Strut-and-Tie Model Based on Crack Band Theory for Deep Beams

Yang, Keun–Hyeok; Ashour, Ashraf

doi:10.1061/(asce)st.1943-541x.0000351

Cited by 29 publications

(5 citation statements)

References 8 publications

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“…The height of the bottom node (hB) (refer to Figure 4) can be assumed as twice the distance between the center of force of the main longitudinal reinforcement and the tension face. According to Yang and Ashour [16] 80%, 88%, 85%, and 75% of the height of the tie according to ACI 318-14[1], AASHTO LRFD [14], EC2 [2], and Model Code 2010 [15], respectively, while the strut angle (θ) can be calculated from geometry using Eq. (1).…”

Section: Fig 3 Crack Patterns and Modes Of Failure 4 Analytical Promentioning

confidence: 99%

Behavior of self-compact reinforced concrete deep beams with small shear span to depth ratio

2018

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This research is devoted to investigate the experimental and theoretical behavior of deep beams under monotonic two points loading. An experimental program examining six RC deep beams is carried out. The investigated parameters include shear span to depth ratio varying from 1.0 to 0.276. A comparative study is conducted in this paper by using finite element software ANSYS. The experimental and numerical results show that concrete strength and shear span to depth ratio are the two most important parameters in controlling the behavior of RC deep beams. Comparison of experimental results was made with corresponding predicted values using the Strut and Tie procedure presented ACI 318M-11Code and with other procedures mentioned in the literature. It was found that the Strut and Tie procedure presented in ACI 318M-11Code give conservative results as compared with the experimental tested results. The results showed reliability of analysis in predicting deep beams behavior in terms of failure load, failure mode as well as crack propagation.

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Section: Fig 3 Crack Patterns and Modes Of Failure 4 Analytical Promentioning

confidence: 99%

Behavior of self-compact reinforced concrete deep beams with small shear span to depth ratio

2018

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“…In the past several decades, many methods have been proposed to analyze the shear strength of deep beams, including the strut-and-tie method (STM) [12,13] and the upper limit theorem of plasticity theory [14,15]. Based on the STM, theoretical methods to calculate the shear strength are proposed, such as compression field theory (CFT) and modified compression field theory (MCFT) [16,17], the theory of softened strut-and-tie model (SSTM) considering the compression softening of concrete [18,19], and strutand-tie model based on the crack band theory [20,21]. Besides, the current design codes, such as ACI 318-14 [2], EN 1992-1-1:2004 [3], and CSA A23.3-04 [22], have recommended the STM approach as a deep beam design tool.…”

Section: Introductionmentioning

confidence: 99%

On the Training Algorithms for Artificial Neural Network in Predicting the Shear Strength of Deep Beams

Nguyen

Thi

et al. 2021

Complexity

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This study aims to predict the shear strength of reinforced concrete (RC) deep beams based on artificial neural network (ANN) using four training algorithms, namely, Levenberg–Marquardt (ANN-LM), quasi-Newton method (ANN-QN), conjugate gradient (ANN-CG), and gradient descent (ANN-GD). A database containing 106 results of RC deep beam shear strength tests is collected and used to investigate the performance of the four proposed algorithms. The ANN training phase uses 70% of data, randomly taken from the collected dataset, whereas the remaining 30% of data are used for the algorithms’ evaluation process. The ANN structure consists of an input layer with 9 neurons corresponding to 9 input parameters, a hidden layer of 10 neurons, and an output layer with 1 neuron representing the shear strength of RC deep beams. The performance evaluation of the models is performed using statistical criteria, including the correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results show that the ANN-CG model has the best prediction performance with R = 0.992, RMSE = 14.02, MAE = 14.24, and MAPE = 6.84. The results of this study show that the ANN-CG model can accurately predict the shear strength of RC deep beams, representing a promising and useful alternative design solution for structural engineers.

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“…Based on STM, many scholars come up with theoretical methods for calculating the shear capacity of deep beams. For instance, compression field theory (CFT) and modified compression field theory (MCFT) [9,10], the theory of softened strut and tie model (SSTM) considering the compression softening of concrete [11,12] and strut and tie model based on the crack band theory [13,14], and so on. These promoted the development and application of STM.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on Shear Capacity of High Strength Reinforcement Concrete Deep Beams with Small Shear Span–Depth Ratio

Zhang

Xie

et al. 2020

Materials

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This study aimed to investigate the shear capacity performance for eight deep beams with HTRB600 reinforced high strength concrete under concentrated load to enable a better understanding of the effects of shear span–depth ratio, longitudinal reinforcement ratio, vertical stirrup ratio and in order to improve design procedures. The dimension of eight test specimens is 1600 mm × 200 mm × 600 mm. The effective span to height ratio l0/h is 2.0, the shear span–depth ratio λ is 0.3, 0.6 and 0.9, respectively. In addition, the longitudinal reinforcement ratio ρs is set to 0.67%, 1.05%, 1.27%, and the vertical stirrup ratio is taken to be 0%, 0.25%, 0.33%, 0.5%. Through measuring the strain of steel bar, the strain of concrete and the deflection of mid-span, the characteristics of the full process of shear capacity, the failure mode and the load deflection deformation curve were examined. The test results showed that the failure mode of deep beams with small shear span–depth ratio is diagonal compression failure, which is influenced by the layout and quantity of web reinforcement. The diagonal compression failure could be classified into two forms: crushing-strut and diagonal splitting. With decreasing of shear span–depth ratio and increasing longitudinal reinforcement ratio, the shear capacity of deep beams increases obviously, while the influence of vertical web reinforcement ratio on shear capacity is negligible. Finally, the shear capacity of eight deep beams based on GB 50010-2010 is calculated and compared with the calculation results of ACI 318-14, EN 1992-1-1:2004 and CSA A23.3-04, which are based on strut-and-tie model. The obtained results in this paper show a very good agreement with GB50010-2010 and ACI 318-14, while the results of EN 1992-1-1:2004 and CSA A23.3-04 are approved to be conservative.

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Strut-and-Tie Model Based on Crack Band Theory for Deep Beams

Cited by 29 publications

References 8 publications

Behavior of self-compact reinforced concrete deep beams with small shear span to depth ratio

Behavior of self-compact reinforced concrete deep beams with small shear span to depth ratio

On the Training Algorithms for Artificial Neural Network in Predicting the Shear Strength of Deep Beams

Experimental Study on Shear Capacity of High Strength Reinforcement Concrete Deep Beams with Small Shear Span–Depth Ratio

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