• Title/Summary/Keyword: Curvature linear equation

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Relationship between Curvature Ductility and Displacement Ductility of RC Bridge Circular Columns (철근콘크리트 원형교각의 연성도 상관관계에 관한 연구)

  • 손혁수;조재원;이재훈
    • Proceedings of the Korea Concrete Institute Conference
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    • 2002.10a
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    • pp.111-116
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    • 2002
  • The flexural ductility capacity of reinforced concrete columns can be expressed either in terms of curvature ductility or displacement ductility. To evaluate ductility capacity of reinforced concrete columns, analytical models and a non-linear analysis program, NARCC have been developed, which is applicable to the RC columns subjected to seismic loading. The analytical results by using computer program NARCC are in good agreement with the test results. In order to develop relationships between the curvature ductility and the displacement ductility, the analysis for total 21,600 RC circular columns using the computer program NARCC have been carried out for parametric studies. Based on the results from the parametric studies, a correlation equation between the curvature ductility and the displacement ductility was developed.

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The Study about Measuring Method in Radius of Eyeglasses Lens Curvature by using Keratometer (각막곡률계를 이용한 안경렌즈 곡률반경 측정방법에 관한 연구)

  • Cha, Jung Won
    • Journal of Korean Ophthalmic Optics Society
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    • v.17 no.2
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    • pp.127-133
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    • 2012
  • Perpose: The aim of this study is to investigate the measuring method in radius of eyeglasses lens curvature by using keratometer in noncontact method. Methods: A trial lens for vision test in diopter range from -9.00 D to -11.50 D were attached in front part of keratometer, after that we set eyeglasses lens at the place where eyeglasses lens is apart about 25 cm from front position of keratometer. We measured the radius of curvature from observation of clear mire image while the position of eyeglasses lens is changed in a small quantity. After that, we made some formulas for compensation of radius of curvature by using spherometer. Results: The radius of curvature was successfully measured by keratometer with trial lens in front part of it. The measured radius of curvature was changed to compensation value using spherometer data, and the 5 kind of linear equation to make compensation value was made. Any kind of lenses measured by using keratometer that trial lens was attached in front part of it, after that it was confirmed that the result of calculation from line equation is exact in error ratio below 3.5%. Conclusions: It was confirmed that radius of eyeglasses lens curvature can be measured by using keratometer by noncontact method, and the accuracy is higher than "lens measure".

Modeling for the Natural Vibration Analysis of a Rotating Thick Ring (회전하는 두꺼운 링의 고유진동 해석을 위한 모델링)

  • Kim, Chang-Boo;Kim, Bo-Yeon
    • Proceedings of the KSR Conference
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    • 2007.11a
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    • pp.107-114
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    • 2007
  • In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

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Nonlinear Moment-Curvature Relations and Numerical Structural Analysis of High-Strength PSC Flexural Members (고강도 PSC 휨부재의 비선형 모멘트-곡률 관계와 전산구조해석)

  • 연정흠;이제일
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.1
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    • pp.95-104
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    • 2002
  • A methods to calculate non-linear moment-curvature relations of high-strength PSC flexural members for numerical analysis has been proposed. The moment-curvature relations were calculated with assumptions of design codes and by the layer method. The results of the proposed procedures for moment-curvature relations and numerical analysis were compared with those of pre-existing tests. The absorption energy rate of the design codes was about 30% larger than that of the layer method. The ultimate load and the external work of the layer method were 90% and 85% of those of tests, respectively The ultimate load of the strength design method was 97% of that of tests, but the external work was over-estimated with 122%. The ultimate load and external work by the proposed equation of the CEB-FIP Model Code were 113% and 173% of those of tests, respectively. It show that the use of ultimate strain of 0.0035 should be over-estimated for high-strength concrete. The procedure of non-linear numerical analysis of this research could be stably simulated the behavior of concrete flexural members until the ultimate state, and calculate results of the load-deflection relation and cracking pattern were very similar with those of tests.

New Seismic Design Concept for RC Bridge Columns

  • Lee, Jae-Hoon;Son, Hyeok-Soo
    • Proceedings of the Korea Concrete Institute Conference
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    • 2003.05a
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    • pp.204-209
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    • 2003
  • The purpose of this study is to develop new seismic design concept based on ductility demand for reinforced concrete bridge columns in areas of low to moderate seismicity. In developing the ductility based design approach, relationship between ductility demand and transverse reinforcement demand should be quantitatively developed. To evaluate ductility capacity of reinforced concrete columns, analytical models and a non-linear analysis program, NARCC have been developed. Based on analytical and experimental results, an equation for relationship between curvature ductility and displacement ductility, an equation for designing the transverse confinement reinforcement for ductility demand, and a new seismic design concept of RC bridge columns are presented.

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FE Based Numerical Model to Consider Bond-slip Effect in Composite Beams (합성보의 부착슬립 효과를 고려한 유한요소 기반의 수치해석모델)

  • Kwak, Hyo-Gyoung;Hwang, Jin-Wook
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.1
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    • pp.95-110
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    • 2010
  • A numerical model to simulate bond-slip behavior of composite beam bridges is introduced in this paper. Assuming a linear bond stress-slip relation along the interface between the slab and girder, the slip behavior is implemented into a finite element formulation. Adopting the introduced model, the slip behavior can be taken account even in a beam element which is composed of both end nodes only. Governing equation of the slip behavior, based on the linear partial interaction theory, can be determined from the force equilibrium and a constant curvature distribution across the section of a composite beam. Since the governing equation for the slip behavior requires the moment values at both end nodes, the piecewise linear distribution of the constant bending moment in an element is assumed. Analysis results by the model are compared with numerical results and experimental values, and load-displacement relations of composite beams were then evaluated to verify the validity of the proposed model.

Wave load resistance of high strength concrete slender column subjected to eccentric compression

  • Jayakumar, M.;Rangan, B.V.
    • Structural Engineering and Mechanics
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    • v.50 no.3
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    • pp.287-304
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    • 2014
  • A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

Statistical Study on Correlation Between Design Variable and Shape Error in Flexible Stretch Forming (가변스트레치성형 설계변수와 성형오차의 상관관계에 대한 통계적 연구)

  • Seo, Y.H.;Heo, S.C.;Kang, B.S.;Kim, J.
    • Transactions of Materials Processing
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    • v.20 no.2
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    • pp.124-131
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    • 2011
  • A flexible stretch forming process is useful for small quantity batch production because various shape changes of the flexible die can be achieved conveniently. In this study, the design variables, namely, the punch size, curvature radius and elastic pad thickness, were quantitatively evaluated to understand their influence on sheet formability using statistical methods such as the correlation and regression analyses. Forming simulations were designed and conducted by a three-way factorial design to obtain numerical values of a shape error. Linear relationships between the design variables and the shape error resulted from the Pearson correlation analysis. Subsequently, a regression analysis was also conducted between the design variables and the shape error. A regression equation was derived and used in the flexible die design stage to estimate the shape error.

Free vibrations of inclined arches using finite elements

  • Chucheepsakul, Somchai;Saetiew, Wasuroot
    • Structural Engineering and Mechanics
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    • v.13 no.6
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    • pp.713-730
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    • 2002
  • This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).