Modified strut-and-tie models for reinforced concrete deep beams with externally bonded CFRP systems

Reinforced concrete (RC) deep beams can be defined as the main structural component used in buildings and bridges to transfer heavy loads. Due to their relatively low shear span to depth ratio (less than 2.0), a linear strain distribution cannot be applied, thus there is a need for a rational model to address this nonlinearity. Numerous codes of practice and research recommended the use of the strut-and-tie model (STM) to analyse the discontinuity regions (D-regions) and consequently deep beams. The STM is an effective shear design method based on the lower-bound plasticity theorem. The significance of this method is that in D- regions, the STM model can predict the shear strength of members with better accuracy than traditional flexure theory. Since the last decades, using carbon fibre reinforced polymer (CFRP) as strengthening material for RC beams has become a topic of interest among researchers and CFRP has been suggested for structures including concrete deep beams. Moreover, RC structures may be subjected to various dynamic loading types. Considering all these loading types, it is important to understand the effect of loading rate on such structures. Nevertheless, scarce studies have been reported regarding the loading rates effect. In view of these cases, STM is not being able to predict the shear strength of deep beams, effectively. Thus, the objective of this study is to modify the STM to analyse concrete deep beams for the two cases. This study also highlights the development of an energy absorption capacity model of concrete beams under different loading rates. An STM of unstrengthened concrete deep beam is modified in two cases: (1) deep beam strengthened with FRP sheet under static loads, and (2) deep beam subjected to different loading rates. Unlike existing STMs, this study implements two FRP failure modes, namely FRP debonding and tensile rupture failure mode. Moreover, the particle swarm optimization (PSO) algorithm was used to search for the optimum set of unknown coefficients which are stress distribution and concrete tensile reduction factors. The optimum proposed model was built based on the data collected from existing experimental programs and the proposed finite element models. The proposed models have been verified against experimental data collected from this study and existing literature. The proposed STM approaches exhibit efficiency in assessing ultimate shear strength capacity comparison with the experimental results and can be used as design guides. The experimental results show that the growth of energy absorption of CFRP-strengthened RC deep beams varies from approximately 15% to 51% for shear span-to-effective depth ratios of 1.0 to 1.75 and 15% to 86% for shear reinforcement ratios of 0% to 0.4%, respectively. The results show that the PSO technique is suitable for assessing structural engineering problems and can be used as an efficient tool to explore the optimal solutions for different structural problems.

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