• Computers and Concrete
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• v.21 no.1
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• pp.95-102
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• 2018

Reinforced concrete corbel beams (span to depth ratio of a corbel is less than one) are designed with primary reinforcement bars to account for bending moment and with the secondary reinforcement placed parallel to the primary reinforcement (shear stirrups) to resist shear force. It is interesting to note that most of the available analytical procedures employ empirical formulas for the analysis of reinforced concrete corbels. In the present work, a generalized and a simple strut and tie models were employed for the analysis of reinforced corbel beams. The models were benchmarked against experimental results available in the literature. It was shown here that increase of shear stirrups increases the load carrying capacity of reinforced concrete corbel beams. The effect of horizontal load on the load carrying capacity of the corbel beams has also been examined in the present paper. It is observed from the strut and tie models that the resistance of the corbel beam subjected to combined horizontal and vertical load did not change with increase in shear stirrups if the failure of the corbel is limited by concrete crushing. In other words, the load carrying capacity was independent of the horizontal load when failure of the beam occurred due to concrete crushing.

• Structural Engineering and Mechanics
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• v.33 no.3
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• pp.357-371
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• 2009

Test results of thirteen reinforced concrete corbels with shear span-to-depth ratio greater than unity are reported. The main variables studied were compressive strength of concrete, shear span-to-depth ratio and parameter of vertical stirrups. The test results indicate that the shear strengths of corbels increase with an increase in compressive strength of concrete and parameter of vertical stirrups. The shear strengths of corbels also increase with a decrease in shear span-to-depth ratio. The smaller the shear span-to-depth ratio of corbel, the larger the stiffness and the shear strength of corbel are. The higher the concrete strength of corbel, the higher the stiffness and the shear strength of corbel are. The larger the parameter of vertical stirrups, the larger the stiffness and the shear strength of corbel are. The softened strut-and-tie model for determining the shear strengths of reinforced concrete corbels is modified appropriately in this paper. The shear strengths predicted by the proposed model and the approach of ACI Code are compared with available test results. The comparison shows that the proposed model can predict more accurately the shear strengths of reinforced concrete corbels than the approach of ACI Code.

• Computers and Concrete
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• v.15 no.2
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• pp.279-304
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• 2015

In this study, reliability analyses of steel fiber reinforced concrete (SFRC) corbels based on stochastic finite element were performed for the first time in literature. Prior to stochastic finite element analysis, an experimental database of 84 sfrc corbels was gathered from literature. These sfrc corbels were modeled by a special finite element program. Results of experimental studies and finite element analysis were compared and found to be very close to each other. Furthermore experimental crack patterns of corbel were compared with finite element crack patterns and were observed to be quite similar. After verification of the finite element models, stochastic finite element analyses were implemented by a specialized finite element module. As a result of stochastic finite element analysis, appropriate probability distribution functions (PDF's) were proposed. Finally, coefficient of variation, bias and strength reduction (resistance) factors were proposed for sfrc corbels as a consequence of stochastic based reliability analysis.

• Journal of the Korean Society of Safety
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• v.23 no.3
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• pp.58-64
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• 2008

In order to identify the exact behavior of corbel section, the horizontal force acting on corbel section should be considered as well as the vertical force. In this study, a new corbel section, which is economical and easy to construct, is developed by evaluating the exact strength of the section. Experiments were performed to verify the strengths of the proposed sections comparing with those of the currently used section. The summary of the experiment results are as follows: 1) In order to minimize the horizontal force effect, it was found that the use of pre-stressing was most effective, and that TB type corbel section is a most efficient section in terms of economy and workability. 2) The experimentally obtained strength of corbel section matched well with that estimated using shear friction theory. Therefore, it is concluded that shear friction theory would be very useful if a precise crack angie in the corbel section, which is pre-stressed by PS strings and threaded bolts, is available.

• Computers and Concrete
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• v.19 no.5
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• pp.589-597
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• 2017

Strut-and-tie modeling method, which evolved on truss-model approach, has generally been preferred for the design of complex reinforced concrete structures and structural elements that have critical shear behavior. Some structural members having disturbed regions require exceptional detailing for all support and loading conditions, such as the beam-column connections, deep beams, short columns or corbels. Considering the general expectation of exhibiting brittle behavior, corbels are somewhat dissimilar to other shear critical structures. In this study, reinforcement layout of a corbel model was determined by the participation of structural optimization and strut-and-tie modeling methods, and an experimental comparison was performed against a conventionally designed model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1081-1094
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• 2014

The strut-tie model approach has proven to be effective in the ultimate analysis and design of structural concrete with disturbed regions. For the reliable analysis and safe design of the structural concrete, however, the effective strengths of concrete struts must be determined accurately. In this study, the equations of the effective strengths of concrete struts, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete corbels, were proposed. The effects of shear span-to-effective depth ratio, the vertical-to-horizontal force ratio, and flexural and horizontal shear reinforcement ratios were reflected in the development of the proposed equations. To examine the appropriateness of the proposed and existing equations, the ultimate strengths of 243 reinforced concrete corbels tested to failure were evaluated by using the three types of corbel strut-tie models.

• Computers and Concrete
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• v.10 no.3
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• pp.259-276
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• 2012

A total of nine reinforced concrete corbels were tested, in this study. Six were externally strengthened with carbon fiber reinforced plastics (CFRP), in the horizontal direction. The cross-sectional area of CFRP and the shear span-to-effective depth ratios are the parameters considered, in this study. Test results indicate that the higher the cross-sectional area of CFRP, the higher is the shear strength of the corbels, and the lower the shear span-to-effective depth ratios, the higher is the shear strength of corbels. The shear strength predicted by the design provisions in section 11.8 of the ACI Code, the strut-and-tie model in Appendix A of the ACI Code, and the softened strut-and-tie (SST) model were compared with the test results. The comparisons show that both the strut-and-tie model in Appendix A of the ACI Code, and the SST model can accurately predict the shear strength of reinforced concrete corbels, strengthened with CFRP.

• Computers and Concrete
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• v.20 no.1
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• pp.65-75
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• 2017

In this study, a novel application of symbolic regression (SR) is employed for the prediction of ultimate shear strength of steel fiber reinforced (SFRC) and glass fiber reinforced (GFRC) corbels without stirrups, for the first time in the literature. A database is created using the test results (42 tests) conducted by the authors of current paper as well as the previous studies available in the literature. A symbolic regression based empirical formulation is proposed using this database. The formulation is unique in a way that it has the capability to predict the shear strength of both SFRC and GFRC corbels. The performance of proposed model is tested against randomly selected testing set. Additionally, a parametric study with a wide range of variables is carried out to test the effect of each parameter on the shear strength. The results confirm the high prediction capacity of proposed model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1065-1079
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• 2014

The ultimate behavior of reinforced concrete corbel is complicated due to the primary design variables including the shear span-to-effective depth ratio a/d, flexural reinforcement ratio, load condition, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strength and complicated structural behavior is proposed for the design of the reinforced concrete corbels with shear span-to-effective depth ratio of $a/d{\leq}1$. A load distribution ratio, defined as the fraction of applied load transferred by horizontal truss mechanism, is also proposed to help structural designers perform the design of reinforced concrete corbels by using the strut-tie model approaches of current design codes. For the development of the load distribution ratio, numerous material nonlinear finite element analyses of the proposed indeterminate strut-tie model were conducted by changing primary design variables. The ultimate strengths of reinforced concrete corbels tested to failure were evaluated by incorporating the proposed strut-tie model and load distribution ratio into the ACI 318-11's strut-tie model method. The validity of the proposed model and load distribution ratio was examined by comparing the strength analysis results with those by the ACI 318-11's conventional design method and strut-tie model methods of current design codes.

• 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.