• 제목/요약/키워드: elastic modulus equation

검색결과 143건 처리시간 0.025초

서울·경기지역 화강암의 탄성파속도와 탄성계수에 의한 암석의 일축압축강도와의 상관성 연구 (A Study on the Correlation between Uniaxial Compressive Strength of Rock by Elastic Wave Velocity and Elastic Modulus of Granite in Seoul and Gyeonggi Region)

  • 손인환;김병국;이벽규;장승진;이수곤
    • 한국재난정보학회 논문집
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    • 제15권2호
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    • pp.249-258
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    • 2019
  • 연구목적: 본 연구에서는 서울 경기지역의 화강암을 대상으로 시추조사 시 채취된 암석 시료에서 측정된 물리적 특성 중 탄성파속도와 탄성계수로부터 암석의 일축압축강도와의 상관성을 분석하여 암석의 일축압축강도를 추정하는 것을 목적으로 한다. 연구방법: 119개의 화강암 시추 코아 시료를 대상으로 탄성파 속도와 탄성계수 그리고 일축압축강도와의 상관관계를 도출하기 위하여 실내 암석 실험을 실시하였다. 연구결과: 화강암에 대하여 탄성파속도와 일축압축강도 그리고 탄성계수와의 상호 관계를 단순회귀와 다중회귀로 분석한 결과는 전반적으로 관계식에 나타난 것처럼 신뢰도가 낮음을 확인하였다. 이는 화강암의 구성 입자가 균질하지 못하여 탄성파속도와 탄성계수를 이용한 압축강도 추정에 대한 활용성이 낮은 원인으로 사료된다. 결론: 본 연구에서 암석의 탄성파속도와 탄성계수로부터 일축압축강도를 추정하기 위한 상관관계를 분석하기 위하여 단순회귀분석과 다중회귀분석 방법을 이용하였다. 단순회귀분석은 결정계수($R^2$)가 0.61~0.67 이었으며, 다중회귀분석은 0.71로 나타났다. 따라서 다중회귀분석을 이용하여 암석의 일축압축강도를 추정할 때 다소 신뢰성이 높아질 수 있다. 또한, 향후 탄성파 속도와 탄성계수를 이용한 암석의 일축압축강도를 추정할 때 다양한 통계분석 기법(회귀분석, 인공신경망, 빅데이터 분석 등)을 활용하면 보다 신뢰성이 높은 결과를 얻을 수 있을 것으로 본다.

Ultrasound Attenuation in the Assessment of Bone Mineral Density and Elastic Modulus of Human Trabecular Bone

  • Han, S.M.;Kim, M.S.
    • 대한의용생체공학회:의공학회지
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    • 제19권2호
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    • pp.171-176
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    • 1998
  • 본 연구에서는 뼈의 특성을 파악하는 초음파감쇠 파라미터를 재평가하였다. 초음파 속도, 특정 주파수(0.5MHz)에서의 초음파감쇠 및 광역 밴드 초음파감쇠와 같은 초음파 파라미터들을 해면골 입방체 시편의 세 직교방향(전/후, 내/외, 상/하)에서 측정하였다. 그리고 컴퓨터 영상장치를 사용하여 골밀도를 측정했으며, 골 시편의 무게와 부피를 이용하여 외형밀도도 함께얻었다. 이와같이 구해진 외형밀도와 초음파 속도로부터 초음파 탄성영률을 계산하였다. 주파수 0.5MHz에서의 초음파감쇠와 광역밴드감쇠는 골밀도 및 세 직교방향의 초음파 영률과 서로 관련시켜 연관성을 조사하였다. 그 결과 특정 주파수 초음파감쇠가 골밀도 및 탄성영률을 평가하는 능력에 있어서 광역밴드 감쇠보다 우수함을 알 수 있었다. 따라서 광역밴드 초음파감쇠를 측정하여 골의 상태를 평가하는 형행 초음파 진단 기법이 재검토 되어야 하며 본 연구에서 증명된 특정주파수(0.5MHz) 초음파감쇠를 이용하여 골 다공증 진단 예측율을 향상시킬 수 있다.

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콘크리트의 초기재령특성을 고려한 합성형 휨 부재의 유한요소 거동해석 (Finite Element Analysis of Flexural Composite Members Considering Early-Age Concrete Properties)

  • 강병수;주영태;신동훈;이용학
    • 한국콘크리트학회:학술대회논문집
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    • 한국콘크리트학회 2003년도 봄 학술발표회 논문집
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    • pp.463-468
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    • 2003
  • A finite element formulation to predict the flexural behavior of composite girder is presented in which the early-age properties of concrete are specified including maturing of elastic modulus, creep and shrinkage. The time dependent constitutive relation accounting for the early-age concrete properties is derived in an incremental format by expanding the total form of stress-strain relation by the first order Taylor series with respect to the reference time. The total potential energy of the flexural composite member is minimized to derive the time dependent finite element equilibrium equation. Numerical applications are made for the 3-span double composite steel box girders which is a composite bridge girder filled with concrete at the bottom of the steel box in the negative moment region. The numerical analysis with considering the variation of concrete elastic modulus are performed to investigate the effect of it on the early-age behavior of composite structures. The one dimensional finite element analysis results are compared with the analytical method based on the sectional analysis. Close agreement is observed among the two methods.

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Prediction model for the hydration properties of concrete

  • Chu, Inyeop;Amin, Muhammad Nasir;Kim, Jin-Keun
    • Computers and Concrete
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    • 제12권4호
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    • pp.377-392
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    • 2013
  • This paper investigates prediction models estimating the hydration properties of concrete, such as the compressive strength, the splitting tensile strength, the elastic modulus,and the autogenous shrinkage. A prediction model is suggested on the basis of an equation that is formulated to predict the compressive strength. Based on the assumption that the apparent activation energy is a characteristic property of concrete, a prediction model for the compressive strength is applied to hydration-related properties. The hydration properties predicted by the model are compared with experimental results, and it is concluded that the prediction model properly estimates the splitting tensile strength, elastic modulus, and autogenous shrinkage as well as the compressive strength of concrete.

Use of waste glass as coarse aggregate in concrete: mechanical properties

  • Yan, Lan-lan;Liang, Jiong-Feng
    • Advances in concrete construction
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    • 제8권1호
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    • pp.1-7
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    • 2019
  • The possibility of using recycled coarse glass aggregates as a substitute for natural crushed stone are relatively limited. In order to promote it for engineering application, this paper reports the effect of coarse glass aggregate on mechanical behavior of concrete. The coarse aggregates are substituted for coarse glass aggregate (CGA) as 0%,20%,40%,60%,80% and 100%.The results show that increasing the coarse glass aggregate content cause decrease in compressive strength, the elastic modulus, the splitting tensile strength, the flexural strength. An equation is presented to generate the relationship between cube compressive strength and prism compressive strength, the relationship between cube compressive strength and elastic modulus, the relationship between cube compressive strength and splitting tensile strength, the relationship between cube compressive strength and flexural strength of coarse glass concrete.

On the receding contact between a two-layer inhomogeneous laminate and a half-plane

  • Liu, Zhixin;Yan, Jie;Mi, Changwen
    • Structural Engineering and Mechanics
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    • 제66권3호
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    • pp.329-341
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    • 2018
  • This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

횡등방성 암석에서 겉보기 탄성정수의 방향성 변화와 탄성정수 제약조건 (Directional Variation of Apparent Elastic Constants and Associated Constraints on Elastic Constants in Transversely Isotropic Rocks)

  • 이연규
    • 터널과지하공간
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    • 제33권3호
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    • pp.150-168
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    • 2023
  • 암석의 이방성 거동은 조암광물들의 방향성 배열과 미세균열의 분포 특성이 주된 원인이다. 특히, 퇴적암과 변성암은 횡등방성 강도 및 변형 특성을 또렷이 나타내는 경우가 많다. 그러므로 암석역학적 설계과정에서는 횡등방성 암석의 변형 및 파괴 특성을 정확하게 이해하는 것이 중요하다. 횡등방성 암석의 변형은 실내시험을 통해 측정할 수 있는 5개의 독립된 탄성정수를 이용하여 기술된다. 이 연구에서는 문헌에 보고된 실험자료를 이용하여 횡등방성 암석의 겉보기 탄성정수의 방향성 변화 특성을 분석하였다. 임의 방향으로 회전된 직각좌표계에서 겉보기 탄성정수 값을 효율적이고 체계적으로 계산하기 위해 Mehrabadi & Cowin의 구성방정식을 도입하였다. 문헌에 보고된 4개 횡등방성 암석을 선택하여 연약면의 방향 변화가 겉보기 탄성계수, 겉보기 전단 탄성계수, 겉보기 포아송비의 변화에 미치는 영향을 분석하였다. 이러한 분석 결과를 바탕으로 새로운 탄성정수 제약 조건식을 제안하였다. 제안한 제약 조건식을 만족하면 횡등방성 암석에서 겉보기 탄성정수의 방향성 변화는 직관적으로 예측되는 경향과 일치하게 된다.

Influence of time-dependency on elastic rock properties under constant load and its effect on tunnel stability

  • Aksoy, C.O.;Aksoy, G.G. Uyar;Guney, A.;Ozacar, V.;Yaman, H.E.
    • Geomechanics and Engineering
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    • 제20권1호
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    • pp.1-7
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    • 2020
  • In structures excavated in rock mass, load progressively increases to a level and remains constant during the construction. Rocks display different elastic properties such as Ei and ʋ under different loading conditions and this requires to use the true values of elastic properties for the design of safe structures in rock. Also, rocks will undergo horizontal and vertical deformations depending on the amount of load applied. However, under constant loads, values of Ei and ʋ will vary in time and induce variations in the behavior of the rock mass. In some empirical equations in which deformation modulus of the rock mass is taken into consideration, elastic parameters of intact rock become functions in the equation. Hence, the use of time dependent elastic properties determined under constant loading will yield more reliable results than when only constant elastic properties are used. As well known, rock material will play an important role in the deformation mechanism since the discontinuities will be closed due to the load. In this study, Ei and ʋ values of intact rocks were investigated under different constant loads for certain rocks with high deformation capabilities. The results indicated significant time dependent variations in elastic properties under constant loading conditions. Ei value obtained from deformability test was found to be higher than the Ei value obtained from the constant loading test. This implies that when static values of elastic properties are used, the material is defined as more elastic than the rock material itself. In fact, Ei and ʋ values embedded in empirical equations are not static. Hence, this workattempts to emerge a new understanding in designing of safer structures in rock mass by numerical methods. The use of time-dependent values of Ei and ʋ under different constant loads will yield more accurate results in numerical modeling analysis.

Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation

  • Mohamed, Nazira;Eltaher, Mohamed A.;Mohamed, Salwa A.;Seddek, Laila F.
    • Structural Engineering and Mechanics
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    • 제70권6호
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    • pp.737-750
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    • 2019
  • This paper investigates the static and dynamic behaviors of imperfect single walled carbon nanotube (SWCNT) modeled as a beam structure by using energy-equivalent model (EEM), for the first time. Based on EEM Young's modulus and Poisson's ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The equation governed the motion of curved CNTs is a nonlinear integropartial-differential equation. It is derived in terms of only the lateral displacement. The nonlinear integro-differential equation that governs the buckling of CNT is numerically solved using the differential integral quadrature method (DIQM) and Newton's method. The linear vibration problem around the static configurations is discretized using DIQM and then is solved as a linear eigenvalue problem. Numerical results are depicted to illustrate the influence of chirality angle and imperfection amplitude on static response, buckling load and dynamic behaviors of armchair and zigzag CNTs. Both, clamped-clamped (C-C) and simply supported (SS-SS) boundary conditions are examined. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

풍력과 지진하중을 고려한 압력용기의 피로해석 (Fatigue analysis of pressure vessel in view of wind and seismic loads)

  • 박진용;황운봉;박상철;박동환
    • 대한기계학회논문집
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    • 제15권2호
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    • pp.596-603
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    • 1991
  • Fatigue life prediction of pressure vessel is studied analytically using cumulative damage models and linear elastic fracture mechanics method. The stresses are analyzed by finite element method. During operation, the maximum stress occurs at the outside of neck region while fatigue analysis indicates that the bottom of nozzle part has the shortest fatigue life. Previously proposed fatigue life prediction equation and cumulative damage model are modified successfully by introducing reference fatigue modulus. It is found that the modified life prediction equation and damage model are useful for lower stress level application.