Analysis of Concrete Deep Beams with Fibre Reinforced Polymer Reinforcements using Indeterminate Strut-and-Tie Method
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Fibre-reinforced polymer (FRP) bars have gained popularity in industry to reinforce concrete. They are noncorrosive, strong in tension, but they are less stiff than traditional steel bars and fail in a brittle manner. Therefore, the behaviour of concrete beams reinforced with FRP bars is different in many ways than the behaviour of traditional steel bars reinforced beams. Development of rational design provisions for these beams is essential for wide acceptance of FRP bars in industry and for safe designs of FRP reinforced concrete. In order to develop these design principles, a good analysis model for such structural elements is needed. Strut-and-tie (ST) modelling is one accepted way to analyze reinforced concrete deep members, however the classical ST method was developed for steel reinforced concrete, where the ST method is based on steel yielding. Such ST method cannot be directly applied to FRP reinforced concrete. Based on the work done by Krall (2014), the indeterminate strut-and-tie (IST) method developed initially for steel reinforced deep beams that does not assume steel yielding and includes the nonlinear behavior of concrete can predict good results for FRP reinforced deep beams. In this thesis, the IST methodology for FRP reinforced concrete is developed and analyzed. Several aspects are studied to be the most essential features of IST method, which are the proposed geometries for the ST models, the softened concrete stress-strain relationships, the assumed heights of the compression nodes (h𝐶) and the softening factors for concrete struts (𝜁). Different ways to compute these features can affect the results predicted by the IST method, thus four ST models for deep beams with vertical reinforcement, four softened concrete stress-strain relationships, four approaches of h𝐶 , and four approaches of softening factors are developed. Some of the approaches and models are modified from existing ones, and the others are newly proposed in this research. The approaches and models are analyzed with specimens tested in different research programs having different reinforcement design, different beam sizes and different slenderness ratios, in order to find if the approaches and models can work properly with the IST method on different kinds of deep beams. As a result, an improved IST method is proposed, which can predict accurate results and can capture how different factors affect the shear strengths. Although the selected combinations of the approaches and models for the features are slightly different for beams with and without vertical reinforcement, the proposed IST method is proved to work properly on all kinds of deep beams. It is also found that the proposed IST method cannot properly predict the shear strength of FRP reinforced concrete slender beams, thus it shall only apply to find the shear strength of FRP reinforced concrete deep beams governed by arch action.
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Shuqing Liu (2022). Analysis of Concrete Deep Beams with Fibre Reinforced Polymer Reinforcements using Indeterminate Strut-and-Tie Method. UWSpace. http://hdl.handle.net/10012/18569