Byung-Hun Kim

An Indeterminate Strut-Tie Model and Load Distribution Ratio for RC Deep Beams - (I) Model & Load Distribution Ratio

The ultimate strength of simply supported reinforced concrete deep beams is governed by the capacity of the shear resistance mechanism. The structural behavior of the deep beams is controlled mainly by the mechanical relationships between the primary design variables including shear span-to-effective depth ratio, flexural reinforcement ratio, and the compressive strength of concrete. In this study, a simple indeterminate strut-tie model which reflects all characteristics of the ultimate strength and behavior of the deep beams was presented. A load distribution ratio, defined as the fraction of load transferred by a truss mechanism, was also proposed to help structural designers perform the rational design of 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 which ensures the ductile shear design of the deep beams was introduced, and the effect of the primary design variables was reflected through numerous numerical analyses of the presented indeterminate strut-tie model. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them to the evaluation of ultimate strength of 234 simply supported reinforced concrete deep beams tested to failure.

An Indeterminate Strut-Tie Model and Load Distribution Ratio for RC Deep Beams- (II) Validity Evaluation

In this study, the ultimate strength of 234 simply supported reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-08s strut-tie model approach implemented with the indeterminate strut-tie model and load distribution ratio of the companion paper. The ultimate strength of the deep 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 presented indeterminate 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 compressive strength of concrete. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of 234 deep beams fairly accurately compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of deep beams consistently and accurately.

Indeterminate Strut-Tie Model and Load Distribution Ratio of Continuous RC Deep Beams (I) Proposal of Model ＆ Load Distribution Ratio

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.

Indeterminate Strut-Tie Model and Load Distribution Ratio of Continuous RC Deep Beams (II) Validity Evaluation

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.

Strut-Tie Model Evaluation of Haunch Effects in Concrete Structures

This paper evaluates the effects of haunches and the characteristic differences of haunch design regulations through design of pier and box structures with/without haunches. The design of the pier and box structures was conducted by using the linear elastic plane stress finite element analysis, the DIN 1045 and ACI 318-99 codes, the suggested experimental design equations, and the strut-tie model approach. To prove the validity of design results obtained by the strut-tie model approach, the ultimate strength of two haunched reinforced concrete beams tested to failure was evaluated by using the approach. According to the comparison and evaluation of the design results, it is concluded that the design results of haunched reinforced concrete structures by using conventional and design codes need to be complemented with those by using the strut-tie model approach that reflected the effects of haunches in design comparatively well through the actions of arch and direct transfer of applied loads.