• Steel and Composite Structures
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• v.47 no.3
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• pp.383-393
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• 2023

Conventional reinforced concrete design codes assume ideal strain evolution in semi-deep beams with externally bonded fiber-reinforced polymer (EB-FRP) web strips. However, there is a strain interaction between internal stirrups and web strips, leading to a notable difference between code-based and experimental shear strengths. Current study provides an experiment-verified detailed numerical framework to assess the potential strain interaction under quasi-static monotonic load. Based on the observations, steel stirrups are effective only for low EB-FRP amounts and the over-strengthening of semi-deep beams prevents the stirrups from yielding, reducing its shear strength contribution. A notable difference is detected between the code-based and the study-based EB-FRP strain values, which is a function of the normalized FRP stress parameter. Semi-analytical relations are proposed to estimate the effective strain and stress of the components considering the potential strain interaction. For the sake of simplification, a linearized correction factor is proposed for the EB-FRP web strip strain, assuming its restraining effect as constant for all steel stirrup amounts.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.2
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• pp.201-210
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• 2011

This paper presents a nonlinear finite element analysis procedure for the seismic performance assessment of deep beam-and-interior column joints. A computer program, named RCAHEST(Reinforced Concrete Analysis in Higher Evaluation System Technology), for the analysis of reinforced concrete structures was used. Horizontal cyclic load tests were conducted to estimate the strength, ductility, and behavioral characteristics of deep beam-and-interior column joints. Experimental parameters are axial forces and amount of transverse reinforcement. The proposed numerical method for the seismic performance assessment of deep beam-and-interior column joints is verified by comparison of its results with reliable experimental results.

• Advances in concrete construction
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• v.13 no.3
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• pp.243-254
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• 2022

Reinforced concrete (RC) deep beams are critical structural elements used in offshore pile caps, rectangular cross-section water tanks, silo structures, transfer beams in high-rise buildings, and bent caps. As a result of the low shear span ratio to effective depth (a/d) in deep beams, arch action occurs, which leads to shear failure. Several studies have been carried out to improve the shear resistance of RC deep beams and avoid brittle fracture behavior in recent years. This study was performed to investigate the behavior of RC deep beams numerically and experimentally with different reinforcement arrangements. Deep beams with four different reinforcement arrangements were produced and tested under monotonic static loading in the study's scope. The horizontal and vertical shear reinforcement members were changed in the test specimens to obtain the effects of different reinforcement arrangements. However, the rebars used for tension and the vertical shear reinforcement ratio were constant. In addition, the behavior of each deep beam was obtained numerically with commercial finite element analysis (FEA) software ABAQUS, and the findings were compared with the experimental results. The results showed that the reinforcements placed diagonally significantly increased the load-carrying and energy absorption capacities of RC deep beams. Moreover, an apparent plastic plateau was seen in the load-displacement curves of these test specimens in question (DE-2 and DE-3). This finding also indicated that diagonally located reinforcements improve displacement ductility. Also, the numerical results showed that the FEM method could be used to accurately predict RC deep beams'behavior with different reinforcement arrangements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.40-46
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• 1996

Three procedures are currently used for the design of deep beams, which are Empirical design method, Nonlinear analysis, and Truss models. The engineering logic and decisions inherent in these design procedures are dependent on the acquired knowledge and experience of the structural engineer. Knowledge-based system is useful to solve problems which require human experties. Therefore, this study presents an application of Knowledge-Based System for design of reinforced concrete deep beams with web openings.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.577-582
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• 2000

This study is aimed to evaluate the shear strength of reinforced concrete deep beams subject to concentrated loads, using a simplified strut-tie model. For the shear strength prediction of deep beams, it is prerequisite to evaluate the effective width of strut and to verify the efficiency factors proposed by MacGregor et al.. The results analyzed by truss models have been compared with those calculated by domestic code for the existing data of 90 deep beam specimens. The shear strength of deep beams were reviewed with respect to concrete strength, the shear span-depth ratio, and the ratio of web reinforcements. The results showed that the shear strength of the proposed model gave a better agreement than the domestic code approach.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.4
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• pp.305-312
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• 2014

The current American Concrete Institute(ACI), Canadian Standard Associate(CSA) and CEB-FIP Model Code 2010 provisions on the shear strength of a simply supported deep beam suggest that deep beams should be designed using the strut-and-tie model. Although this is a useful methodology to design members in disturbed regions, the quality of the design is highly dependent on the truss model that designers create. However, Hong et al. derived the shear strength equations of reinforced concrete deep beams. This thesis investigates the validity of the current ACI, CSA and CEB-FIP code provisions on the shear strength of simply supported reinforced concrete deep beams by comparing them with the shear strength equations proposed by Hong et al. The comparison shows that all of these code provisions provide reasonable estimates on the shear strength of concrete deep beam members and the selection of an internal truss model plays an important role on the estimation of shear strength.

• Computers and Concrete
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• v.16 no.3
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• pp.357-380
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• 2015

In this study, a simple indeterminate strut-tie model which reflects complicated characteristics of the ultimate structural behavior of continuous reinforced concrete deep beams was proposed. In addition, the load distribution ratio, defined as the fraction of applied load transferred by a vertical tie of truss load transfer mechanism, was proposed to help structural designers perform 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 was introduced to ensure the 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 compressive strength of concrete were reflected upon. To verify the appropriateness of the present study, the ultimate strength of 58 continuous reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-11's strut-tie model approach associated with the presented indeterminate strut-tie model and load distribution ratio. The ultimate strength of the continuous deep beams was also estimated by the experimental shear equations, conventional design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the proposed strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of the continuous deep beams fairly well compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of the continuous deep beams consistently and reasonably. The present study may provide an opportunity to help structural designers conduct the rational and practical strut-tie model design of continuous deep beams.

• 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.

• Computers and Concrete
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• v.25 no.3
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• pp.193-204
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• 2020

In the study, a new, simple and alternative formula is proposed to calculate numerically crack widths of concrete on a finite element (FE) model. By considering more general tension softening behavior of concrete, the proposed expression is derived irrespective of any tension softening model given in the literature or design codes. The test results of six reinforced concrete (RC) deep beams having different geometrical and material properties selected from a recent existing experimental study of the authors are used to verify the accuracy and reliability of the proposed formula and the created numerical FE models of the specimens. Moreover, the crack width results obtained from the FE models are compared with the test results to see the performance of the proposed formula. The results of the study demonstrate that the proposed formula gives very accurate results in a comparison with the test results. The ratios of errors on the results stay commonly at an acceptable level as well. Consequently, the proposed formula is quite simple, unique, and robust to determine crack widths of RC deep beams on an FE model.

• Architectural research
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• v.19 no.4
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• pp.117-124
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• 2017

In this research, we carried out finite element analysis depends on the variations such as the strength of the main bar, concrete, shear-span ratio(a/d) and existence of shear reinforcing bar. Throughout the results of FEM analysis, we were able to figure out how each variation can effect on shear performance. As the strength of concrete increased, the maximum shear force enhancement effect of each specimen was evaluated. As a result, the shear strengthening effect was 51~97% for shear reinforced specimens, and 26~44% for non-shear reinforced specimens. As the yield strength of reinforcing bars increases, the shear reinforcement effect of the specimen the specimens without shear reinforcement were 3%~6% higher than those with shear reinforcement. Theoretical and analytical values were compared using the design equations obtained from the CEB code. Theoretical and analytical values were compared using the design equations obtained from the CEB code. As a result, the error rate was the highest at 3.64 in the S1.0-C0 series and the lowest at 1.46 in the S1.7-C1 series. Therefore, the design equation of the CEB code is estimated to underestimate the actual shear strength of deep beams that are not subjected to shear reinforcement.