• Structural Engineering and Mechanics
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• v.58 no.1
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• pp.1-19
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• 2016

Recently, the high-strength concrete is increasingly used in the construction of reinforced concrete structures due to its benefits, but this use is influenced negatively on the local ductility of structural elements. The objective of this study is the prediction of a new approach to evaluate the curvature ductility factor of high strength concrete beams according to Eurocode 2. After the presentation of the Constitutive laws of materials and the evaluation method of curvature ductility according to the Eurocode 2, we conduct a parametric study on the factors influencing the curvature ductility of inflected sections. The calibrating of the obtained results allows predicting a very simple approach for estimating the curvature ductility factor. The proposed formula allows to calculate the curvature ductility factor of high strength concrete beams directly according to the concrete strength $f_{ck}$, the yield strength of steel $f_{yk}$ and the ratio of tension and compression reinforcements ${\rho}$ and ${\rho}^{\prime}$ respectively, this proposed formula is validated by theoretical and experimental results of different researchers.

• Computers and Concrete
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• v.20 no.2
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• pp.129-143
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• 2017

Seismic design of reinforced concrete (RC) structures requires a certain minimum level of flexural ductility. For example, Eurocode EN1998-1 directly specifies a minimum flexural ductility for RC beams, while Chinese code GB50011 limits the equivalent rectangular stress block depth ratio at peak resisting moment to achieve a certain nominal minimum flexural ductility indirectly. Although confinement is effective in improving the ductility of RC beams, most design codes do not provide any guidelines due to the lack of a suitable theory. In this study, the confinement for desirable flexural ductility performance of both normal- and high-strength concrete beams is evaluated based on a rigorous full-range moment-curvature analysis. An effective strategy is proposed for flexural ductility design of RC beams taking into account confinement. The key parameters considered include the maximum difference of tension and compression reinforcement ratios, and maximum neutral axis depth ratio at peak resisting moment. Empirical formulae and tables are then developed to provide guidelines accordingly.

• Computers and Concrete
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• v.16 no.3
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• pp.399-414
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• 2015

Nowadays, fiber reinforced polymer (FRP) composites are widely used for rehabilitation, repair and strengthening of reinforced concrete (RC) structures. Also, recent advances in concrete technology have led to the production of high strength concrete, HSC. Such concrete due to its very high compression strength is less ductile; so in seismic areas, ductility is an important factor in design of HSC members (especially FRP strengthened members) under flexure. In this study, the Adaptive Neuro-Fuzzy Inference System (ANFIS) and multiple regression analysis are used to predict the curvature ductility factor of FRP strengthened reinforced HSC (RHSC) beams. Also, the effects of concrete strength, steel reinforcement ratio and externally reinforcement (FRP) stiffness on the complete moment-curvature behavior and the curvature ductility factor of the FRP strengthened RHSC beams are evaluated using the analytical approach. Results indicate that the predictions of ANFIS and multiple regression models for the curvature ductility factor are accurate to within -0.22% and 1.87% error for practical applications respectively. Finally, the effects of height to wide ratio (h/b) of the cross section on the proposed models are investigated.

• Journal of the Korea Concrete Institute
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• v.11 no.3
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• pp.131-140
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• 1999

This paper presents a study on the flexural ductility of reinforced concrete beams, 16beams with different concrete strength, reinforcement ratio, reinfo- rcement strength. For the purpose of inducing flexural failure, the reinforce ratio ($\rho$-$\rho$') was made not to be more than $0.75\rho$b in accordance with ACi code 318-89. From the test results, it is found that in case of a concrete strength increased from 240 to 650kg/$\textrm{cm}^2$, the displacement and curvature ductility factore are increased by about 31-231 percents. And also increased in case of increased from 650 to 900kg/$\textrm{cm}^2$, but the increasing ratio is gradually decreasing accoding to a concrete strength increases. And also found that as the Double Re-bar Ratio (($\rho$-$\rho$')/$\rho$b) increases, so the displacement and curvature ductility ratio would decrease, but in case of increased from 650 to /$900kg\textrm{cm}^2$ the decreasing ration is bigger than in case of increased from 240 to $650kg/\textrm{cm}^2$.

• Structural Engineering and Mechanics
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• v.12 no.5
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• pp.459-474
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• 2001

The complete moment-curvature curves of doubly reinforced concrete beams made of normal- or high-strength concrete have been evaluated using a newly developed analytical method that takes into account the stress-path dependence of the constitutive properties of the materials. From the moment-curvature curves and the strain distribution results obtained, the post-peak behavior and flexural ductility of doubly reinforced normal- and high-strength concrete beam sections are studied. It is found that the major factors affecting the flexural ductility of reinforced concrete beam sections are the tension steel ratio, compression steel ratio and concrete grade. Generally, the flexural ductility decreases as the amount of tension reinforcement increases, but increases as the amount of compression reinforcement increases. However, the effect of the concrete grade on flexural ductility is fairly complicated, as will be explained in the paper. Quantitative analysis of such effects has been carried out and a formula for direct evaluation of the flexural ductility of doubly reinforced concrete sections developed. The formula should be useful for the ductility design of doubly reinforced normal- and high-strength concrete beams.

• Computers and Concrete
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• v.6 no.6
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• pp.451-472
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• 2009

Based on a numerical method to analyse the full-range behaviour of prestressed concrete beams with unbonded tendons, parametric studies are carried out to investigate the influence of 11 parameters on the curvature ductility of unbonded prestressed concrete (UPC) beams. It is found that, among various parameters studied, the depth to prestressing tendons, depth to non-prestressed tension steel, partial prestressing ratio, yield strength of non-prestressed tension steel and concrete compressive strength have substantial effects on the curvature ductility. Although the curvature ductility of UPC beams is affected by a large number of factors, rather simple equations can be formulated for reasonably accurate estimation of curvature ductility. Conversion factors are introduced to cope with the difference in partial safety factors, shapes of equivalent stress blocks and the equations to predict the ultimate tendon stress in BS8110, EC2 and ACI318. The same equations can also be used to provide conservative estimates of ductility of UPC beams with compression steel.

• 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.

• 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.

• Structural Engineering and Mechanics
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• v.89 no.6
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• pp.579-588
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• 2024

The present paper investigates the curvature ductility of confined reinforced concrete (RC) beams with normal (NSC) and high strength concrete (HSC). For the purpose of predicting the curvature ductility factor, an analytical model was developed based on the equilibrium of internal forces of confined concrete and reinforcement. In this context, the curvatures were calculated at first yielding of tension reinforcement and at ultimate when the confined concrete strain reaches the ultimate value. To best simulate the situation of confined RC beams in flexure, a modified version of an ancient confined concrete model was adopted for this study. In order to show the accuracy of the proposed model, an experimental database was collected from the literature. The statistical comparison between experimental and predicted results showed that the proposed model has a good performance. Then, the data generated from the validated theoretical model were used to train the artificial neural network (ANN) prediction model. The R² values for theoretical and experimental results are equal to 0.98 and 0.95, respectively which proves the high performance of the ANN model. Finally, a parametric study was implemented to analyze the effect of different parameters on the curvature ductility factor using theoretical and ANN models. The results are similar to those extracted from experiments, where the concrete strength, the compression reinforcement ratio, the yield strength, and the volumetric ratio of transverse reinforcement have a positive effect. In contrast, the ratio and the yield strength of tension reinforcement have a negative effect.

• 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.