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Reinforced concrete deep beams are vital structural members serving as load transferring elements. The behavior of reinforced concrete deep beams is complex. Nonlinear distribution of strain and stress must be considered. Prior to 1999, ACI 318 Codes included an empirical design equation for reinforced concrete deep beams. Since 2002, the strut and tie model and nonlinear analysis have been required. However, both methods have disadvantages of complexity or lack of transparency. The objective of this study is to produce a simple, reliable design equation for reinforced concrete deep beams. A nonlinear finite element program, ATENA, was used for analyzing and predicting the behavior of concrete and reinforced concrete structures. First, applicability of ATENA was verified by developing the computer models of simply supported and two span continuous deep beams based on Birrcher’s tests of simply supported deep beams. Tests by Rogowsky and Macgregor and by Ashour are the basis for the models of continuous two span deep beams. Those tests were selected because the researchers reported adequate details of the experimental program and on specimen behavior. Then a series of simply supported and two span continuous deep beam models were developed based on the details and geometry of Birrcher's beams. The computer models were used to investigate the following parameters: the compressive strength of concrete, shear span to depth ratios, longitudinal reinforcement ratios, web reinforcement, effect of member depth, and loading conditions. Finally, a proposed design equation for shear strength of reinforced concrete deep beams was derived based on the observed the behavior of reinforced concrete deep beam tests, the results of the analytical study, and a plastic truss model. The proposed equations were in good agreement with test values and provide an alternate approach to current design procedures for deep beams. / text

yes / Twenty two reinforced concrete continuous deep beams with openings and two companion solid deep beams were tested to failure. The main variables investigated were the configuration of web reinforcement around openings, location of openings, and shear span-to-overall depth ratio. The influence of web reinforcement on controlling diagonal crack width and load capacity of continuous deep beams with openings was significantly dependent on the location of openings. The development of diagonal crack width and load capacity of beams having openings within exterior shear spans were insensitive to the configuration of web reinforcement. However, for beams having openings within interior shear spans, inclined web reinforcement was the most effective type for controlling diagonal crack width and increasing load capacity. It has also observed that higher load and shear capacities were exhibited by beams with web reinforcement above and below openings than those with web reinforcement only above openings. The shear capacity at failed shear span of continuous beams tested is overestimated using Kong et al’s formula developed for simple deep beams with openings.

Yes / The test results on eight two-span deep beams made of self-compacting concrete (SCC) are presented and discussed in this paper. The main parameters investigated were the shear span-to-depth ratio, and the amount and configuration of steel reinforcement. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the other block resting on the other two supports. Both concrete compressive strength and web reinforcement had a major effect in controlling the shear capacity of the beams tested. For the shear span-to-depth ratio considered, the vertical web reinforcement had more influence on the shear capacity of the specimens than the horizontal web reinforcement. The shear provisions of the ACI 318M-11 are unconservative for most of the beams tested. Comparisons of test results with the strut-and-tie model (STM) suggested by ACI 318M-11, EC2 and CSA23.4-04 showed that the predictions are reasonable for continuous deep beams made with low and medium compressive strength. Although the equation suggested by ACI 318M-11 is very simple, its prediction is more accurate than the STM suggested by different design codes. / This research investigation was funded by the Higher Education Ministry in The Libyan Government.

Yes / The current design codes, such as ACI 318-14, EC2 and CSA23.3-04, in addition to previous research investigations suggested different expressions for concrete effectiveness factor for use in limit state design of concrete structures. All these equations are based on different design parameters and proposed for normal concrete deep beams. This research evaluates the use of different effectiveness factor equations in the upper and lower bond analyses of continuously-supported self-compacting concrete (SCC) deep beams. Moreover, a new effectiveness factor expression is suggested to be used for upper and lower bound solutions with the aim of improving predictions of the load capacity of continuously-supported SCC deep beams. For the range of deep beams considered, the strut-and-tie method with the proposed effectiveness factor formula achieved accurate predictions, with a mean of 1.01, a standard deviation of 6.7% and a coefficient of variation of 6.8%. For the upper-bound analysis, the predictions of the proposed effectiveness factor equation were more accurate than those of the formulas suggested by previous investigations. Overall, although the proposed effectiveness factor achieved very accurate predictions, further validation for the proposed formula is needed since the only data available on continuous SCC deep beams are those collected form the current study.

Yes / Nine continuous concrete deep beams reinforced with glass fibre reinforced polymer (GFRP) bars were experimentally tested to failure. Three main parameters were investigated, namely, shear span-to-overall depth ratio, web reinforcement and size effect. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. The experimental results were employed to evaluate the applicability of the methods suggested by the American, European and Canadian codes as well as the previous studies to predict the load capacities of continuous deep beams reinforced with GFRP bars. It was found that these methods were unable to reflect the influences of size effect and/or web reinforcement, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper-bound analysis was developed to predict the load capacity of the tested specimens considering a reduced bond strength of GFRP bars. A good agreement between the predicted results and the experimental ones was obtained with the mean and coefficient of variation values of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis. / Higher Committee of Education Development in Iraq (HCED)

yes / Ten reinforced-concrete continuous deep beams with openings were tested to failure. The main variables investigated were the shear span-to-overall depth ratio, and the size and location of openings. Two failure modes influenced by the size and location of web openings regardless of the shear span-to-overall depth ratio were observed. The normalised load capacity of beams having a web opening area ratio of 0·025 within exterior shear spans was approximately similar to that of their companion solid beams. Continuous deep beams having web openings within interior shear spans exhibited a higher load capacity reduction with the increase of the opening size, similar to simply supported deep beams with web openings. Formulae based on the upper bound analysis of the plasticity theory were proposed to predict the load capacity of continuous deep beams with web openings. Comparisons between the measured and predicted load capacities showed a good agreement.

The present research is conducted to investigate the structural behaviour of continuously supported deep beams made with SCC. A series of tests on eight reinforced two-span continuous deep beams made with SCC was performed. The main parameters investigated were the shear span-to-depth ratio, the amount and configuration of web reinforcement and the main longitudinal reinforcement ratio. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the rest of the beam fixed on the other two supports. The amount and configuration of web reinforcement had a major effect in controlling the shear capacity of SCC continuous deep beams. The shear provisions of the ACI 318M-11 reasonably predicted the load capacity of SCC continuous deep beams. The strut-and-tie model recommended by different design codes showed conservative results for all SCC continuous deep beams. The ACI Building Code (ACI 318M-11) predictions were more accurate than those of the EC2 and Canadian Code (CSA23.3-04). The proposed effectiveness factor equations for the strut-and-tie model showed accurate predictions compared to the experimental results. The different equations of the effectiveness factor used in upper-bound analysis can reasonably be applied to the prediction of the load capacity of continuously supported SCC deep beams although they were proposed for normal concrete (NC). The proposed three dimensional FE model accurately predicted the failure modes, the load capacity and the load-deflection response of the beams tested.

The present research is conducted to investigate the structural behaviour of continuously supported deep beams made with SCC. A series of tests on eight reinforced two-span continuous deep beams made with SCC was performed. The main parameters investigated were the shear span-to-depth ratio, the amount and configuration of web reinforcement and the main longitudinal reinforcement ratio. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the rest of the beam fixed on the other two supports. The amount and configuration of web reinforcement had a major effect in controlling the shear capacity of SCC continuous deep beams. The shear provisions of the ACI 318M-11 reasonably predicted the load capacity of SCC continuous deep beams. The strut-and-tie model recommended by different design codes showed conservative results for all SCC continuous deep beams. The ACI Building Code (ACI 318M-11) predictions were more accurate than those of the EC2 and Canadian Code (CSA23.3-04). The proposed effectiveness factor equations for the strut-and-tie model showed accurate predictions compared to the experimental results. The different equations of the effectiveness factor used in upper-bound analysis can reasonably be applied to the prediction of the load capacity of continuously supported SCC deep beams although they were proposed for normal concrete (NC). The proposed three dimensional FE model accurately predicted the failure modes, the load capacity and the load-deflection response of the beams tested. / Higher Education Institute in the Libyan Government

This research aims to investigate the behaviour of glass fibre reinforced polymer bars (GFRP) reinforced continuous concrete deep beams. For this purpose, experimental, analytical and numerical studies were conducted. Nine continuous concrete deep beams reinforced with GFRP bars and one specimen reinforced with steel bars were experimentally tested to failure. The investigated parameters included shear span-to-overall depth ratio (𝑎/ℎ), size effect and web reinforcement ratio. Two 𝑎/ℎ ratios of 1.0 and 1.7 and three section heights of 300 mm, 600 mm and 800 mm as well as two web reinforcement ratios of 0% and 0.4% were used. The longitudinal reinforcement, compressive strength and beam width were kept constant at 1.2%, ≈55 MPa and 175 mm, respectively. The web reinforcement ratio achieved the minimum requirements of the CSA S806-12. The experimental results highlighted that the web reinforcement ratio improved the load capacities by about 10% and 18% for specimens having 𝑎/ℎ ratios of 1.0 and 1.7, respectively. For specimens with web reinforcement, the increase of 𝑎/ℎ ratio from 1.0 to 1.7 led to reductions in the load carrying capacity by about 33% and 29% for beams with overall depths of 300 mm and 600 mm, respectively. Additionally, a considerable reduction occurred in the shear strength due to the increase of the section depth from 300 mm to 600 mm. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. In this study, the STM was illustrated and simplified to be adopted for GFRP RC continuous deep beams, and then, the experimental results obtained from this study were employed to assess the performance of the effectiveness factors suggested by the STMs of the American (ACI 318-2014), European (EC2-04) and Canadian (S806-12) codes as well as those factors recommended by the previous studies to predict the load capacities. It was found that these methods were unable to reflect the influences of member size and/or web reinforcement reasonably, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper bound analysis was developed to predict the load capacities of the tested specimens considering a reduced bond strength of GFRP bars after assessing the old version recommended for steel RC continuous deep beams. A good agreement between the predicted results and the measured ones was obtained with the mean and coefficient of variation values for experimental/calculated results of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis. A 2D finite element analysis using ABAQUS/Explicit approach was carried out to introduce a model able to estimate the response of GFRP RC continuous deep beams. Based on the experimental results extracted from the pullout tests, the interface between the longitudinal reinforcement and concrete surface was modelled using a cohesive element (COH2D4) tool available in ABAQUS. Furthermore, a perfect bond between the longitudinal reinforcement and surrounding concrete was also modelled to evaluate the validity of this assumption introduced by many previous FE studies. To achieve a reasonable agreement with the test results, a sensitivity analysis was implemented to select the proper mesh size and concrete model variables. The suitability and capability of the developed FE model were demonstrated by comparing its predictions with the test results of beams tested experimentally. Model validation showed a reasonable agreement with the experiments in terms of the failure mode, total failure load and the load-deflection responses. The perfect bond model has overestimated the predicted results in terms of stiffness behaviour and failure load, while the cohesive element model was more suitable to reflect the behaviour of those specimens. The validated FE model was then employed to implement a parametric study for the key parameters that govern the behaviour of beams tested and to achieve an in depth understanding of such elements. The parametric study showed that the higher the 𝑎/ℎ ratio the more pronounced the effect of web and the longitudinal reinforcements and the lower the effect of concrete compressive strength; and vice versa when 𝑎/ℎ ratio reduces.