Keywords: FRP composites, strengthening, reinforced concrete, design guides.

Repairing and upgrading of reinforced concrete (RC) structures by means of externally bonded fibre reinforced polymer (FRP) plates is increasingly receiving attention. FRP materials offer a good alternative to steel based technology because of their striking ease of installation and adaptation to the shape of structural elements and because of the preservation of their properties under a wide range of environmental conditions. The reduction of manufacturing costs has contributed to spread their use in the civil engineering field.

Design models for FRP flexural strengthening must account not only for the contribution of the plate to the flexural, compressive or shear strength to be achieved in the RC element, but also for the different failure modes that have been identified up to now. The prediction of these failure modes is one of the most important topics related to FRP strengthening and although higher-order analytical solutions have been proposed, simple closed-form solutions are preferred instead for their implementation within design rules. This paper describes and compares the flexural strengthening problem according to the European "fib Bulletin 14", the British Techincal Report 55 (TR 55) and the North American ACI 440.2R.

The calculation of the flexural capacity of the FRP strengthened RC section depends on the expected failure mode. Concrete crushing failure occurs if concrete reaches its ultimate compressive strain. FRP rupture happens when it is the plate that reaches its ultimate strain first. However, most likely, the flexural capacity will be governed by the flexural-crack induced debonding which entails the loss of the full composite action between the plate and the RC beam. The aforementioned guidelines deal with this type of failure by limiting the strain at the FRP to a certain value, although it is also recommended to verify the anchorage of the plate and the transmission of forces through the interface between the FRP and the concrete substrate. These guidelines include designing models for other reported failures such as the shear-crack induced debonding, the end-shear failure and the concrete cover separation. The latter is the most usually reported of them all, as well as the most complex to characterize. Finally, serviceability limit states are typically assessed by limiting the service stresses of materials.

Each of the design guidelines presented above was implemented on an optimization application programmed in MATLAB. The objective function was the amount of CFRP used for strengthening a RC beam and the constraints were the different ultimate and service limit states defined in the different code proposals. The design variables were the length and the characteristics of the CFRP plate. These were codified through one discrete variable, which was to be selected from a database that had been built with the specifications for sizes and mechanical properties of the CFRP plates supplied by a manufacturer. The optimization problem was solved through using a genetic algorithm (GA) which was found to provide satisfying results.

This application is used for solving a flexural strengthening problem, by means of which a more detailed comparison is made between the guidelines discussed in the present paper. The paper includes diagrams that represent the flexural capacity of the FRP strengthened beam when different CFRP plates from the aforementioned database are installed on the RC beam. No great differences are observed in the flexural strength estimated through each of the guidelines, but it must be taken into account that the plate size and stiffness have influence on the evaluation of other failure modes. The programmed application has proved its adaptability for the inclusion of current and future models for the assessment of failure modes, which constitutes and important advantage as newer and more reliable models become incorporated by national design guidelines for FRP strengthening.

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