• Computers and Concrete
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• v.12 no.6
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• pp.831-850
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• 2013

The high strength materials have been more widely used in reinforced concrete structures because of the benefits of the mechanical and durable properties. Generally, it is known that 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. Especially, when a reinforced concrete structure may be subjected an earthquake, the members need to have a sufficient ductility. So, each design code has specified to provide a consistent level of minimum flexural ductility in seismic design of concrete structures. Therefore, it is necessary to assess accurately the ductility of the beam sections with high strength materials in order to ensure the ductility requirement in design. In this study, the effects of concrete strength, yield strength of reinforcement steel and amount of reinforcement including compression reinforcement on the complete moment-curvature behavior and the curvature ductility factor of doubly reinforcement concrete beam sections have been evaluated and a newly prediction formula for curvature ductility factor of doubly RC beam sections has been developed considering the stress of compression reinforcement at ultimate state. Based on the numerical analysis results, the proposed predictions for the curvature ductility factor are verified by comparisons with other prediction formulas. The proposed formula offers fairly accurate and consistent predictions for curvature ductility factor of doubly reinforced concrete beam sections.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.689-694
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• 2004

We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

• Computers and Concrete
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• v.16 no.2
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• pp.191-207
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• 2015

It is generally accepted that, in the interest of safety, it is essential to provide a minimum level of flexural ductility, which will allow energy dissipation and moment redistribution as required. If one wishes to be uniformly conservative across all of the design variables, curvature ductility and moment redistribution factor should be calculated using a probabilistic method, as is the case for other design parameters in reinforced concrete mechanics. In this study, simple expressions are derived for the evaluation of curvature ductility and moment redistribution factor, based on the concept of demand and capacity rotation. Probabilistic models are then derived for both the curvature ductility and the moment redistribution factor, by means of central limit theorem and through taking advantage of the specific behaviour of moment redistribution factor as a function of curvature ductility and plastic hinge length. The Monte Carlo Simulation (MCS) method is used to check and verify the results of the proposed method. Although some minor simplifications are made in the proposed method, there is a very good agreement between the MCS and the proposed method. The proposed method could be used in any future probabilistic evaluation of curvature ductility and moment redistribution factors.

• 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.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.585-594
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• 2021

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.

• Journal of Life Science
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• v.16 no.5
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• pp.859-865
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• 2006

When thin slits (e.g., $1mm{\times}10mm$) of maize (Zea mays) coleoptiles were floated on a buffer, they spontaneously curved outward because of unbalanced tissue tension between inner and outer faces. Exogenously applied auxin induced inward curvature of the thin strip of the maize coleoptile in a dose-dependent manner. This bioassay system was used to screen endogenous substances that work together with auxin. In methanol extract of maize coleoptiles including the leaves inside, Active fractions that promote the auxin-induced inward curvature of maize coleoptile slices were found. The curvature-enhancing activity of the extract was not related to energy supply. The active substances were adsorbed to $C_{18}$ cartridges even at pH 10 and eluted in two fractions by 50% and 80% methanol. These substances were named as Curvature-Enhancing Factor-1 (CEF-1) and Curvature-Enhancing Factor-2 (CEF-2), respectively. The CEF-2 was resolved on a reversed phase $C_{18}$ column by HPLC.

• Journal of Korean Neurosurgical Society
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• v.52 no.5
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• pp.447-451
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• 2012

Objective : To characterize the importance of the vertical angle of the sacral curvature (VASC) in lumbar disc herniations. Methods : Morphological data derived from lumbar sagittal MRI imaging. The statistical significance of the findings are discussed. The angles of 60 female patients with lumbar disc herniations (LDH) were compared with the 34 female patients without LDH. Results : 128 of the 185 patients met our inclusion criteria. The vertical angle of sacral curvature is statistically significantly bigger in females with lumbar disc herniations when compared to subjects in control group, 28.32 and 25.4, respectively. (p=0.034<0.05). Same difference was not seen in males. Conclusion : The vertical angle of sagittal sacral curvature may be another risk factor in females with lumbar disc herniations.

• 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.

• 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.

• 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.