• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.4
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• pp.801-814
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• 2015

In this study, a statically simple indeterminate strut-tie model is proposed for the rational analysis and design of simply supported prestressed concrete beams by reflecting all characteristics of nonlinear structural behavior and load transfer mechanisms. In addition, a load distribution ratio that allows to transform the proposed indeterminate strut-tie model to a determinate model is also suggested to help structural designers conduct the structural analysis and design of simply supported prestressed concrete beams by using the strut-tie model method of current design codes. For verifying of the validity of the proposed model and load distribution ratio, the ultimate strengths of 47 simply supported prestressted concrete beams tested to failure were estimated and the results were compared with those by the strut-tie model methods of current design codes.

• Proceedings of the Korea Concrete Institute Conference
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• 2009.05a
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• pp.193-194
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• 2009

In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strengths and complicated structural behavior of pre-tensioned concrete deep beams is presented. In addition, a load distribution ratio, defined as a magnitude of load transferred by a vertical truss mechanism, is proposed to help structural designers perform the strength analysis of pre-tensioned concrete deep beams by using the strut-tie model approaches of current design codes.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.269-279
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• 2008

In this study, the ultimate strengths of 229 simply supported reinforced concrete deep beams tested to shear failure were evaluated by the ACI 318-05's strut-tie model approach implemented with the presented indeterminate strut-tie model and its load distribution ratio. The ultimate strengths of the deep beams were also estimated by the experimental shear equations, design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the present strut-tie model and its load distribution ratio was examined through the comparison of the strength analysis results classified according to the prime design variables of the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.197-200
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• 2008

The RC corbels with the ratio of shear span-to-effective depth less than 1 are commonly used to transfer loads from beams to columns. The ultimate strengths and structural behaviors of RC corbels are controlled by the shear span-to-effective depth ratio, strength of concrete, shape and quantity of the reinforcement, and geometry of corbels. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strengths and complicated structural behaviors is presented for the design of RC corbels. In addition, a load distribution ratio, defined as a magnitude of load transferred by a horizontal truss mechanism, is proposed to help structural designers perform the design of RC corbels by using the strut-tie model approaches of current design codes. The ultimate strengths of 30 RC corbels tested to failure are evaluated by using the ACI 318-05's strut-tie model code for the validity check of the proposed indeterminate strut-tie model and load distribution ratio.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.3-12
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• 2011

The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure a ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.257-265
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• 2016

The failure behavior of reinforced concrete beams is governed by the mechanical relationships between the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, two simple indeterminate strut-tie models which can reflect all characteristics of the failure behavior of reinforced concrete beams were proposed. The proposed models are effective for the beams with shear span-to-effective depth ratio of less than 3. For each model, a load distribution ratio, defined as the fraction of load transferred by a truss mechanism, is also proposed to help structural designers perform the rational design of the beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratios, the effect of the primary design variables including shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete was reflected through numerous material nonlinear analysis of the proposed indeterminate strut-tie models. In the companion paper, the validity of the proposed models and load distribution ratios was examined by applying them to the evaluation of the failure strength of 335 reinforced concrete beams tested to failure by others.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.259-267
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• 2008

The ultimate strengths of reinforced concrete deep beams are governed by the capacity of the shear resistance mechanism composed of concrete and shear reinforcing bars, and the structural behaviors of the beams are mainly controlled by the mechanical relationships according to the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strengths and complicated structural behaviors is presented for the design of simply supported reinforced concrete deep beams. In addition, a load distribution ratio, defined as a magnitude of load transferred by a vertical truss mechanism, is proposed to help structural designers perform the design of simply supported reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of a load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the prime design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete influencing the ultimate strength and behavior are reflected upon based on various and numerous numerical analysis results. In the companion paper, the validity of presented model and load distribution ratio was examined by employing them to the evaluation of the ultimate strengths of various simply supported reinforced concrete deep beams tested to failure.

• Journal of the Korea Concrete Institute
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• v.23 no.1
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• pp.13-22
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• 2011

In this study, ultimate strengths of 51 continuous reinforced concrete deep beams were evaluated by the ACI 318M-08's strut-tie model approach implemented with the presented indeterminate strut-tie model and load distribution ratio of the companion paper. The ultimate strengths of the continuous deep beams were also estimated by the shear equations derived based on experimental results, conventional design codes based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the presented strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables of shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength. The present study results of ultimate strengths obtained using the indeterminate strut-tie model and load distribution ratio of the continuous deep beams agree fairly well with those obtained using other approaches. In addition, the present approach reflected the effect of the primary design variables on the ultimate strengths of the continuous deep beams consistently and accurately. Therefore, the present study will help structural designers to conduct rational and practical strut-tie model designs of continuous deep beams.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.267-278
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• 2016

In this study, the ultimate strength of 335 simply supported reinforced concrete beams with shear span-to-effective depth ratio of less than 3 was evaluated by the ACI 318-14's strut-tie model approach implemented with the indeterminate strut-tie models and load distribution ratios of the companion paper. The ultimate strength of the beams was also estimated by using the experimental shear strength models, the theoretical shear strength models, and the current strut-tie model design codes. The validity of the proposed strut-tie models and load distribution ratios was examined by comparing the strength analysis results classified according to the prime design variables of the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete.