• 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.

• 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.

• Computers and Concrete
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• v.26 no.4
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• pp.351-365
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• 2020

This work presents numerical and experimental analyses of the behavior of reinforced-concrete deep beams with unconventional geometries. The main goal here is to experimentally and numerically study these geometries to find possible new behaviors due to the material nonlinearity of reinforced concrete with complex geometries. Usually, unconventional geometries result from innovative designs; in general, studies of reinforced concrete structures are performed only on conventional members such as beams, columns, and labs. To achieve the goal, four reinforced-concrete deep beams with geometries not addressed in the literature were tested. The models were numerically analyzed with the Adaptive Micro Truss Model (AMTM), which is the proposed method, to address new geometries. This work also studied the main parameters of the constitutive model of concrete based on a statistical analysis of the finite element (FE) results. To estimate the ultimate loads, FE simulations were performed using the Monte Carlo method. Based on the obtained ultimate loads, a probabilistic distribution was created, and the final ultimate loads were computed.

• 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.

• 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.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.

• Journal of the Korea Concrete Institute
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• v.21 no.2
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• pp.121-127
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• 2009

The failure behavior of RC structure was exceedingly affected by the size and the local strain distribution of the failure zone due to the strain localization behavior on the tension softening materials. However, it is very difficult to quantify and assess the local strain occurring in the failure zone by the conventional test method. In this study, image processing technology, which is available to measure the strain up to the complete failure of RC structures, was used to estimate the local strain distribution and the size of failure zone. In order to verify the reliability and validity for the image processing technology, the strain transition acquired by the image processing technology was compared with strain values measured by the concrete gauge on the uniaxial compressive specimens. Based on the verification of image processing technology for the uniaxial compressive specimens, the size and the local strain distribution of the failure zone of deep beam was measured using the image processing technology. With the results of test, the principal tensile/compressive strain contours were drawn. Using the strain contours, the size of the failure zone and the local strain distribution on the failure of the deep beam was evaluated. The results of strain contour showed that image processing technology is available to assess the failure behavior of deep beam and obtain the local strain values on the domain of the post-peak failure comparatively.

• Earthquakes and Structures
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• v.18 no.1
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• pp.113-127
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• 2020

In this study, the behavior of external beam-column joints reinforced by plain and deformed bars with non-seismic reinforcement details is investigated and compared. The beam-column joints represented in this study include a benchmark specimen by seismic details in accordance with ACI 318M-11 requirements and four other deficient specimens. The main defects of the non-seismic beam-column joints included use of plain bar, absence of transverse steel hoops, and the anchorage condition of longitudinal reinforcements. The experimental results indicate that using of plain bars in non-seismic beam-column joints has significantly affected the failure modes. The main failure mode of the non-seismic beam-column joints reinforced by deformed bars was the accumulation of shear cracks in the joint region, while the failure mode of the non-seismic beam-column joints reinforced by plain bars was deep cracks at the joint face and intersection of beam and column and there was only miner diagonal shear cracking at the joint region. In the other way, use of plain bars for reinforcing concrete can cause the behavior of the substructure to be controlled by slip of the beam longitudinal bars. The experimental results show that the ductility of non-seismic beam-column joints reinforced by plain bars has not decreased compared to the beam-column joints reinforced by deformed bars due to lack of mechanical interlock between plain bars and concrete. Also it can be seen a little increase in ductility of substructure due to existence of hooks at the end of the development length of the bars.

• 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.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.