• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.3
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• pp.165-172
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• 2019

In this study, the shear strength of prestressed concrete deep beams is predicted using finite element analysis, and the variation in the shear strength according to the degree of prestressing is investigated. Numerical analysis results are compared with results obtained by the strut-and-tie model and associated experiments. Numerical analyses are performed on prestressed concrete deep beams with different values of concrete strength, effective prestress, ratio of tensile reinforcement, and shear span to effective depth ratio. The shear strength predicted by the numerical analysis is similar to the experimental value obtained, with an error of less than 5%. However, the strut-and-tie model highly overestimated the shear strength of prestressed concrete deep beams with a concentrated loading area. The ultimate shear capacity of prestressed concrete deep beams increased linearly with increasing prestresss applied to the tendon.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.734-737
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• 2010

이 연구에서는 프리스트레스트 콘크리트 깊은 보의 비선형해석을 위한 전산플랫폼을 개발하였다. 프리스트레스트 콘크리트 깊은 보의 전단거동을 정확하게 파악하고 합리적이면서 경제적인 설계기준의 개발을 위한 자료를 제공하는데 그 목적이 있다. 재료적 비선형성에 대해서는 균열콘크리트에 대한 인장, 압축, 전단모델과 콘크리트 속에 있는 철근모델을 조합하여 고려하였다. 사용된 부착 또는 비부착 텐던요소는 유한요소법에 근거하며 프리스트레스트 콘크리트 부재의 콘크리트와 텐던의 상호작용을 구현할 수 있다. 이 연구에서는 프리스트레스트 콘크리트 깊은 보의 전단거동을 파악하기 위해 제안한 해석기법을 신뢰성 있는 연구자의 실험 결과와 비교하여 그 타당성을 검증하였다.

• 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.25 no.6
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• pp.683-691
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• 2013

Failure behaviour of deep beams is largely depend on shear span to effective depth ratio(a/d). For deep beams with $a/d{\leq}1.0$, the diagonal splitting of the web and local crushing of concrete near applied loads or supports is the most common failure mode. If the beam contains sufficient web reinforcement, area of local crushing will be increased while area of diagonal splitting is decreased. When web reinforcement above purpose, web should be reinforced both in the horizontal and vertical directions or be reinforced in perpendicular direction to diagonal cracks. For deep beams with 1.0${\leq}2.5$, the increment of shear strength by the horizontal web reinforcement are hardly expected unless amount of main bars very small that the main bars should be reached yielding state when shear failure occurs. In contrast, the vertical web reinforcement prevent the beam from being transferred to tied arch mechanism, and as a result th shear strength of beam increase. In this study, formulas based on upper bound theorem of plastic theory are proposed to predict the shear strength of reinforced concrete deep beams with $a/d{\leq}1.0$. Comparisons with other experiment results are performed, and good agreement between measured and predicted value by proposed formulas is obtained.

• Journal of the Korea Concrete Institute
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• v.15 no.5
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• pp.689-696
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• 2003

Recently, Appendix A of ACI 318∼02 Code introduced the Strut-and-Tie Model(STM) procedure in shear design of deep flexural members. The STM procedure is widely used in the design of concrete regions where the distribution of longitudinal strains is significantly nonlinear, such as deep beams, beams with large openings, corbels, and dapped-end beams. Experimental study included five high-strength reinforced concrete deep beams with different detailing schemes for the horizontal and vertical reinforcement. The specimens were designed as simply supported beams subjected to concentrated loads on the top face and supported on the bottom face. At failure, all specimen exhibited primary diagonal crack running from the support region to the point load. Specimens which had mechanical anchorages(terminators) gives better representation of the load-carrying mechanism than the specimen had standard 90-degree anchorage at failure in deep flexural members. Based on the test results, shear design procedures contained in the ACI 318-99 Code, Appendix A of the ACI 318-02 Code, CSA A23.3-94 Code and CIRIA Guide-2 were evaluated. The Shear design of ACI 318-99 Code, Appendix A of the ACI 318-02 Code and CIRIA Guide-2 shown to be conservative predictions from 10% to 36% in the shear strength of the single-span deep beam which was tested. ACI 318-99 Code was the lowest standard deviation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2195-2209
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• 2013

The effective strength of concrete struts must be determined accurately for the reliable strut-tie model analysis and design of structural concrete. In this study, the equations of the effective strength, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete deep beams employed in current design codes, are proposed. The effects of shear span-to-effective depth ratio, compressive strength of concrete, and flexural and shear reinforcement ratios are reflected in the development of the proposed equations. To examine the appropriateness of the proposed equations, the strengths of 241 reinforced concrete deep beams, all tested to shear failure, are evaluated by using the three types of strut-tie models with the existing and proposed equations.

• Journal of the Korea Concrete Institute
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• v.13 no.6
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• pp.619-628
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• 2001

In building construction, openings of the story-height deep beams are usually required for accessibility and service lines such as air conditioning ducts, drain pipes and electric units. It is known that the main parameters affecting the load bearing capacity of deep beams with web openings are size, shape, location and reinforcements of openings. However, there have been no pertinent theories and national design codes for predicting ultimate shear strength of reinforced concrete deep beams with web openings. In this study, the shear behavior of simply supported reinforced concrete deep beams with web openings subject to concentrated loads has been scrutinized experimentally. A total of 34 specimens, the geometry of openings, its reinforcements and shear span to depth ratio, being taken as the experimental variables, has been cast and tested in the laboratory. The effects of these structural parameters on the shear strength and crack initiation and propagation have been carefully checked and analyzed. From the tests, it has been observed that the failures of all specimens were due to shear mechanism and the ultimate strength of specimens varies according to the location of openings, by which the formation of compression struts between the loading points and supports are deterred. All of the test results of specimens have been compared with the formulas proposed by previous researchers. The results were closely coincident with the formulas given by Ray and Kong's equation except for some X series specimens having a larger dimension of openings beyond the geometric limits of proposed equations.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.874-882
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• 2002

Currently, deep beams are designed according to ACT 318-99 equations derived from experimental data for slender beams with normal-strength concrete. In addition, there is relatively limited information on high-strength concrete deep beams with shear reinforcement. The purpose of this experimental study is to investigate the shear behavior of high-strength concrete deep beams and to grasp the conservatism of ACI shear design provisions. Experimental results on the shear behavior of 22 deep beams under two equal symmetrically placed point loads are reported. compressive strength of concrete cylinder was 800kgf/$\textrm{cm}^2$, and main variables were vertical and horizontal shear reinforcement and shear span-to-overall depth ratio (а/h). Test results showed that for high-strength concrete deep beams with shear span-to-overall depth ratio exceeding 0.75, the vertical shear reinforcement more effectively resisted the shear load than horizontal shear reinforcement. In high-strength concrete deep beams, ACI shear design provisions tended to underestimate the effect of strut-tie action and vertical shear reinforcement and overestimate the ones of horizontal shear reinforcement. Based on the experimental results of high-strength concrete deep beams and shear friction theory, this study modified the equations on the shear capacity specified by the ACI provisions.

• 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.