• Computers and Concrete
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• v.8 no.1
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• pp.59-70
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• 2011

A theoretical model known as the modified rotating-angle softened-truss model (MRA-STM), which is a modification of Rotating-Angle Softened-Truss Model and Modified Compression Field Theory, is presented for the analysis of reinforced concrete membranes in shear. As an application, shear strength and behaviour of reinforced concrete exterior beam-column joints are analysed using the MRA-STM combining with the deep beam analogy. The joints are considered as RC panels and subjected to vertical and horizontal shear stresses from adjacent columns and beams. The strut and truss actions in a beam-column joint are represented by the effective transverse compression stresses and a softened concrete truss in the proposed model. The theoretical predictions of shear strength of reinforced concrete exterior beam-column joints from the proposed model show good agreement with the experimental results.

• Structural Engineering and Mechanics
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• v.44 no.6
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• pp.705-733
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• 2012

In this work, an experimental examination was carried out to study interfacial stresses developed at the junction zones between carbon fiber reinforced plastic (CFRP) fabrics (~1 mm thickness) and tensile concrete portion in CFRP retrofitted RC beams. In this respect, initially six similar RC beams of $150{\times}150{\times}1000mm$ dimensions were prepared. Three of which were strengthened with CFRP fabrics at the tensile side of the beams. Furthermore, a notch was cut at the center of the bottom surface for all of the studied beams. The notch was 15 mm deep and ran across the full width of tension side of the beams. The mentioned interfacial stresses could be calculated from strains measured using strain gauges mounted on the interface zone of the tensile concrete and the CFRP sheet. Based on the results obtained, it is shown that interfacial stresses developed between CFRP fabrics and RC beam had a noticeable effect on debonding failure mode of the latter. The load carrying capacity of CFRP strengthened RC specimens increased ~75% compared to that of the control RC beams. This was attributed to the enhancement of flexural mode of the former. Finally, finite element analysis was also utilized to verify the measured experimental results.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.817-822
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• 2002

In this paper, the strengthening analysis by strut-tie model for strengthened shear failed RC deep beam by the so-called the Steel Clamping Unit (SCU), which is a strengthening equipment, is carried out. The analysis considers the span-to-depth ratio, the existence of prestressing and stirrup, the shape of shear crack, and the strengthening position of the SCU. Based on analytical results, optimized strengthening analysis and design are carried out by investigating the behavior of the strengthened deep beams. The comparison between analytical results and experimental results shows that optimum strengthening effect by the SCU can be obtained when compressive strut zone created by SCU is away from major shear crack of the beam as far as possible.

• Architectural research
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• v.19 no.4
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• pp.109-115
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• 2017

This study is done to evaluate how existence of shear-span ratio and shear reinforcing bar effects on shear performance from through shear experiment using PVA fiber reinforced ferroconcrete building. Ratio of shear-span was set 1, 1.7, and arrangement of shear reinforcing bar was set with KCI2012 regulation. In result, subject with less shear-span ratio, and shear reinforcing bar with arrangement of bar shows high stiffness. Subjects with high shear-span ratio show large difference depending on existence of shear reinforcing bar. Therefore, theoretical shear strength followed by CEB code underestimates experimental shear strength by 43.9%. Shear strength of the deep beam with headed bars is more affected by the bearing strength of head than the bond strength of bar.

• Advances in concrete construction
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• v.8 no.4
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• pp.285-294
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• 2019

In the present paper, the fiber theory has been employed to model the reinforced concrete (RC) deep beams (DBs) considering the reinforcing steel bar-concrete interaction. To simulate numerically the behavior of materials, the uniaxial materials' constitutive laws have been employed for reinforcements and concrete and the bond stress-slip between the reinforcing steel bars and surrounding concrete are taken into account. Because of the high sensitivity of DBs to shear deformations, the Timoshenko beam theory has been applied. The shear stress-strain (S-SS) relationship has been defined by the modified compression field theory (MCFT) model. By modeling about 300 RC panels and employing a produced numerical database, a study has been carried out to show the sensitivity of the MCFT model. This is performed based on the multiple linear regression (MLR) models. The results of this research also illustrate how different parameters such as characteristic compressive strength of concrete, yield strength of reinforcements and the percentages of reinforcements in different directions get involved in the shear behavior of RC panels without applying complex theories. Based on the results obtained from the analysis of the MCFT S-SS model, a relatively simplified numerical S-SS model has been proposed. Application of the proposed S-SS model in modeling and analyzing the considered samples indicates that there is a good agreement between the simulated and the experimental test results. The comparison between the proposed S-SS model and the MCFT model indicates that in addition to the advantage of better accuracy, the main advantage of the proposed method is simplicity in application.

• Computers and Concrete
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• v.30 no.1
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• pp.43-74
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• 2022

Machine learning technique is recently opening new opportunities to identify the complex shear transfer mechanisms of reinforced concrete (RC) beam members. This study employed 1224 shear test specimens to train decision tree-based machine learning (ML) programs, by which strong correlations between shear capacity of RC beams and key input parameters were affirmed. In addition, shear contributions of concrete and shear reinforcement (the so-called V_c and V_s) were identified by establishing three independent ML models trained under different strategies with various combinations of datasets. Detailed parametric studies were then conducted by utilizing the well-trained ML models. It appeared that the presence of shear reinforcement can make the predicted shear contribution from concrete in RC beams larger than the pure shear contribution of concrete due to the intervention effect between shear reinforcement and concrete. On the other hand, the size effect also brought a significant impact on the shear contribution of concrete (V_c), whereas, the addition of shear reinforcements can effectively mitigate the size effect. It was also found that concrete tends to be the primary source of shear resistance when shear span-depth ratio a/d<1.0 while shear reinforcements become the primary source of shear resistance when a/d>2.0.

• Computers and Concrete
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• v.14 no.1
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• pp.19-40
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• 2014

Reinforced concrete deep beams are structural beams with low shear span-to-depth ratio, and hence in which the strain distribution is significantly nonlinear and the conventional beam theory is not applicable. A strut-and-tie model is considered one of the most rational and simplest methods available for shear strength prediction and design of deep beams. The strut-and-tie model approach describes the shear failure of a deep beam using diagonal strut and truss mechanism: The diagonal strut mechanism represents compression stress fields that develop in the concrete web between diagonal cracks of the concrete while the truss mechanism accounts for the contributions of the horizontal and vertical web reinforcements. Based on a database of 406 experimental observations, this paper proposes a new strut-and-tie-model for accurate prediction of shear strength of reinforced concrete deep beams, and further improves the model by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. Seven existing deterministic models from design codes and the literature are compared with the proposed method. Finally, a limit-state design formula and the corresponding reduction factor are developed for the proposed strut-andtie model.

• Computers and Concrete
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• v.22 no.5
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• pp.493-500
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• 2018

Due to the fact that the ratio of their height to their openings is very large compared to normal beams, there are difficulties in the design and analysis of deep beams, which differ in behavior. In this study, the optimum horizontal and vertical reinforcement diameters of 5 different beams were determined by using genetic algorithms (GA) due to the openness/height ratio (L/h), loading condition and the presence of spaces in the body. In this study, the effect of different mutation operators and improved double times sensitive mutation (DTM) operator on GA's performance was investigated. In the study following random mutation (RM), boundary mutation (BM), non-uniform random mutation (NRM), Makinen, Periaux and Toivanen (MPT) mutation, power mutation (PM), polynomial mutation (PNM), and developed DTM mutation operators were applied to five deep beam problems were used to determine the minimum reinforcement diameter. The fitness values obtained using developed DTM mutation operator was higher than obtained from existing mutation operators. Moreover; obtained reinforcement weight of the deep beams using the developed DTM mutation operator lower than obtained from the existing mutation operators. As a result of the analyzes, the highest fitness value was obtained from the applied double times sensitive mutation (DTM) operator. In addition, it was found that this study, which was carried out using GAs, contributed to the solution of the problems experienced in the design of deep beams.

• Structural Engineering and Mechanics
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• v.38 no.4
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• pp.385-403
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• 2011

Continuous deep girders which transmit the gravity load from the upper wall to the lower columns have frequently long end shear spans between the boundary of the upper wall and the face of the lower column. This paper presents the results of tests and analyses performed on three 1:2.5 scale specimens with long end shear spans, (the ratios of shear-span/total depth: 1.8 < a/h < 2.5): one designed by the conventional approach using the beam theory and two by the strut-and-tie approach. The conclusions are as follows: (1) the yielding strength of the continuous RC deep girders is controlled by the tensile yielding of the bottom longitudinal reinforcements, being much larger than the nominal strength predicted by using the section analysis of the girder section only or using the strut-and-tie model based on elastic-analysis stress distribution. (2) The ultimate strengths are 22% to 26% larger than the yielding strength. This additional strength derives from the strain hardening of yielded reinforcements and the shear resistance due to continuity with the adjacent span. (3) The pattern of shear force flow and failure mode in shear zone varies depending on the amount of vertical shear reinforcement. And (4) it is necessary to take into account the existence of the upper wall in the analysis and design of the deep continuous transfer girders that support the upper wall with a long end shear span.

• Structural Engineering and Mechanics
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• v.77 no.2
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• pp.273-291
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• 2021

The strut-and-tie method (STM) has been widely accepted and used as a rational approach for the design of disturbed regions ('D' regions) of reinforced concrete members such as in corbels and deep beams, where traditional flexure theory does not apply. This paper evaluates the applicability of the equilibrium based STM in strength predictions of deep beams (with rectangular and circular cross-section) and corbels using the available experiments in literature. STM is found to give fairly good results for corbel and deep beams. The failure modes of these deep members are also studied, and an optimum amount of distribution reinforcement is suggested to eliminate the premature diagonal splitting failure. A comparison with existing empirical and semi empirical methods also show that STM gives more reliable results. The nonlinear finite element analysis (NLFEA) of 50 deep beams and 20 corbels could capture the complete behaviour of deep members including crack pattern, failure load and failure load accurately.