• Journal of the Korea Concrete Institute
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• v.13 no.6
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• pp.553-560
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• 2001

The ductility capacity should be estimated for inelastic analysis and design of reinforced concrete flexural members. Therefore, to estimate the ductility capacity, the model of moment-curvature relationship of reinforced concrete flexural member is assumed in this study. The curvature, rotation, and displacement(deflection) of reinforced concrete cantilever beams are analyzed and tested. The analytical results are compared with the test results. According to the analytical and test results, the assumed model of moment-curvature relationship in this study is adequate in flexural analysis of reinforced concrete members because the analytical results are well agreed with the test results, and it is resonable to express the ductility capacity in the rotation or displacement ductility, Because the curvature ductility is the limited index in a certain section. It is investigated that the ductility capacity is proportional to lateral reinforcement and compression reinforcement and inversely proportional to tension reinforcement.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.483-493
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• 2013

The high strength materials have been more widely used in a large reinforced concrete structures. It is known that the use of high strength material in RC structures give the benefits of the mechanical and durable properties, but the ductility decreases with an increase in the strength of the materials. In the design of a reinforced concrete beam, both the flexural strength and ductility need to be considered. So, it is necessary to assess accurately the ductility of the beam with high strength materials in order to ensure the ductility requirement in design. In this study, the effects of the material strength on the flexural behavior and curvature ductility factor of reinforcement concrete beam sections with various reinforcement conditions have been evaluated and a newly prediction formula for curvature ductility factor of RC beam has been developed considering the stress of compression reinforcement at ultimate state. The proposed predictions for the curvature ductility factor which is applicable to both singly and doubly reinforced concrete beam are verified by comparisons with other prediction formulas and the proposed formula offers fairly accurate within 9% error and consistent predictions for curvature ductility factor of reinforced concrete beam.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.4
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• pp.51-61
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• 2003

This research is a park of a research program to develope a new design method for reinforced concrete bridge columns under axial load and cyclic lateral load. The objectives of this paper are to investigate the relationship between curvature ductility and displacement ductility and to propose a correlation equation for designing of reinforced concrete bridge columns under axial load and cyclic lateral load. Computer program NARCC was used for parametric study, which was proved to provide good and conservative analytical result especially for deformation capacity and ductility factor compared with test result. A total of 7,200 spirally reinforced concrete columns were selected considering the main variables such as section diameter, aspect ratio, concrete strength, yielding strength of longitudinal and confinement steel, longitudinal steel ratio, axial load ratio, and confinement steel ratio. A new equation between curvature ductility factor displacement ductility factor with the aspect ratio was proposed by investigation of 21,600 data produced from the selected column models by applying 3 different definitions of yield displacement.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.3
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• pp.1-12
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• 2004

Due to the 1989 Loma Prieta, 1995 Hyogoken Nambu earthquakes, etc, a number of bridge columns  were collapsed in flexure-shear failures as a consequence of the premature termination of the column longitudinal reinforcement. Nevertheless, previous researches for the performance of bridge columns were concentrated on the flexural failure mode. It is well understood that the seismic behaviour of RC bridge piers was dependent on the performance of the plastic hinge of RC bridge piers, the ductility of which was desirable to be computed on the basis of the curvature. Experimental investigation was made to evaluate the variation of the curvature of the plastic hinge  region for the seismic performance of earthquake-damaged RC columns in flexure-shear failure mode. Seven test specimens in the aspect ratio of 2.5 were made with test parameters: confinement ratios, lap splices, and retrofitting FRP materials. They were damaged under series of artificial earthquakes that could be compatible in Korean peninsula. Directly after the pseudo-dynamic test, damaged columns were retested under inelastic reversal cyclic loading under a constant axial load, $P=0.1f_{ck}A_g$. Residual seismic capacity of damaged specimens was evaluated by analzying the moment-curvature hysteresis and the curvature ductility. Test results show that the biggest curvature was developed around 15cm above the footing, which induced the column failure. It was observed that RC bridge specimens with lap-spliced longitudinal steels appeared to fail at low curvature ductility but significant improvement was made in the curvature ductility of RC specimens with FRP straps wrapped around the plastic hinge region. Based on the experimental variation of the curvature of RC specimens, new equivalent length of the plastic hinge region was proposed by considering the lateral confinement in this study. The analytical and experimental relationship between the displacement and the curvature ductility were compared based on this proposal, which gave excellent result.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.12
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• pp.6542-6549
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• 2013

In highly elevated piers and long span beams, a hollow section is often used to reduce the self-weight and increase the flexural rigidity of members. Numerical analysis was conducted to obtain the moment-curvature curves and curvature ductility factor for the RC hollow section beams under a range of hollow portion sizes and reinforcement conditions in the upper flange and web. The curvature ductility factor was constantly maintained until the hollow portion size($b_i/b_o/h_i/h_o$) was less than or equal to 0.5. The curvature ductility factor decreased sharply if ($b_i/b_o/h_i/h_o$) was 0.7 or more. The curvature ductility factor of the beam decreased if reinforcement was provided in the web of the RC hollow section beam. To obtain the same level of the ductility factor as the singly reinforced section, the reinforcement should be provided in the upper flange as much as the web reinforcement.

• Journal of the Korea Concrete Institute
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• v.25 no.3
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• pp.283-294
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• 2013

The high strength materials have been more widely used in reinforced concrete structures, specially, the reinforcing steel is permitted to used in RC structures up to yielding strength of 600 MPa. The strength of materials in RC beam section effects on the behavior and ductility of the RC members. In this study, the numerical analysis has been conducted to obtain the complete moment-curvature relation and the curvature ductility factor for the rectangular RC beams sections under the various reinforcement conditions and the effects of concrete strength, yield strength of reinforcement steel on the behavior and the curvature ductility factor of RC beam sections have been evaluated. The compressive strength of concrete and yield strength of steel have effected in various manner on the behavior and the curvature ductility factor of RC beam sections under reinforcement conditions. In the case of beam sections with equal resisting moment. the curvature ductility factor of RC beam section decreased with an increase in the yield strength of steel and increased with an increase in the concrete strength. When the yield strength of steel increased from 400 MPa to 600 MPa, the curvature ductility factor reduced about 30% and as the concrete strength increased from 30 MPa to 70 MPa, the curvature ductility factor of RC beam section increased about 3 times.

• Journal of Korean Society of Steel Construction
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• v.22 no.4
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• pp.377-388
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• 2010

The flexural behavior of composite HSB600 and HSB800 I-girders under a positive moment was investigated using the material non-linear moment-curvature analysis method. Three representative composite sections with different ductility properties were selected as the baseline sections in this study. Using these baseline sections, the moment-curvature program was verified by comparing the flexural strength and the moment-curvature curve obtained from the program with those obtained using the non-linear FE analysis of ABAQUS. In the FE analysis, the composite girders were modeled three-dimensionally with flanges, the web, and the concrete slab as thin shell elements, and initial imperfections and residual stresses were imposed on the FE model. In the moment-curvature and FE analyses, the 28-day compressive strength of the concrete slab was assumed to be 30-50 MPa, and the HSB600 and HSB800 steels were modeled as elasto-plastic strain-hardening materials, with the concrete as the CEB-FIP model. The effects of the ductility ratio of the composite girder, the type of steel, the compressive strength of the concrete deck, and the location of the plastic neutral axis on the flexural characteristics were analyzed.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.279-288
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• 2016

The present study simplified the moment-curvature relationship to straightforwardly determine the flexural behavior of reinforced concrete (RC) columns. For the idealized column section, moments and neutral axis depths at different stages(first flexural crack, yielding of tensile reinforcing bar, maximum strength, and 80% of the maximum strength at the descending branch) were derived on the basis of the equilibrium condition of forces and compatibility condition. Concrete strains at the extreme compression fiber beyond the maximum strength were determined using the stress-strain relationship of confined concrete, proposed by Kim et al. The lateral load-displacement curves converted from the simplified moment-curvature relationship of columns are well consistent with test results obtained from column specimens under various parameters. The moments and the corresponding neutral axis depth at different stages were formulated as a function of longitudinal reinforcement and transverse reinforcement indices and/or applied axial load index. Overall, curvature ductility of columns was significantly affected by the axial load level as well as concrete compressive strength and the amount of longitudinal and transverse reinforcing bars.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.391-402
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• 1994

One of the most important design concept for reinforced concrete structures is to achieve a ductile failure mode, and also moment redistribution for economic design is possible in case that adequate ductility is provided. Flexural ductility index is, therefore, used as a reference for possibility of moment redistribution as well as for prediction of flexural behavior of designed R.C. structures. Ductility index equations, however, provide approximate values due to the linear concrete compressive stress assumption at the tension steel yielding state. Theoretically more exact ductility index is calculated by a numerical analysis with the realistic stress-strain curves for concrete and steel to be compared with the result from tire ductility index equations. Variation of ductility index for the selected variables and the reasonable maximum tension steel ratio for doubly reinforced section are investigated. A moment-curvature curve model is also proposed for future research on moment redistribution.

• Journal of the Korea Concrete Institute
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• v.26 no.6
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• pp.687-694
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• 2014

This study established a displacement ductility ratio model for ductile design for the boundary element of shear walls. To determine the curvature distribution along the member length and displacement at the free end of the member, the distributions of strains and internal forces along the shear wall section depth were idealized based on the Bernoulli's principle, strain compatibility condition, and equilibrium condition of forces. The confinement effect at the boundary element, provided by transverse reinforcement, was calculated using the stress-strain relationship of confined concrete proposed by Razvi and Saatcioglu. The curvatures corresponding to the initial yielding moment and 80% of the ultimate state after the peak strength were then conversed into displacement values based on the concept of equivalent hinge length. The derived displacement ductility ratio model was simplified by the regression approach using the comprehensive analytical data obtained from the parametric study. The proposed model is in good agreement with test results, indicating that the mean and standard deviation of the ratios between predictions and experiments are 1.05 and 0.19, respectively. Overall, the proposed model is expected to be available for determining the transverse reinforcement ratio at the boundary element for a targeted displacement ductility ratio.