• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.361-379
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• 2005

Reinforced concrete deep beams have useful applications in tall buildings and foundations. Over the past two decades, numerous design models for deep beams were suggested. However even the latest design manuals still offer little insight into the design of deep beams in particular when complexities exist in the beams like web openings. A method commonly suggested for the design of deep beams with openings is the strut-and-tie model which is primarily used to represent the actual load transfer mechanism in a structural concrete member under ultimate load. In the present study, the development of the strut-and-tie model is transformed to the topology optimization problem of continuum structures. During the optimization process, both the stress and displacement constraints are satisfied and the performance of progressive topologies is evaluated. The influences on the strut-and-tie model in relation to different size, location and number of openings, as well as different loading and support conditions in deep beams are examined in some detail. In all, eleven deep beams with web openings are optimized and compared in nine groups. The optimal strut-and-tie models achieved are also compared with published experimental crack patterns. Numerical results have shown to confirm the experimental observations and to efficiently represent the load transfer mechanism in concrete deep beams with openings under ultimate load.

• Advances in concrete construction
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• v.13 no.3
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• pp.243-254
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• 2022

Reinforced concrete (RC) deep beams are critical structural elements used in offshore pile caps, rectangular cross-section water tanks, silo structures, transfer beams in high-rise buildings, and bent caps. As a result of the low shear span ratio to effective depth (a/d) in deep beams, arch action occurs, which leads to shear failure. Several studies have been carried out to improve the shear resistance of RC deep beams and avoid brittle fracture behavior in recent years. This study was performed to investigate the behavior of RC deep beams numerically and experimentally with different reinforcement arrangements. Deep beams with four different reinforcement arrangements were produced and tested under monotonic static loading in the study's scope. The horizontal and vertical shear reinforcement members were changed in the test specimens to obtain the effects of different reinforcement arrangements. However, the rebars used for tension and the vertical shear reinforcement ratio were constant. In addition, the behavior of each deep beam was obtained numerically with commercial finite element analysis (FEA) software ABAQUS, and the findings were compared with the experimental results. The results showed that the reinforcements placed diagonally significantly increased the load-carrying and energy absorption capacities of RC deep beams. Moreover, an apparent plastic plateau was seen in the load-displacement curves of these test specimens in question (DE-2 and DE-3). This finding also indicated that diagonally located reinforcements improve displacement ductility. Also, the numerical results showed that the FEM method could be used to accurately predict RC deep beams'behavior with different reinforcement arrangements.

• Computers and Concrete
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• v.15 no.3
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• pp.357-372
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• 2015

This study reports the test results of twelve reinforced concrete deep beams. The deep beams were tested with loads applied through and supported by columns. The main variables studied were the shear span-to-depth ratios, and the horizontal and vertical stirrups. The shear strengths can be effectively enhanced for deep beams reinforced with both horizontal and vertical stirrups. The test results indicate the shear strengths of deep beams increase with the decrease of the shear span-to-depth ratios. The normalized shear strengths of the deep beams did not increase proportionally with an increase in effective depth. An analytical method for predicting the shear strengths of deep beams is proposed in this study. The shear strengths predicted by the proposed method and the strut-and-tie model of the ACI Code are compared with available test results. The comparison shows the proposed method can predict the shear strengths of reinforced concrete deep beams more accurately than the strut-and-tie model of the ACI Code.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.77-97
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• 2008

In this paper, a strut-and-tie model approach has been proposed to directly calculate the amount of reinforcements in deep beams, and the force transfer mechanisms for this approach were investigated using linear finite element analysis. The proposed strut-and-tie model provides quite similar force transfer mechanisms to the results of linear finite element analysis for the 28 deep beams. The load-carrying capacities calculated from the proposed method are both accurate and conservative with little scatter or trends for the 214 deep beams. The deep beams have different concrete strengths including high-strength, various combinations of web reinforcements, and wide range of and a/d ratios. Good accuracy was also obtained using VecTor2, nonlinear finite element analysis tool based on the Modified Compression Field Theory. Since the proposed method provides a safe and reliable means for design of deep beams, this can serve to improve design provisions in future adjustments and development of design guidelines.

• Smart Structures and Systems
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• v.16 no.3
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• pp.497-519
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• 2015

This study discusses the use of Adaptive-Network-Based-Fuzzy-Inference-System (ANFIS) in predicting the shear strength of reinforced-concrete deep beams. 139 experimental data have been collected from renowned publications on simply supported high strength concrete deep beams. The results show that the ANFIS has strong potential as a feasible tool for predicting the shear strength of deep beams within the range of the considered input parameters. ANFIS's results are highly accurate, precise and therefore, more satisfactory. Based on the Sensitivity analysis, the shear span to depth ratio (a/d) and concrete cylinder strength ($f_c^{\prime}$) have major influence on the shear strength prediction of deep beams. The parametric study confirms the increase in shear strength of deep beams with an equal increase in the concrete strength and decrease in the shear span to-depth-ratio.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.657-680
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• 2016

Reinforced concrete (RC) deep beams are structural members that predominantly fail in shear. Therefore, determining the shear strength of these types of beams is very important. The strut-and-tie method is commonly used to design deep beams, and this method has been adopted in many building codes (ACI318-14, Eurocode 2-2004, CSA A23.3-2004). In this study, the efficiency of artificial neural networks (ANNs) in predicting the shear strength of RC deep beams is investigated as a different approach to the strut-and-tie method. An ANN model was developed using experimental data for 214 normal and high-strength concrete deep beams from an existing literature database. Seven different input parameters affecting the shear strength of the RC deep beams were selected to create the ANN structure. Each parameter was arranged as an input vector and a corresponding output vector that includes the shear strength of the RC deep beam. The ANN model was trained and tested using a multi-layered back-propagation method. The most convenient ANN algorithm was determined as trainGDX. Additionally, the results in the existing literature and the accuracy of the strut-and-tie model in ACI318-14 in predicting the shear strength of the RC deep beams were investigated using the same test data. The study shows that the ANN model provides acceptable predictions of the ultimate shear strength of RC deep beams (maximum $R^2{\approx}0.97$). Additionally, the ANN model is shown to provide more accurate predictions of the shear capacity than all the other computed methods in this study. The ACI318-14-STM method was very conservative, as expected. Moreover, the study shows that the proposed ANN model predicts the shear strengths of RC deep beams better than does the strut-and-tie model approaches.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.393-396
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• 2004

The objective of this experimental study is to understand the shear behavior of reinforced concrete continuous deep beams. The main variables considered were concrete strength and shear span-to-depth ratio. Specimens of 4 two-span continuous deep beams were tested and compared with the strength of simple span beams. The results show that the influence of concrete strength on the shear strength of continuous deep beams is comparable to that on simple span deep beams. However, the effect of span-to-depth ratio is significantly greater than simple span deep beams.

• Journal of Ocean Engineering and Technology
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• v.13 no.3B
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• pp.56-64
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• 1999

An experimental study was carried out to examine the structural behavior of reinforced concrete deep beams strengthened with aramid fiber sheets, carbon fiber sheets and plates, and to propose the reasonable strengthening method for the deteriorated R.C. deep beams. Results show that the most significant differences in behavior of reinforced concrete deep beams strengthened with fiber sheet and plate were mainly due to various fiber orientations and anchorage. Deep beams diagonally strengthened with carbon fibers show better performance compared with those of vertically, horizontally strengthened specimens and produce the increase in the shear resistance through the redistribution of internal forces after the initial cracks occur. However, strengthened deep beams without anchorages might show unreasonable, brittle peeling-off failure of fiber reinforcements.

• Advances in concrete construction
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• v.13 no.1
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• pp.1-10
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• 2022

Concrete is a brittle material and weak in tension. Traditionally, web reinforcement in the form of vertical stirrups is used in reinforced concrete (RC) beams to take care of principal stresses that may cause failure when they are subjected to shear stresses. In recent decades, the potential of various types of fibers for improving post-cracking behavior of RC beams and replacing stirrups completely or partially have been studied. It has been shown that the use of steel fibers randomly dispersed and oriented in concrete has a significant potential for enhancing mechanical properties of RC beams. However, the studies on deep steel fiber reinforced concrete (SFRC) beams are limited when compared to those focusing on slender beams. An experimental program consisting of three RC and nine SFRC deep beams without stirrups were conducted in this study. Besides, various models developed for predicting the ultimate shear strength and diagonal cracking strength of SFRC deep beams without stirrups were applied to experimental data obtained from the literature and this study.

• Computers and Concrete
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• v.2 no.4
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• pp.267-291
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• 2005

To date, many studies have been conducted for the analysis and design of reinforced concrete members with disturbed regions. However, prestressed concrete deep beams have not been the subject of many investigations. This paper presents an evaluation of the behavior and strength of three pre-tensioned concrete deep beams failed by shear and bond slip of prestressing strands using a nonlinear strut-tie model approach. In this approach, effective prestressing forces represented by equivalent external loads are gradually introduced along strand's transfer length in the nearest strut-tie model joints, the friction at the interface of main diagonal shear cracks is modeled by the aggregate interlock struts along the direction of the cracks in strut-tie model, and an algorithm considering the effect of bond slip of prestressing strands in the strut-tie model analysis and design of pre-tensioned concrete members is implemented. Through the strut-tie model analysis of pre-tensioned concrete deep beams, the nonlinear strut-tie model approach proved to present effective solutions for predicting the essential aspects of the behavior and strength of pre-tensioned concrete deep beams. The nonlinear strut-tie model approach is capable of predicting the strength and failure modes of pre-tensioned concrete deep beams including the anchorage failure of prestressing strands and, accordingly, can be employed in the practical and precise design of pre-tensioned concrete deep beams.