• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.189-194
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• 2001

In this study, ultimate strength of concrete deep beams with an opening is predicted by using Strut-and-Tie Model with a new effective compressive strength. First crack occurs around an opening by stress concentration due to geometric discontinuity. This results in decreasing ultimate strength of deep beams with an opening compared with general deep beams. With fundamental notion that ultimate strength of deep beam with an opening decreases as a result of reduction in effective compressive strength of a concrete strut, an equivalent effective compressive strength formula is proposed in order to reflect ultimate strength reduction due to an opening located in a concrete strut. An equivalent effective compressive strength formula which can reflect opening size and position is added to a testified algorithm of predicting ultimate strength of concrete deep beams. Therefore, ultimate strength of concrete deep beam with an opening is predicted by using a simple and rational STM algorithm including an equivalent effective compressive strength formula, not by finite element analysis or a former complex Strut-and-Tie Model

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.241-246
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• 2000

In the strut-tie model design of structural concrete, the importance of the effective strength of concrete strut has been overlooked by many practitioners. The authors believe that the effective strength of concrete strut is an important factor not only in determining steel tie forces but also in verifying the nodal zone strength and geometric compatibility condition of a selected strut-tie model. This study evaluate the effect of the effective strength of concrete strut on structural concrete design by applying the different effective strut strengths to the strut-tie model design of a post-tensioned anchorage zone and a continuous concrete deep beam.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.403-413
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• 2014

For the reliable design of the structural concrete by the strut-tie model approaches of current design codes, the effective strengths of concrete struts must be determined with sufficient accuracy. Many values and equations for the effective strengths have been suggested until now. As those are for the two-dimensional concrete struts, however, it is inappropriate to employ them in the strut-tie model designs of three-dimensional structural concretes. In this study, an approach, that determines the effective strengths of three-dimensional concrete struts consistently and accurately by reflecting the state of 3-dimensional stresses, the 3-dimensional failure criteria of concrete, the degree of cracks (or tensile strains of reinforcing bars crossing the struts), the strut's longitudinal length, the deviation angle between strut orientation and compressive principal stress flow, compressive strength of concrete, and the degree of concrete confinement by reinforcing bars, is proposed. To examine the validity of the proposed approach, the ultimate strength analyses of 115 reinforced concrete pile caps tested to failure by previous investigators were conducted by the ACI 318-11's strut-tie model approach with the existing and proposed effective strengths of concrete struts.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.617-622
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• 2000

In this study, effective compressive strength and nodal zone of Strut-and-Tie Model are studied to propose a new design method for RC T-type pier coping for prevention of sudden brittle failure. The coping which transmits loads of bridge to pier should be properly designed to retain ductile behavior. In order to carry out this proper design using STM, tie must yield before concrete fails, and a stress at strut should not exceed a certain effective stress. Therefore, reasonable determination of the effective compressive strength of strut by considering stress states at the nodal zone exactly is very important. Since conventional STM is applied under assumption that all nodes are under hydrostatic stress state, actual non-hydrostatic stress state in nodal zone caused by geometrical characteristics, loading conditions, support conditions of structures can not be considered properly. In order to apply STM for design of RC T-type pier coping, the non-hydrostatic stress state of nodal zone is considered and effective compressive strength is proposed. Then, a new design method of RC T-type pier coping which applies the principle of superposition to obtain optimum ductile behavior is rationally designed.

• Journal of the Korea Concrete Institute
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• v.18 no.5 s.95
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• pp.639-648
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• 2006

A shear experiment of one-way monotonic loading was carried out with the shear span ratio as the main experimental variable for reinforced concrete beam. Using the finite element analysis as the experimental analysis tool and the analysis method to compute the shear resistance of small shear span ratio, a new macro-model composed of crooked main strut and sub strut is proposed in consideration of the effect of bond action between re-bar and concrete based on the experimental result. The experimental finding affirmed the validity of the proposed macro-model when the shear span ratio was at or below 0.75 and confirmed that the experimental result was the most consistent with the computed analysis result when the effective factor of concrete compressive strength was set at 0.75.

• 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.

• 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 Earthquake Engineering Society of Korea
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• v.13 no.6
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• pp.1-9
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• 2009

This study carried out a shear experiment on concrete deep beam reinforced AFRP to investigate the shear strength of deep beam. The test was conducted on 8 specimens, and the variables were shear span ratio, reinforcement ratio, effective depth, and rebar type. We compared shear strength using ACI 318-08 STM with proposed equations that considered arching action according to shear span ratio. As a result, it was found that shear strength of deep beam reinforced AFRP rebar presented higher shear strength than steel rebar. ACI STM's predictions are more accurate than other predicting equations, and thus this research proposed model versus effective compressive strength of the concrete strut that considered strut size effect based on test results. The predictions obtained using the proposed model are in better agreement than previous equations and codes.

• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.415-420
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• 1998

In this paper, 2D SUB-3D STM approach for analysis and design of 3D structural concrete is presented. In the approach several 2D sub strut-tie models which are representations of compressive and tensile stress flows of each projected plane of 3D structural concrete are utilized in the sketch of a 3D strut-tie model, in the evaluation of effective strengths of compressive concrete struts, and in the verification of geometric compatibility and bearing capacity of critical nodal zones of 3D strut-tie model. To prove the validity and rationality of the suggested approach, the behavior and strength of a prestressed box girder diaphragm tested to failure are evaluated.