• Title/Summary/Keyword: curvature equation

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An Experimental Study on the Flexural Stiffness and Plastic Hinge Ratation Capacity of Reinforced High Performance Concrete Beams (고성능 철근콘크리트 보의 휨강성 및 소성힌지의 회전능력에 관한 실험적 연구)

  • 고만영;김상우;김용부
    • Magazine of the Korea Concrete Institute
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    • v.10 no.4
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    • pp.93-100
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    • 1998
  • This paper presents a study on the flexural stiffness, plastic hinge length and plastic hinge rotation capacity of reinforced high performance concrete beams. 15 beams with different strength of concrete, reinforcement ratio and the pattern of loadings were tested. From the test results of reinforced normal strength concrete beams and reinforced high performance concrete beams with the concrete which has cylinder compressive strength of 700kg/${cm}^2$, slump value of 20~25cm and slump-flow value of 60~70cm. It is found that an extreme fiber concrete compressive strain of ${\varepsilon}_{cu}=0.0047$ may be used in ultimate curvature computations of reinforced high performance concrete beams. An empirical equation is proposed to estimate the effective moment of inertia. length and rotation capacity of plastic hinge of simply supported reinforced high performance concrete beams. The estimated deflections using this equation agree well with the experimental values.

Pipeline deformation caused by double curved shield tunnel in soil-rock composite stratum

  • Ning Jiao;Xing Wan;Jianwen Ding;Sai Zhang;Jinyu Liu
    • Geomechanics and Engineering
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    • v.36 no.2
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    • pp.131-143
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    • 2024
  • Shield tunneling construction commonly crosses underground pipelines in urban areas, resulting in soil loss and followed deformation of grounds and pipelines nearby, which may threaten the safe operation of shield tunneling. This paper investigated the pipeline deformation caused by double curved shield tunnels in soil-rock composite stratum in Nanjing, China. The stratum settlement equation was modified to consider the double shield tunneling. Moreover, a three dimensional finite element model was established to explore the effects of hard-layer ratio, tunnel curvature radius, pipeline buried depth and other influencing factors. The results indicate the subsequent shield tunnel would cause secondary disturbance to the soil around the preceding tunnel, resulting in increased pipeline and ground surface settlement above the preceding tunnel. The settlement and stress of the pipeline increased gradually as buried depth of the pipeline increased or the hard-layer ratio (the ratio of hard-rock layer thickness to shield tunnel diameter within the range of the tunnel face) decreased. The modified settlement calculation equation was consistent with the measured data, which can be applied to the settlement calculation of ground surface and pipeline settlement. The modified coefficients a and b ranged from 0.45 to 0.95 and 0.90 to 1.25, respectively. Moreover, the hard-layer ratio had the most significant influence on the pipeline settlement, but the tunnel curvature radius and the included angle between pipeline and tunnel axis played a dominant role in the scope of the pipeline settlement deformation.

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.

Prediction of Curvature Effects on the Electromagnetic Flowmeter Characteristics with Numerical Simulation (Laminar flow) (곡관의 곡률에 따른 전자기유량계 설치효과의 수치모사에 의한 특성 예측(충류))

  • Lim, Ki Won;Choi, Sang Kyu;Chung, Myung Kyoon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.11
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    • pp.1453-1463
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    • 1999
  • An electromagnetic flowmeter, based on a magnetic induction principle; provides an obstructionless flowmeter that essentially averages the velocity distribution over the pipe cross-sectional area. To predict the installation effects, the flowmeter installed near $90^{\circ}$ elbow is simulated by using a commercial code FLUENT(ver. 4.48) for the laminar flow field and a code developed through this study for magnetic field. The installation effects of the flowmeter are estimated by varying a number of the dependent parameters such as the radius of the elbow(Rc=1D, 1.5D, 2D, 3D), the location, Reynolds number and the direction of electrodes plane(${\varphi}$). It was found that all these factors affect the performance of the electromagnetic flowmeter significantly. The longer installation distance from the elbow is not always optimal to minimize the error, and also there exists an optimal location to install the EMF for a minimum error. Especially the flow signal with the electrodes plane direction of ${\varphi}=45^{\circ}$ is shown to yield smallest measurement error regardless of the Reynolds number and the curvature of elbow.

Deformation Characteristics of Compound Curved Plate Bending by Asymmetric Rollers (상하 비대칭 롤러를 이용한 이중곡면 성형의 변형특성에 대한 연구)

  • 최양렬;신종계
    • Journal of Ocean Engineering and Technology
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    • v.16 no.2
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    • pp.38-43
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    • 2002
  • Die-less forming is a cold forming process which is to bend thick flat plates into compound curved plates using two asymmetric rollers. This forming method has several advantages compared with line heating which is widely used to fabricate compound curved pieces in shipyards. The die-less forming, however, has scarcely been studied. Even the deformation mechanism in this forming process has not been understood clearly. So, in this paper, the deformation characteristics of die-less forming is investigated analytically and numerically. for the analytic investigation, slab method based on equilibrium equation is applied. And the mechanism of curvature generation is derived for the asymmetry in roller applied. And three dimensional numerical analyses are performed with realistic modeling of interactions between the rollers and work-piece using finite element program, ABAQUS. It is shown that curvature generation is mainly due to the difference of normal positive strain distribution between the top and bottom surface of the work-piece. And a convex-type curved plate is formed if the center region of the work-piece is rolled with asymmetric rollers of which the lower is larger than the upper in diameter.

Moment-Curvature Analysis of Steel Fiber-Reinforced Ultra High Performance Concrete Beams with Tension Softening Behavior (인장연화거동을 고려한 강섬유 보강 초고성능 콘크리트 보의 모멘트-곡률 해석)

  • Yang, In-Hwan;Joh, Chang-Bin;Kim, Byung-Suk
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.3
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    • pp.237-248
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    • 2011
  • Tensile softening characteristics play an important role in the structural behavior of steel fiber-reinforced ultra high performance concrete. Tension softening modeling and numerical analysis method are necessary for the prediction of structural performance of steel fiber-reinforced concrete. The numerical method to predict the flexural behavior is proposed in this study. Tension softening modeling is carried out by using crack equation based on fictitious crack and inverse analysis in which load-crack opening displacement relationship is considered. Thereafter material modeling is performed considering tension softening. The comparison of moment-curvature curves of the numerical analysis results with the test results indicates a reasonable agreement. Therefore, the present numerical results prove that good prediction of flexural behavior of steel fiber-reinforced ultra high performance concrete beams can be achieved by employing the proposed method.

Curvature Radius of Equivalent Lens Obtained by Recursive Numerical Solving of Gaussian Equations (재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산)

  • Lee, Kyu Haeng
    • Korean Journal of Optics and Photonics
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    • v.33 no.6
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    • pp.275-286
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    • 2022
  • As a first step in the optical design process, we derive a recursive numerical calculation method that can give a solution to the Gaussian equation that the paraxial rays satisfy. Given the refractive power, the angle of incidence to the first principal plane of the lens, the angle of exit to the second principal plane of the lens, and the distance between the principal planes, the radii of curvature of the front and back surfaces of a lens can be obtained by applying the recursive numerical calculation method proposed in this paper according to the thickness of the lens. If a module consists of two or more lenses, the thickness and radius of curvature of each lens can be similarly determined after selecting the distance between the principal planes of the lens under the condition of the design specification while increasing the number of lenses one by one.

A Study on Elastic Shear Buckling Coefficients of Horizontally Curved Plate Girder Web Panels (강곡선 플레이트거더 복부판의 전단좌굴계수에 관한 연구)

  • Lee, Doo-Sung;Lee, Sung-Chul
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.3A
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    • pp.367-373
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    • 2008
  • In the design of horizontally curved plate girder web panels, it is required to evaluate accurately the elastic buckling strength under pure shear. Currently, elastic shear buckling coefficients of curved web panels stiffened by transverse intermediate stiffeners are determined by assuming conservatively that straight web panels without curvature are simply supported at the juncture between the flange and web. However, depending upon the geometry and the properties of the curved plate girder, the elastically restrained support may behave rather closer to a fixed support. The buckling strength of curved girder web is much greater (maximum 38%) than that of a straight girder calculated under the assumption that all four edges are simply supported in Lee and Yoo (1999). In the present study, a series of numerical analyses based on a 3D finite element modeling is carried out to investigate the effects of geometric parameters on both the boundary condition at the juncture and the horizontal curvature of web panel, and the resulting data are quantified in a simple design equation.

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.

Flexural Strength of Composite HSB Girders in Positive Moment (HSB 강합성거더 정모멘트부의 휨저항강도)

  • Cho, Eun-Young;Shin, Dong-Ku
    • Journal of Korean Society of Steel Construction
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    • v.22 no.4
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    • pp.389-398
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    • 2010
  • The flexural strength of composite HSB I-girders under a positive moment was investigated using the moment-curvature analysis method to evaluate the applicability of the current AASHTO LRFD design specifications to such girders. A total of 2,391 composite I-girder sections that satisfied the section proportion limits of the AASHTO LRFD specifications was generated by the random sampling technique to consider a wide range of section properties. The flexural capacities of the sections were calculated inthe nonlinear moment-curvature analysis in which the HSB600 and HSB800 steels were modeled as an elasto-plastic strain-hardening material, and the concrete, as a CEB-FIP model. The effects of the ductility ratio and the compressive strength of the concrete slab on the flexural strength of the composite girders made of HSB and SM520-TMC steels were analyzed. The numerical results indicated that the current AASHTO LRFD equation can be used to calculate the flexural strength of composite girders made of HSB600 steel. In contrast, the current AASHTO LRFD equation was found to be non-conservative in its prediction of the flexural strength of composite HSB800 girders. Based on the numerical results of this study for 2,391 girders, a new design equation for the flexural strength of composite HSB800 girders in a positive moment was proposed.