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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 / 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.

The shear capacity of reinforced concrete pier caps in existing bridge support systems can be a factor which limits the capacity of an existing bridge. In their usual configuration, pier caps behave as deep beams and have the ability to carry load through tied arch action after the formation of diagonal cracks. Externally bonded fiber reinforced polymer (FRP) reinforcement has been shown to increase the shear capacity of reinforced concrete members which carry load through beam action. However, there is an insufficient amount of research to make it a viable strengthening system for beams which carry load through arch action, such as pier caps. Accordingly, this research was aimed at investigating the behavior of reinforced concrete pier caps through a coordinated experimental and analytical program and to recommend an external strengthening method for pier caps with perceived deficiencies in shear strength. The experimental study was performed on laboratory specimens based on an existing bridge in Georgia. A number of factors were examined, including size, percentage longitudinal reinforcement and crack control reinforcement. The results showed that increasing the longitudinal tension reinforcement increased the beam capacity by changing the shape of the tied arch. In contrast, the presence of crack control reinforcement did not change the point at which diagonal cracking occurred, but it did increase the ultimate capacity by reinforcing the concrete against splitting. The results of the experimental study were used in conjunction with a larger database to examine different analytical methods for estimating the ultimate capacity of deep beams, and a new method was developed for the design of external strengthening. Two specimens were tested with externally bonded FRP reinforcement applied longitudinally to increase the strength of the tension tie. The test results correlated well with the proposed method of analysis and showed that increasing the strength of the longitudinal tension tie is an effective way to increase the strength of a reinforced concrete deep beam.

Several recently built inverted-T bent caps in Texas have shown significant inclined cracking triggering concern about current design procedures for such structures. The repair of such structures is very costly and often requires lane closures. For these reasons TxDOT funded Project 0-6416 aimed at obtaining a better understanding of the structural behavior of inverted-T bent caps and developing new design criteria to minimize such cracking in the future. Several tasks of the aforementioned project are addressed in this dissertation with particular focus on developing design criteria for strength and serviceability of inverted-T bent caps. Literature review revealed a scarcity of experimental investigation of inverted-T specimens. As part of this dissertation, an inverted-T database was assembled with experimental results from the literature and the current project. An extensive experimental program was completed to accomplish the objectives of the project with thirty one full-scale tests conducted on inverted-T beams. Experimental parameters varied in the study were: ledge length, ledge depth, web reinforcement, number of point loads, web depth, and shear span-to-depth ratio. The dissertation focuses on the effects of ledge length, ledge depth, number of point loads, and developing design criteria for strength and serviceability of inverted-T beams. Most inverted-T bent caps in Texas are designed using the traditional empirical design procedures outlined in the TxDOT bridge design manual LRFD (2011 current version) that follows closely the AASHTO LRFD bridge design specifications (2012 current version). Given the observed cracking in inverted-T bent caps, the accuracy and conservatism of the traditional design methods were evaluated based on experimental results. The accuracy and conservatism of STM design provisions recently developed in a TxDOT study (TxDOT Project 0-5253, Strength and Serviceability Design of Reinforced Concrete Deep Beams) were also evaluated. / text

No / Optimum multi-layered feed-forward neural network (NN) models using a resilient back-propagation algorithm and early stopping technique are built to predict the shear capacity of reinforced concrete deep and slender beams. The input layer neurons represent geometrical and material properties of reinforced concrete beams and the output layer produces the beam shear capacity. Training, validation and testing of the developed neural network have been achieved using 50%, 25%, and 25%, respectively, of a comprehensive database compiled from 631 deep and 549 slender beam specimens. The predictions obtained from the developed neural network models are in much better agreement with test results than those determined from shear provisions of different codes, such as KBCS, ACI 318-05, and EC2. The mean and standard deviation of the ratio between predicted using the neural network models and measured shear capacities are 1.02 and 0.18, respectively, for deep beams, and 1.04 and 0.17, respectively, for slender beams. In addition, the influence of different parameters on the shear capacity of reinforced concrete beams predicted by the developed neural network shows consistent agreement with those experimentally observed.

Yes / Although the depth of reinforced concrete deep beams is much higher than that of slender beams, extensive existing tests on deep beams have focused on simply supported beams with a scaled depth below 600 mm. In the present paper, test results of 12 two-span reinforced concrete deep beams are reported. The main parameters investigated were the beam depth, which is varied from 400 mm to 720 mm, concrete compressive strength and shear span-tooverall depth ratio. All beams had the same longitudinal top and bottom reinforcement and no web reinforcement to assess the effect of changing the beam depth on the shear strength of such beams. All beams tested failed owing to a significant diagonal crack connecting the edges of the load and intermediate support plates. The influence of beam depth on shear strength was more pronounced on continuous deep beams than simple ones and on beams having higher concrete compressive strength. A numerical technique based on the upper bound analysis of the plasticity theory was developed to assess the load capacity of continuous deep beams. The influence of the beam depth was covered by the effectiveness factor of concrete in compression to cater for size effect. Comparisons between the total capacity from the proposed technique and that experimentally measured in the current investigation and elsewhere show good agreement, even though the section depth of beams is varied.

Yes / This paper reviews the application of the plasticity theory to reinforced concrete deep beams. Both the truss analogy and mechanism approach were employed to predict the capacity of reinforced concrete deep beams. In addition, most current codes of practice, for example Eurocode 1992 and ACI 318-05, recommend the strut-and-tie model for designing reinforced concrete deep beams. Compared with methods based on empirical or semi-empirical equations, the strut-and-tie model and mechanism analyses are more rational, adequately accurate and sufficiently simple for estimating the load capacity of reinforced concrete deep beams. However, there is a problem of selecting the effectiveness factor of concrete as reflected in the wide range of values reported in the literature for deep beams.

yes / A 9 × 18 × 1 feed-forward neural network (NN) model trained using a resilient back-propagation algorithm and early stopping technique is constructed to predict the shear strength of deep reinforced concrete beams. The input layer covering geometrical and material properties of deep beams has nine neurons, and the corresponding output is the shear strength. Training, validation and testing of the developed neural network have been achieved using a comprehensive database compiled from 362 simple and 71 continuous deep beam specimens. The shear strength predictions of deep beams obtained from the developed NN are in better agreement with test results than those determined from strut-and-tie models. The mean and standard deviation of the ratio between predicted capacities using the NN and measured shear capacities are 1·028 and 0·154, respectively, for simple deep beams, and 1·0 and 0·122, respectively, for continuous deep beams. In addition, the trends ascertained from parametric study using the developed NN have a consistent agreement with those observed in other experimental and analytical investigations.