• 제목/요약/키워드: Equivalent stress and strain

검색결과 256건 처리시간 0.023초

Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar

  • Torres, Lluis;Barris, Cristina;Kaklauskas, Gintaris;Gribniak, Viktor
    • Structural Engineering and Mechanics
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    • 제53권5호
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    • pp.997-1016
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    • 2015
  • The contribution of tensioned concrete between cracks (tension-stiffening) cannot be ignored when analysing deformation of reinforced concrete elements. The tension-stiffening effect is crucial when it comes to adequately estimating the load-deformation response of steel reinforced concrete and the more recently appeared fibre reinforced polymer (FRP) reinforced concrete. This paper presents a unified methodology for numerical modelling of the tension-stiffening effect in steel as well as FRP reinforced flexural members using the concept of equivalent deformation modulus and the smeared crack approach to obtain a modified stress-strain relation of the reinforcement. A closed-form solution for the equivalent secant modulus of deformation of the tensioned reinforcement is proposed for rectangular sections taking the Eurocode 2 curvature prediction technique as the reference. Using equations based on general principles of structural mechanics, the main influencing parameters are obtained. It is found that the ratio between the equivalent stiffness and the initial stiffness basically depends on the product of the modular ratio and reinforcement ratio ($n{\rho}$), the effective-to-total depth ratio (d/h), and the level of loading. The proposed methodology is adequate for numerical modelling of tension-stiffening for different FRP and steel reinforcement, under both service and ultimate conditions. Comparison of the predicted and experimental data obtained by the authors indicates that the proposed methodology is capable to adequately model the tension-stiffening effect in beams reinforced with FRP or steel bars within wide range of loading.

유한요소법과 샤피충격시험기에 의한 노치각도에 따른 나일론 열가소성 플라스틱 재료의 파괴특성 (Dynamic Fracture Properties of Nylon Thermoplastic Material Depending on Notch Angle with Charpy Impact Machine and Finite Element Method)

  • 박명균;이중원;김태옥
    • 한국가스학회지
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    • 제12권1호
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    • pp.1-6
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    • 2008
  • 샤피충격시험은 동적하중 하에 있는 고분자 재료의 거동을 이해하는데 가장 널리 사용되고 있는 방법이다. 본 연구에서는 샤피충격시험장치에서 얻어지는 파단에너지를 사용하여 나일론 소재 샤피 시편의 노치각도에 따른 에너지 해방율을 구하는 방법을 제시하였다. 또한 샤피충격시험장치를 계장화하여 최대 하중과 파단 시까지 소요되는 에너지 등의 파손인자들을 산출하였다. 그리고 노치각도에 따른 동적파괴 인성치와 유한요소법을 사용하여 중앙집중 하중 하에서 사피 시편의 노치각도에 따른 응력분포를 산출하였다.

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Thermal buckling properties of zigzag single-walled carbon nanotubes using a refined nonlocal model

  • Semmah, Abdelwahed;Beg, O. Anwar;Mahmoud, S.R.;Heireche, Houari;Tounsi, Abdelouahed
    • Advances in materials Research
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    • 제3권2호
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    • pp.77-89
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    • 2014
  • In the present article, the thermal buckling of zigzag single-walled carbon nanotubes (SWCNTs) is studied using a nonlocal refined shear deformation beam theory and Von-Karman geometric nonlinearity. The model developed simulates both small scale effects and higher-order variation of transverse shear strain through the depth of the nanobeam. Furthermore the present formulation also accommodates stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. The equivalent Young's modulus and shear modulus for zigzag SWCNTs are derived using an energy-equivalent model. The present study illustrates that the thermal buckling properties of SWCNTs are strongly dependent on the scale effect and additionally on the chirality of zigzag carbon nanotube. Some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed.

복합체에 대한 연속체 방정식 및 유한요소 프로그램의 개발 (Development of Continuum Equations and Finite Element Method Program for Composite Systems)

  • 임종균;박문호
    • 대한토목학회논문집
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    • 제8권2호
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    • pp.155-166
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    • 1988
  • 본 연구는 복합체의 단부영향을 고려한 등각균등질, 이방성의 모델개발과 이에따른 유한요소해석 프로그램 개발에 중점을 두었다. 복합체는 2차원의 수평층을 가지며 선형, 탄성, 작은변형에 제한을 두었다. 본 연구에서 개발된 등가 균등질의 이론은 복합체의 전반적인 거동을 포함시킴은 물론 층과 수직인 경계면과 그 부근에 형성되는 단부의 영향과 층의 경계면에 생기는 응력집중 현상을 나타낼 수 있게 하였다. 이론개발에 있어 1차변수는 $C_0$연속의 유한요소 근사치를 가지도록 하였으며 이를위해 최고 1차의 미분치가 변형에너지에 나타나도록 변수를 택하였다. 결과적으로 유한요소해석은 매우 간단하고 경제적이었으며 이들의 정당성과 정확도를 입증하기위하여 여러하중 조건하의 복합체를 풀이하였다.

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크리프 물성 평가를 위한 소형 펀치 크리프 해석 (Small Punch Creep Behavior Analysis for Assessment of Creep Properties)

  • 임지우;김범준;김문기;임병수
    • 대한금속재료학회지
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    • 제48권11호
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    • pp.965-973
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    • 2010
  • The small punch creep (SPC) test has recently received much attention as a new alternative to the conventional uniaxial creep test because it needs only a miniature-sized specimen directly detached from an operating system or component without any serious sampling damages. However, it is difficult to obtain the equivalent uniaxial creep data directly from the SPC data. As a specimen is deformed by a punch in the SPC test, the test result is sensitive to the friction between them. Finite element analyses with various friction coefficients was performed and showed a tendency of increased SPC life with an increased friction coefficient. The necking position predicted by the SPC simulation with a proper friction coefficient showed good agreement with that observed from the real SPC test. Finally, a noble method to convert the SPC load and displacement rate into the equivalent uniaxial creep stress and strain rate, respectively, was established in this study.

Numerical study of mono-strand anchorage mechanism under service load

  • Marceau, D.;Fafard, M.;Bastien, J.
    • Structural Engineering and Mechanics
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    • 제18권4호
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    • pp.475-491
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    • 2004
  • Anchorage devices play an important role in post-tensioned bridge structures since they must sustain heavy loads in order to permit the transfer of the prestressing force to the structure. In external prestressing, the situation is even more critical since the anchorage mechanisms, with the deviators, are the only links between the structure and the tendons throughout the service life of the structure. The behaviour of anchorage devise may be studied by using the finite element method. To do so, each component of the anchorage must be adequately represented in order to approximate the anchor mechanism as accurately as possible. In particular, the modelling of the jaw/tendon device may be carried out using the real geometry of these two components with an appropriate constitutive contact law or by replacing these components by a single equivalent. This paper presents the numerical study of a mono-strand anchorage device. The results of a comparison between two different representations of the jaw/tendon device, either as two distinct components or as a single equivalent, will be examined. In the double-component setup, the influence of the wedge configuration composing the jaw, and the influence of lubrication of the anchor, will be assessed.

GFRP 보강 철근 폴리머 콘크리트 T형 보의 휨 특성 (Flexural Characteristics of Reinforced Polymer Concrete T-Beams Strengthened with GFRP)

  • 김남길;황해근;연정흠
    • 콘크리트학회논문집
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    • 제24권5호
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    • pp.585-596
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    • 2012
  • 이 연구는 교량이나 주차장 건물 등에 적용이 가능한 GFRP 보강 철근 폴리머 콘크리트 T형 보의 휨 특성에 관한 연구로서 GFRP 보강 수준에 따른 압축파괴(compression failure: CF), 인장파괴(tension failure: TF) 및 GFRP 보강재의 파괴(fiber sheet failure: FF) 등 파괴모드의 판단과 결정방법을 제시하고, 파괴모드별 설계휨강도 산정식을 제시하였다. GFRP 보강 철근콘크리트 보에서는 FF, TF, CF 등 3가지 파괴모드 중에서 철근항복 ${\rightarrow}$ GFRP 파단 ${\rightarrow}$ 압축측 콘크리트 파괴의 순으로 진행되는 FF 파괴모드가 가장 이상적이다. FF 파괴모드의 경우 압축측 폴리머 콘크리트가 극한변형률(${\varepsilon}_{cu}$)에 도달하기 전에 GFRP가 먼저 파단되므로 콘크리트의 극한상태를 기반으로 하는 기존의 등가직사각형 응력블럭의 개념을 적용할 수 없다. 따라서 이 연구에서는 폴리머 콘크리트의 특성에 부합되는 이상화된 폴리머 콘크리트의 압축응력-변형률 곡선을 제안하고, 폴리머 콘크리트의 변형률을 기반으로 하여 응력블럭 매개변수 ${\alpha}$, ${\beta}$를 도출하였다. 또한 T형 보의 형상비에 따른의 압축응력 분포 및 설계휨강도 특성을 규명하고 적정한 형상비를 2.5로 제시하였으며, GFRP 보강재의 두께 및 높이에 따른 설계휨강도 산정식을 제시하고 그 식의 적정성을 실험과 이론해석에 의해 입증하였다.

디지털 이미지 상관법을 이용한 Methacrylate기질과 Silorane기질 복합레진의 치아 수복 시 중합수축거동 (Polymerization Shrinkage Behavior Measured by Digital Image Correlation for Methacrylate-based and Silorane-based Composites During Dental Restoration)

  • 박정훈;최낙삼
    • Composites Research
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    • 제33권3호
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    • pp.125-132
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    • 2020
  • 치과용 복합레진 Filtek P90 (3M ESPE, USA)과 Clearfil AP-X (Kuraray, Japan)를 대상으로 디지털 이미지 상관법을 이용하여 광중합 시 발생하는 수축거동을 관찰하고 등가탄성계수를 적용한 유한요소해석을 통해 시편표면의 응력분포를 산출하여 수축률분포와 비교하였다. 광조사 중과 광조사 후의 촬영 조건을 달리하여 CCD 카메라를 이용한 시편의 변형사진을 획득하고 디지털 이미지 상관분석을 하였다. DIC 분석 결과 상기의 복합레진 모두에서, 비균일한 수축변형률 분포가 관찰되었으며 링시편 내부의 레진 중심부가 자유로운 유동성으로 레진/링의 계면부보다 큰 수축 변형률이 발생하였다. 레진의 중심으로부터 거리가 멀어질수록 반경방향 평균수축률은 감소하였으며, 광조사동안에 발생한 반경방향 평균수축률은 경화시험종료(10 min) 후 발생한 반경방향 평균수축률 값을 기준으로 P90은 33%, AP-X는 57% 수준이었다. P90과 AP-X가 광조사 중의 수축거동이 크게 달랐음을 확인하였다. 레진/링의 계면부에 가까운 레진에서는 광조사 후에 인장변형률이 급격히 커져서 계면부가 인장응력을 받아 취약하게 됨을 확인하였다.

Design of geocell reinforcement for supporting embankments on soft ground

  • Latha, G. Madhavi
    • Geomechanics and Engineering
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    • 제3권2호
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    • pp.117-130
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    • 2011
  • The methods of design available for geocell-supported embankments are very few. Two of the earlier methods are considered in this paper and a third method is proposed and compared with them. In the first method called slip line method, plastic bearing failure of the soil was assumed and the additional resistance due to geocell layer is calculated using a non-symmetric slip line field in the soft foundation soil. In the second method based on slope stability analysis, general-purpose slope stability program was used to design the geocell mattress of required strength for embankment. In the third method proposed in this paper, geocell reinforcement is designed based on the plane strain finite element analysis of embankments. The geocell layer is modelled as an equivalent composite layer with modified strength and stiffness values. The strength and dimensions of geocell layer is estimated for the required bearing capacity or permissible deformations. These three design methods are compared through a design example. It is observed that the design method based on finite element simulations is most comprehensive because it addresses the issue of permissible deformations and also gives complete stress, deformation and strain behaviour of the embankment under given loading conditions.

강체요소법(剛體要素法)에 의한 보강판(補剛板)의 붕괴해석(崩壞解析) (Collapse Analysis of Stiffened Plates by Rigid Element Method)

  • 임상전;장창두;김남철
    • 대한조선학회지
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    • 제25권4호
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    • pp.47-57
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    • 1988
  • A new discrete method using idealized rigid body-spring model is introduced. This rigid element method is known to be more efficient and accurate than the finite element method in the inelastic range of structural analysis owing to simplified stress-strain and strain-displacement relations This kind of physical concept using idealized rigid model has been already applied among structural engineers to some problems such as rigid-plastic analysis or plastic design considering rigid bodies and plastic hinges. However the most rigorous and systematic research has been recently performed by T. Kawai et al.[1]. In this paper, an attempt is made to analyze the collapse behavior of stiffened plates under lateral loading by some modification and expansion of Kawai's rigid element approach to the collapse of plates without stiffener. Stiffened plates are treated as orthotropic plates which have equivalent bending rigidities. By employing Morley's plate element resubdivision technique, variety is given to mesh-division styles which have greate effect on the accuracy of numerical results. Some examples are shown to verify the validity of applying rigid element method to the ultimate strength analysis of stiffened plates. It is clarified that lateral deflections and detailed collapse patterns up to the ultimate state of stiffened plates can be easily obtained by the present approach.

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