Keywords: inelastic analysis, CFRP, strengthening, composite beam, numerical modelling, peeling failure.

The study describes a numerical approach used to investigate the non-linear behaviour of reinforced concrete beam strengthened with CFRP strip bonded on its soffit. The stiffness method was implemented for the analysis to predict the structural response of the composite beam in elastic as well as inelastic range of loading. The composite beam is divided into a sufficient number of different length segments. The cross section area of the composite beam is also divided into a sufficient number of layers to model different materials used in the beam. The inelastic stiffness of the beam is obtained by predicting the actual strain-stress distribution along the depth of the member using an incremental-iterative approach. Based on the converged strain distribution along the cross section of different member segments, new flexural and axial stiffness are evaluated for each segment and are used to assemble an updated stiffness matrix for the composite member. The algorithm used can predict the inelastic response of the beam in terms of deformation and failure mechanism.

Two beam specimens were analysed using the proposed numerical algorithm. The thicknesses of CFRP in the selected beams are 0.11mm and 0.22mm [1]. Each beam has been discretized into twenty-four segments along its length. The cross-section of the beam is divided into ten concrete layers, two steel layers and one CFRP layer.

The load-deflection responses at the mid-span of the beams obtained from the experimental and present analysis shows a good agreement. The two curves show similar response up to the cracking point after which the theoretical analysis exhibited a little stiffer behaviour compared to the experimental result. This difference might be due to the ignorance of the geometric non-linearity and, or other non-linearity features such as bond slip and degradation of adhesive layer due to cracking of the concrete.

In the first beam, the ultimate load predicted was equal to 80 kN (11% higher than that found experimentally). The maximum deflection found at the mid-span of the beam is 21.4mm (5% higher than that found experimentally). The developed numerical algorithm successfully predicts different stages of the failure of the composite beam; i.e. cracking, steel yielding, concrete non-linearity, softening of concrete after the material reach ultimate stress and the rupture of CFRP plate.

In the second beam, although the numerical analysis predicts a different failure mechanism compared to the beam tested, the ultimate load predicted was equal to 106 kN (23% higher than that found experimentally) and the maximum deflection found at the mid-span of the beam is 22.6mm (33% higher than that found experimentally). This discrepancy in the results was due to the failure of the tested beam in the ripping of concrete cover at the cut of point of CFRP plates. There is a wide discrepancy between the theoretical calculation and the values reported experimentally at the vicinity of cut-off point. However, as the distance from the cut-off point increase, the theoretical prediction matches very well with the experimental result. This is may be due to the large size of the beam segments in the vicinity of the cut-off points. A more refined mesh is required near the cut-off points to improve the results. Similarly, the numerical solution fails in predicting the correct values of shear stresses near the cut-off points and hence in predicting the peeling failure observed in the second beam.

1

Maalej M., Y. Bian, "Interfacial shear stress concentration in FRP-Strengthened beams", Composite Structures 54, 417-426, 2001. doi:10.1016/S0263-8223(01)00078-2

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