• 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 $650kg/\textrm{cm}^2$.

• Steel and Composite Structures
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• v.18 no.4
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• pp.873-887
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• 2015

The continuous composite I-girder should have a sufficient rotation capacity (or ductility) to redistribute the negative bending moment into an adjacent positive bending moment region. However, it is generally known that the ductility of the high strength steel is smaller than that of conventional steel, and application of high strength steel can cause ductility problems in a negative moment region of the I-girder. In this study, moment redistribution of the continuous composite I-girder with high strength steel was studied, where high strength steel with yield stress of 690 MPa was considered (the ultimate stress of the steel was 800 MPa). The available and required rotation capacity of the continuous composite I-girder with high strength steel was firstly derived based on the stress-strain curve of high strength steel and plastic analysis, respectively. A large scale test and a series of non-linear finite element analysis for the continuous composite I-girder with high strength steel were then conducted to examine the effectiveness of proposed models and to investigate the effect of high strength steel on the inelastic behavior of the negative bending moment region of the continuous composite I-girder with high strength steel. Finally, it can be found that the proposed equations provided good estimation of the requited and available rotation capacity of the continuous composite I-girder with high strength steel.

• Earthquakes and Structures
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• v.18 no.1
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• pp.15-25
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• 2020

The seismic behaviour of reinforced concrete (RC) columns made from high-strength materials was investigated experimentally. Six high-strength concrete specimen columns (1:4 scale), which included three with high-strength stirrups (HSSs) and three with normal-strength stirrups (NSSs), were tested under a combination of high axial and reversed cyclic loads. The effects of stirrup strength and the ratio of transverse reinforcement on the cracking patterns, hysteretic response, strength, stiffness, ductility, energy dissipation and strain of transverse reinforcement were studied. The results indicate that good seismic behaviour of an RC column subjected to high axial compression can be obtained by using a well-shaped stirrup. Stirrup strength had little effect on the lateral bearing capacity. However, the ductility was significantly modified by improving the stirrup strength. When loaded with a large lateral displacement, the strength reduction of NSS specimens was more severe than that of those with HSSs, and increasing the stirrup strength had little effect on the stiffness reduction. The ductility and energy dissipation of specimens with HSSs were superior to those with NSSs. When the ultimate displacement was reached, the core concrete could be effectively restrained by HSSs.

• 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.

• Computers and Concrete
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• v.1 no.2
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• pp.115-130
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• 2004

The flexural ductility of solid rectangular reinforced concrete beams has been studied quite extensively. However, many reinforced concrete beams are neither solid nor rectangular; examples include T-, ${\Gamma}$-, ${\Pi}$- and box-shaped beams. There have been few studies on the flexural ductility of non-rectangular reinforced concrete beams and as a result little is known about the possible effect of sectional shape on flexural ductility. Herein, the effect of sectional shape on the post-peak flexural behaviour of reinforced normal and high-strength concrete beams has been studied using a newly developed analysis method that employs the actual stress-strain curves of the constitutive materials and takes into account the stress-path dependence of the stress-strain curve of the steel reinforcement. It was revealed that the sectional shape could have significant effect on the flexural ductility of a concrete beam and that the flexural ductility of a T-, ${\Gamma}$-, ${\Pi}$- or box-shaped beam is generally lower than that of a solid rectangular beam with the same overall dimensions and the same amount of reinforcement provided. Based on the numerical results obtained, a simple method of ensuring the provision of a certain minimum level of flexural ductility to non-rectangular concrete beams has been developed.

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.249-266
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• 2001

Current seismic design provisions allow structures to deform into inelastic range during design level earthquakes since the chance to meet such event is quite rare. For this purpose, design base shear is defined in current seismic design provisions as the value of elastic seismic shear force divided by strength reduction factor, R (${\geq}1$). Strength reduction factor generally consists of four different factors, which can account for ductility capacity, overstrength, damping, and redundancy inherent in structures respectively. In this study, R factor is assumed to account for only the ductility rather than overstrength, damping, and redundancy. The R factor considering ductility is called "ductility factor" ($R_{\mu}$). This study proposes ductility factor with correction factor, C, which can account for dynamic P-${\Delta}$ effect. Correction factor, C is established as the functional form since it requires computational efforts and time for calculating this factor. From the statistical study using the results of nonlinear dynamic analysis for 40 earthquake ground motions (EQGM) it is shown that the dependence of C factor on structural period is weak, whereas C factor is strongly dependant on the change of ductility ratio and stability coefficient. To propose the functional form of C factor statistical study is carried out using 79,920 nonlinear dynamic analysis results for different combination of parameters and 40 EQGM.

• Structural Engineering and Mechanics
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• v.19 no.2
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• pp.185-198
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• 2005

In the design of reinforced concrete beams, it is a standard practice to use the yield stress of the steel reinforcement for the evaluation of the flexural strength. However, because of strain hardening, the tensile strength of the steel reinforcement is often substantially higher than the yield stress. Thus, it is a common belief that the actual flexural strength should be higher than the theoretical flexural strength evaluated with strain hardening ignored. The possible increase in flexural strength due to strain hardening is a two-edge sword. In some cases, it may be treated as strength reserve contributing to extra safety. In other cases, it could lead to greater shear demand causing brittle shear failure of the beam or unexpected greater capacity of the beam causing violation of the strong column-weak beam design philosophy. Strain hardening may also have certain effect on the flexural ductility. In this paper, the effects of strain hardening on the post-peak flexural behaviour, particularly the flexural strength and ductility, of reinforced normal- and high-strength concrete beams are studied. The results reveal that the effects of strain hardening could be quite significant when the tension steel ratio is relatively small.

• Computers and Concrete
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• v.8 no.4
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• pp.473-489
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• 2011

In designing a flexural member for structural safety, both the flexural strength and ductility have to be considered. For this purpose, the flexural ductility of reinforced concrete sections has been studied quite extensively. As there have been relatively few studies on the flexural ductility of prestressed concrete sections, it is not well understood how various structural parameters affect the flexural ductility. In the present study, the full-range flexural responses of reinforced and prestressed concrete sections are analyzed taking into account the nonlinearity and stress-path dependence of constitutive materials. From the numerical results, the effects of steel content, yield strength and degree of prestressing on the yield curvature and ultimate curvature are evaluated. It is found that whilst the concept of flexural ductility in terms of the ductility factor works well for reinforced sections, it can be misleading when applied to prestressed concrete sections. For prestressed concrete sections, the concept of flexural deformability in terms of ultimate curvature times overall depth of section may be more appropriate.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.2
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• pp.37-47
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• 2010

In order to attain enhanced seismic performance of RC bridges, premature shear failure prior to the achievement of target ductilities of the piers should be prevented. For this purpose, a reliable shear strength evaluation is required. The shear strength of an RC column subjected to a lateral force decreases with an increase in ductility. Many empirical equations for the shear strength have been proposed by many researchers. However, there are many discrepancies in the initial shear strength in the low ductility range, and in the decrease rate according to the ductility. In this study, a new empirical equation of shear strength considering the displacement ductility effect has been proposed, in which the initial shear strength equation proposed by the authors was revised on the basis of the investigation of many other researchers' test results. The resulting improvement in accuracy is confirmed by comparison with other empirical equations.

• 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.