Structural Behaviour of Conventional and FRP- Reinforced Concrete Deep Beams

ABSTRACT
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\n Many structural applications such as pile caps, girders, foundation walls and offshore structures include the use of reinforced concrete deep beams as structural elements. The structural behaviour of deep beams is affected by its span to depth ratio, type of loading, reinforcement ratio in vertical and horizontal directions, concrete strength, and type of cross section. Since the traditional beam theory is not applicable for designing deep beams, the strut and tie model (STM) was developed earlier as a rational method for estimating the capacity of a reinforced concrete deep beam and accepted in the current codes and standards for the design of such beams. While for designing a conventional (i.e. steel reinforced) concrete deep beams STM has been available in different codes and standards, for FRP-reinforced concrete deep beams such provisions are not available in most codes and standards. Only in the recent edition of the relevant Canadian standard (i.e., CAN/CSA S-806-12) which came out much later than the commencement of the present research, an STM approach has been provided, which is primarily based on that of conventional deep beams with some adjustments by using FRP reinforcement’s properties to calculate the tie capacity. One of the reasons for the lack of standards or code provisions for such systems in other codes (e.g., ACI and Eurocode) is perhaps the lack of adequate experimental data available on the performance of such beams. As the use of FRP reinforced concrete structures is increasing, there is a need to the development of a design method for FRP-reinforced concrete deep beams, which could be similar to the existing STM method available for the conventional deep beams, similar to the approach taken by the Canadian standard. But, such provisions must be validated and/or modified appropriately and calibrated with experimental studies. 
\n The objectives of the present research are to: (1) Identify the critical parameters governing the behaviour of conventional concrete deep beams; (2) Develop a design procedure for FRP reinforced concrete deep beams; (3) Study the critical factors in FRP-reinforced concrete deep beams and evaluate the proposed design procedure using numerical and experimental tests; and (4) Evaluate the STM procedure outlined in the CSA-S806-12[2012] for designing FRP reinforced deep beams. The current design provisions for conventional concrete deep beams as provided in the following three prominent standards that use the strut–and-tie model have been extensively reviewed: ACI 318-08, Eurocode EN 1992-1-1-2004(E) and Canadian code CSA A23-3-04. The influence of different variables on the ultimate strength of deep beam estimated using STM provisions in the codes are studied. A large database of available experimental studies on conventional deep beams has been created. The ultimate load capacity and failure pattern for each sample in the database have been evaluated using the STM models provided in the above three standards, and compared with the experimental results and critical parameters that have been identified. The results of the preliminary study show that the use of Strut and Tie model are generally appropriate method for beams with shear-span to depth ratio less than or equal to two. Also the study confirmed that both the shear span-to-depth ratio and the amount of shear web reinforcement have the most significant effect on the behaviour of deep beams and on the codes predictions of the ultimate strength of deep beams. 
\n Based on the review of the STM models available for the conventional deep beams as provided in the current standards, a similar model has been developed here to design FRP-reinforced deep beams. Using the proposed method, a set of FRP-reinforced deep beam has been designed and constructed. An experimental program has been carried out to test these beams to study the applicability of the proposed method and effect of the critical design parameters. Nine FRP reinforced concrete deep beams were divided into three groups, based on their shear span-to-depth ratio (a/d), and tested under a single concentrated load to investigate their behaviour and strength. The test variables were the shear span-to-depth ratio and the quantity of web shear reinforcement. The behaviour of deep beams is indicated by their shear strength capacity, mid span deflection, strain at the FRP longitudinal and web reinforcement, crack propagation, and type of failure. A new equation is presented in this study to calculate the contribution of the FRP web reinforcement to the ultimate shear capacity of FRP-reinforced concrete deep beams. As a new version of the CSA standard is available now which provides STM procedure for FRP-reinforced deep beams, the test results have been compared to predictions based on the current CSA design procedure. 
\n This investigation reveals that the Strut and Tie model procedure in the CSA-S806-12 code provides a conservative and convenient design procedure for FRP-reinforced concrete deep beams. However, there are some areas where the code provisions can be improved and some inconsistencies in the way the strut capacity is determined can be removed. In addition, the shear design procedures of the ACI 440.1R-06 Code and of the modified Strut and Tie model (STM) from Appendix A of the ACI 318-08 Code were compared based on their test results and a modified STM procedure based on ACI 318-08 provision has been proposed for the adoption to ACI 440. This investigation reveals that adopting the procedure in the ACI 318-08 Code and taking into consideration the properties of FRP reinforcement provides a conservative and rational design procedure for FRP reinforced concrete deep beams.

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