• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.2
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• pp.287-297
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• 2015

In concrete structural design provisons, there is a minimum allowable strain of steel to ensure a ductility of RC members and a c/d is limited for the same purpose in EC2. In general, a ductility capacity of RC members is evaluated by a displacement ductility which is a ratio of ultimate displacement to yield displacement, and it is necessary to calculate accurately a yield displacement and an ultimate displacement to evaluate a displacement ductility. But a displacement in members is affected by various member characteristics, so it is hard to calculate a displacement exactly. In this study, a displacement ductility is calculated by calculating a yield displacement and an ultimate displacement through a moment-curvature relationship. The main variables examined are concrete strength, yield strength, steel ratio, spacing of confinement, axial force ratio and concrete ultimate strain. As results, as a concrete strength is increased, a ductility displacement is increased. But as yield strength, steel ratio, spacing of confinement and axial force ratio are increased, a displacement ductility is decreased. And a displacement ductility is necessary to calculate a response modification factor (R) of columns for seismic design, so it is appeared that it is important to calculate a displacement ductility more accurately.

• Earthquakes and Structures
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• v.4 no.4
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• pp.365-381
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• 2013

In this paper, a numerical simulation study was conducted on the seismic behavior and ductility demand of single-degree-of-freedom (SDOF) systems with partially self-centering hysteresis. Unlike fully self-centering systems, partially self-centering systems display noticeable residual displacement after unloading is completed. Such partially self-centering behavior has been observed in a number of recently researched self-centering structural systems with energy dissipation devices. It is thus of interest to examine the seismic performance such as ductility demand of partially self-centering systems. In this study, a modified flag-shaped hysteresis model with residual displacement is proposed to represent the hysteretic behavior of partially self-centering structural systems. A parametric study considering the effect of variations in post-yield stiffness ratio, energy dissipation coefficient, and residual displacement ratio on the displacement ductility demand of partially self-centering systems was conducted using a suite of 192 scaled ground motions. The results of this parametric study reveal that increasing the post-yield stiffness, energy dissipation coefficient or residual displacement ratio of the partially self-centering systems generally leads to reduced ductility demand, especially for systems with lower yield strength.

• 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.45 no.5
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• pp.655-676
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• 2013

In this study, strength reduction factors and inelastic displacement ratios are investigated for SDOF systems with period range of 0.1-3.0 s considering soil structure interaction for earthquake motions recorded on soft soil. The effect of stiffness degradation on strength reduction factors and inelastic displacement ratios is investigated. The modified-Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. The effect of negative strain - hardening on the inelastic displacement and strength of structures is also investigated. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. New equations are proposed for strength reduction factor and inelastic displacement ratio of interacting system as a function of structural period($\tilde{T}$, T) ductility (${\mu}$) and period lengthening ratio ($\tilde{T}$/T).

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.683-701
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• 2011

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system ($\tilde{C}_R$) as a function of structural period of interacting system ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}/T$). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• 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 $650kg/\textrm{cm}^2$.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.2
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• pp.39-48
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• 2003

This paper present a summary of the results of statistical study of the ductility factor which is key component of response modification factor(R). To compute the ductility factor, a group of 1,860 ground motions recorded from various earthquake was considered. Based on the local site conditions at the recording station, ground motions were classified into four groups according to average shear wave velocity. Inleastic spectrum were computed for elastic perfectly plastic SDOF systems undergoing different level of inelastic deformation and period. Ductility factors were calculated by deviding elastic response spectrum by inelastic response spectrum. The influence f displacement ductility ratio, site condition, magnitude and epicentral distance on ductility factors were studied. The coefficient of variation was computed to evaluated the dispersion of ductility factors as the defined ratio of the standard deviation to the mean.

• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• 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.

• Earthquakes and Structures
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• v.7 no.4
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• pp.463-484
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• 2014

Solid piers with a rounded rectangular cross-section are widely used in railway bridges for high-speed trains in China. Compared to highway bridge piers, these railway bridge piers have a larger crosssection and less steel reinforcement. Existing material models cannot accurately predict the seismic behavior of this kind of railway bridge piers. This is because only a few parameters, such as axial load, longitudinal and transverse reinforcement, are taken into account. To enable a better understanding of the seismic behavior of this type of bridge pier, a simultaneous influence of the various parameters, i.e. ratio of height to thickness, axial load to concrete compressive strength ratio and longitudinal to transverse reinforcements, on the failure characteristics, hysteresis, skeleton curves, and displacement ductility were investigated. In total, nine model piers were tested under cyclic loading. The hysteretic response obtained from the experiments is compared with that obtained from numerical studies using existing material models. The experimental data shows that the hysteresis curves have significantly pinched characteristics that are associated with small longitudinal reinforcement ratios. The displacement ductility reduces with an increase in ratio of axial load to concrete compressive strength and longitudinal reinforcement ratio. The experimental results are largely in agreement with the numerical results obtained using Chang-Mander concrete model.