• Proceedings of the Korea Concrete Institute Conference
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• 2004.05a
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• pp.544-547
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• 2004

Predicting the failure modes of reinforced concrete corbels is difficult because the reinforced concrete corbels show the shapes of sudden shear failures at even slight deflection. For this reason, an exact analysis method is demanded highly. In this study, the validity of the grid softened strut-tie model method suggested for concrete member analysis was examined through the ultimate strength evaluation of the reinforced concrete corbels tested to failure. The evaluated ultimate strengths by the grid softened strut-tie model method were compared with those by the ACI 318-02 and the softened strut-tie model method.

• 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.

• Journal of the Korea Concrete Institute
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• v.20 no.6
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• pp.747-754
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• 2008

In this study, high strength concrete corbels reinforced with steel fibers and polypropylene fibers, and subjected to the vertical and horizontal loads were constructed and tested. The results showed that performance in terms of load carrying capacities, stiffness, ductility, crack width, and number of cracks was improved, as the steel fibers and polypropylene fibers were added. The polypropylene fiber reinforced concrete corbels resulted in higher ductility in presence of horizontal loads, but showed larger crack width than the steel fiber reinforced concrete corbels. And, the heads of the headed bars provided excellent end anchorage of the main tension tie reinforcement. Experimental results presented in this paper are also compared with various prediction models proposed by codes and researchers. The refined strut-and-tie model showed more accurate and conservative predictions in presence of horizontal loads, and the truss model proposed by Fattuhi provides fairly good predictions for fiber reinforced concrete corbels.

• Journal of the Korea Concrete Institute
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• v.21 no.6
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• pp.697-703
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• 2009

High-strength concrete corbels with varying percentage of steel fibers and two different anchorage types (welding to transverse bar, headed) for the main tension tie were constructed and tested. The results showed that performance in terms of load carrying capacities, stiffness, ductility, and crack width was improved, as the percentage of steel fibers was increased. In addition, the corbel specimens in which headed bars were used as the main tension tie reinforcements showed superior load carrying capacities, stiffness, and ductility compared to the corbel specimens in which the main tension ties were anchored by welding to the transverse bars. From the test results, it is expected that load carrying capacities, durability, and constructibility of high strength concrete corbels would be improved by using steel fibers and headed bars. Experimental results presented in this paper were also compared with various prediction models proposed by researchers and presented in codes. The truss model proposed by Fattuhi provides fairly good predictions for fiber reinforced high-strength concrete corbels.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.13-16
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• 2008

Corbels are short cantilevers that project from the faces of a column and are a type of stress disturbed member, resisting both the ultimate shear force applied to them by the beam, and the ultimate horizontal force caused by shrinkage, temperature changes, and creep of the supported elements. Recently, as there have been an increase in the use of high-strength concrete and the concern about corrosion problems, lots of researches about hybrid reinforcing technique, applying strategically high performance reinforcements to the concrete elements, are performed. In this study, fiber reinforced high strength concrete corbels were constructed and tested for applying hybrid reinforcing technique to the corbels using steel fibers and headed bars. The results showed that the performance in terms of load carrying capacities, stiffness, ductility, and crack width was improved, as the steel fibers were added and the percentage of steel fibers was increased. In addition, the corbel specimens used headed bars as main tension ties showed superior load carrying capacities, stiffness, and ductility to the corbel specimens anchored main tension ties by welding to the transverse bars.

• 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.

• Computers and Concrete
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• v.3 no.2_3
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• pp.123-144
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• 2006

Reinforced concrete corbels are structural elements widely used in practical engineering. The complex response of these elements is described in design codes in a simplified manner. These formulations are not sufficient to show the real behavior, which, however, is an essential prerequisite for the manufacturing of numerous elements. Therefore, a deterministic and probabilistic study has been performed, which is described in this contribution. Real complex structures have been modeled by means of the finite element method supported primarily by experimental works. The main objective of this study was the detection of uncertainties effects and safety margins not captured by traditional codes. This aim could be fulfilled by statistical considerations applied to the investigated structures. The probabilistic study is based on advanced Monte Carlo simulation techniques and sophisticated nonlinear finite element formulations.

• 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.

• 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.