs and the surrounding concrete.

Stage IV (residual friction): at this stage the conical struts have failed and only a residual frictional stress transfer is active.

The interfacial stresses associated with the interaction mechanisms de- scribed, are of different nature and very variable along the bar. For the pur- pose of the analysis of a reinforced concrete structural element these stresses need to be spatially averaged. By carrying out this spatial averaging we de- fine a bond stress that can be used to define a bond slip relation that simplify considerably the treatment of this problem Figure 4.5, 4.6, 4.7.

The mechanisms of stress transfer of stages one to three are considered primary mechanisms as they can be found within the serviceability load limits of the structure. The residual frictional stress transfer of stage IV is considered a secondary mechanism (whose effect combined with all the others is present since the beginning of the loading process anyway) as steel bars are considered debonded if this is the only resistance mechanism active. In Figure 4.6 typical failure modes of the concrete surrounding the rebars are shown.

We now need to establish an appropriate constitutive law for the interface. The bond slip relation should depend, in principle, upon the type of

Figure 4.6: Modes of bond failure: (a) pull out; (b) splitting-induced pull out accompanied by crushing and/or shearing-off in the concrete under the rib action; (c) splitting accompanied by slip on the rib faces (Coirus, Andreasen, 1992).

Figure 4.7: Bond splitting in reinforced concrete (deformed bars): (a) typical stress peak in the elastic phase; (b) bar concrete slip and wedging action of the bar; (c) main parameters.

s1 (mm) s2 (mm) s3 (mm) τ1 (MPa) τ2 (MPa) Ω

Confined conc. _{1 3} Clear rib

spacing 2.5(fck)1/2 (fck)1/2 0.4

Unconfined conc. _{0.6 0.6 10 2.0(f}

ck)1/2 0.6(fck)1/2 0.4

Table 4.1: Bond slip law parameters

bar, the concrete strength, the confinement regime and the conditions of the materials (rusting of steel, carbonation of concrete). Workmanship of the structure is also relevant.

However, a constitutive low depending only on the concrete strength and confinement regime is given in the CEB-FIP Model Code 1990. This is based on a work by Ciampi at al.. In this model the primary zone is non linear and it is modeled by: τ = ρ₁sΩ (4.21) where ρ₁ = τ1 ρΩ 1 (4.22) Ω is an empirical constant (Ω < 1) that describe the shape of the bond- stress-slip curve. The model includes a plateau at the peak stresses (τ1),

followed by a linear degradation zone. The bond stress due to the secondary bond mechanism is assumed constant.

The model is characterised by the parameters: s1, s2, s3, τ1, τ2, and Ω;

refer to Figure 4.8 for the meaning of these parameters.

These parameters are given in the Model Code as functions of the clear rib spacing of the rebars, the concrete strength and the confinement regime. Their expression is reported in Table 4.1

For implementation reasons the above relation has been simplified, in the FEM models, to the one with a linear initial branch followed by linear softening described in Figure 4.9.

The parameters characterizing the model adopted have been derived im- posing the same peak stress as in the CEB-FIP model, a slip displacement at the peak stress (so) equal to s1 and a fracture energy Gc equal to the energy

obtained integrating the CEB-FIP relation between zero and the slip dis- placement s3. This is equivalent to neglecting the the residual bond stresses.

Figure 4.8: Analytical model for local bond stress-slip relationship (Ciampi et al., 1981; Eligehausen et al., 1983); monotonic loading.

Area = G

s

τ

s

s

s

τ

τ

s

Figure 4.9: Bond slip relation used in the FEM models.