• Title/Summary/Keyword: Constant normal stiffness

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Lateral Force Calibration of Colloidal Probe in Liquid Environment Using Reference Cantilever (기준 외팔보를 이용한 액체 환경에서 Colloidal Probe의 수평방향 힘 교정)

  • Je, Youngwan;Chung, Koo-Hyun
    • Tribology and Lubricants
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    • v.29 no.3
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    • pp.160-166
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    • 2013
  • There is an indispensable need for force calibration for quantitative nanoscale force measurement using atomic force microscopy. Calibrating the normal force is relatively straightforward, whereas doing so for the lateral force is often complicated because of the difficulty in determining the optical lever sensitivity. In particular, the lateral force calibration of a colloidal probe in a liquid environment often has a larger uncertainty as a result of the effects of the epoxy, the location of the colloidal particle on the cantilever, and a decrease in the quality factor. In this work, the lateral force of a colloidal probe using a reference cantilever with a known spring constant was calibrated in a liquid environment. By obtaining the spring constant and the lateral sensitivity at the equator of a spherical colloidal particle, the damage to the bottom surface of the colloidal particle could be eliminated. Further, it was shown that the effect of the contact stiffness on the determination of the lateral spring constant of the cantilever could be minimized. It was concluded that this method can be effectively used for the lateral force calibration of a colloidal probe in a liquid environment.

Effect of stud corrosion on stiffness in negative bending moment region of steel-concrete composite beams

  • Yulin Zhan;Wenfeng Huang;Shuoshuo Zhao;Junhu Shao;Dong Shen;Guoqiang Jin
    • Steel and Composite Structures
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    • v.48 no.1
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    • pp.59-71
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    • 2023
  • Corrosion of the headed studs shear connectors is an important factor in the reduction of the durability and mechanical properties of the steel-concrete composite structure. In order to study the effect of stud corrosion on the mechanical properties in the negative moment region of steel-concrete composite beams, the corrosion of stud was carried out by accelerating corrosion method with constant current. Static monotonic loading was adopted to evaluate the cracking load, interface slip, mid-span deflection, and ultimate bearing capacity of four composite beams with varying corrosion rates of headed studs. The effect of stud corrosion on the stiffness of the composite beam's hogging moment zone during normal service stage was thoroughly examined. The results indicate that the cracking load decreased by 50% as the corrosion rate of headed studs increase to 10%. Meanwhile, due to the increase of interface slip and mid-span deflection, the bending stiffness dropped significantly with the same load. In comparison to uncorroded specimens, the secant stiffness of specimens with 0.5 times ultimate load was reduced by 25.9%. However, corrosion of shear studs had no obvious effect on ultimate bending capacity. Based on the experimental results and the theory of steel-concrete interface slip, a method was developed to calculate the bending stiffness in the negative bending moment region of composite beams during normal service stage while taking corrosion of headed studs into account. The validity of the calculation method was demonstrated by data analysis.

The Role of the Plastic Flow Rules in the Elasto-Plastic Formulation of Joint behaviour (절리거동의 탄소성해석에서 소성유동법칙의 역할)

  • 이연규
    • Tunnel and Underground Space
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    • v.10 no.2
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    • pp.173-179
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    • 2000
  • The influence of the plastic flow rules on the elasto-plastic behaviour of a discrete joint element was investigated by performing the numerical direct shear tests under both constant normal displacement and normal displacement conditions. The finite interface elements obeying Plesha’s joint constitutive law was used to allow the relative motion of the rock blocks on the joint surface. Realistic results were obtained in the tests adopting the non-associated flow rule, while the associated flow rule overestimated the joint dilation. To overcome the computational drawbacks coming from the non-symmetric element stiffness matrix in the conventional non-associated plasticity, the symmetric formulation of the tangential stiffness matrix for a non-associated joint element was proposed. The symmetric elasto-plastic matrix it derived by assuming an imaginary equivalent joint with associated flow rule which shows the same plastic response as that of original Joint with non-associated flow rule. The validity of the formulation was confirmed through the numerical direct shear tests under constant normal stress condition.

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The Influence of Rock Joint Roughness and Normal Stress on Shear Behaviour (거칠기와 수직응력에 따른 암석 절리면의 전단거동)

  • Lee, Myoung-Ho;Kim, Jong-Woo;Chang, Kwang-Taek
    • Tunnel and Underground Space
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    • v.17 no.3 s.68
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    • pp.186-196
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    • 2007
  • In this study, direct shear tests were carried out on the 30 rock joint samples in order to investigate the influence of roughness and normal stress on the shear behaviour. Joint roughness profiles were measured by use of 3D laser profiler, and then the samples were equally classified into three individual groups according to the roughness index of rock joints. Peak shear strength, residual shear strength, shear stiffness, dilation angle of rock joints were investigated in condition of five different constant normal load. Peak shear strength was increased as roughness index was increased, and the influence of roughness on strength was found to be more considerable in case of lower normal stress condition. Residual shear strength and shear stiffness were increased as roughness index and normal stress were increased. Finally dilation angle was decreased as normal stress was increased, but it was increased as roughness index was increased in the same normal stress condition.

A Study on Distinct Element Modelling of Dilatant Rock Joints (팽창성 암석절리의 개별요소 모델링에 관한 연구)

  • 장석부;문현구
    • Tunnel and Underground Space
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    • v.5 no.1
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    • pp.1-10
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    • 1995
  • The behavior of a jointed rock mass depends mainly on the geometrical and mechanical properties of joints. The failure mode of a rock mass and kinematics of rock blocks are governed by the orientation, spacing, and persistence of joints. The mechanical properties such as dilation angle, shear strength, maximum closure, strength of asperities and friction coeffiient play important roles on the stability and deformation of the rock mass. The normal and shear behaviour of a joint are coupled due to dilation, and the joint deformation depends also on the boundary conditions such as stiffness conditons. In this paper, the joint constitutive law including the dilatant behaviour of a joint is numerically modelled using the edge-to-edge contact logic in distinct element method. Also, presented is the method to quantify the input parameters used in the joint law. The results from uniaxial compression and direct shear tests using the numeical model of the single joint were compared to the analytic results from them. The boundary effect on the behaviour of a joint is verified by comparing the results of direct shear test under constant stress boundary condition with those under constant stiffness boundary condition. The numerical model developed is applied to a complex jointed rock mass to examine its performance and to evaluate the effect of joint dilation on tunnel stability.

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Shear Strength and Deformation Behavior of Rock Joint with Roughness (절리면의 거칠기에 따른 암석 절리의 전단강도 및 변형거동에 관한 연구)

  • 이상돈;강준호;이정인
    • Tunnel and Underground Space
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    • v.4 no.3
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    • pp.261-273
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    • 1994
  • Direct shear tests were carried out on the rock joints and artificial discontinuities to investigate the influence of joint roughness on the shear strength and deformation behaviour. Single direct shear testing apparatus used in experiment was designed and manufactured. Its capacity is 200 tons of shear load, 20 tons of normal load and 50$\textrm{cm}^2$ of maximum shear area. Test samples were cement mortar with artificial discontinuity and sandstone with natural joint. Peak shear strength was increased as joint roughness or normal stress was increased, especially, linearly increased with roughness angle in cement mortar. If joint roughness angle was constant at low normal stress, shear strength was not affected by width and height of joint roughness in cement mortar. Peak shear strengths obtained from tests were larger than the values calculated by Barton's equation, and shear stiffness was increased with joint roughness coefficient.

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Free vibration analysis of a non-uniform beam with multiple point masses

  • Wu, Jong-Shyong;Hsieh, Mang
    • Structural Engineering and Mechanics
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    • v.9 no.5
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    • pp.449-467
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    • 2000
  • The natural frequencies and the corresponding mode shapes of a non-uniform beam carrying multiple point masses are determined by using the analytical-and-numerical-combined method. To confirm the reliability of the last approach, all the presented results are compared with those obtained from the existing literature or the conventional finite element method and close agreement is achieved. For a "uniform" beam, the natural frequencies and mode shapes of the "clamped-hinged" beam are exactly equal to those of the "hinged-clamped" beam so that one eigenvalue equation is available for two boundary conditions, but this is not true for a "non-uniform" beam. To improve this drawback, a simple transformation function ${\varphi}({\xi})=(e+{\xi}{\alpha})^2$ is presented. Where ${\xi}=x/L$ is the ratio of the axial coordinate x to the beam length L, ${\alpha}$ is a taper constant for the non-uniform beam, e=1.0 for "positive" taper and e=1.0+$|{\alpha}|$ for "negative" taper (where $|{\alpha}|$ is the absolute value of ${\alpha}$). Based on the last function, the eigenvalue equation for a non-uniform beam with "positive" taper (with increasingly varying stiffness) is also available for that with "negative" taper (with decreasingly varying stiffness) so that half of the effort may be saved. For the purpose of comparison, the eigenvalue equations for a positively-tapered beam with five types of boundary conditions are derived. Besides, a general expression for the "normal" mode shapes of the non-uniform beam is also presented.

Finite Element Formulation for the Distortion Analysis of Steel Box Girders (강상자거더의 뒤틀림해석에 관한 유한요소 정식화)

  • 최영준;정래영;황선호;강영종
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1999.04a
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    • pp.327-334
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    • 1999
  • Steel box girders are popular to the Practicing engineers for the its large Pure torsional constant. But closed box girders at-e susceptible to the eccentric loading due to the distortion of the cross section. Distorton of the box girder develops the warping normal stress and transverse flexural stress in the cross section and their magnitudes can be large unless internal diaphragms are installed sufficiently. In this study, stiffness matrix and equivalent nodal force vector are formulated on the basis of displacement method. Shape functions are directly derived from the homogeneous solution of the governing differential equation of the distortion. New finite element formulations were coded into a computer program. Several numerical examples were presented to show the validity of developed program.

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Load Transfer Characteristics of Rock-Socketed Drilled Shafts Considering Hole Roughness (굴착면 거칠기를 고려한 암반 근입 현장타설말뚝의 주면하중전이 특성)

  • Seol, Hoon-Il;Jeong, Sang-Seom;Woo, Sang-Yoon
    • Proceedings of the Korean Geotechical Society Conference
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    • 2006.03a
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    • pp.494-505
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    • 2006
  • In this study, using constant normal stiffness(CNS) direct shear tests, side shear load distribution were analyzed by the influencing parameters of unconfined compressive strength, surface roughness, confining stress, and material properties. Based on the CNS tests, side shear load transfer function of drilled shafts in rock is proposed using geological strength index(GSI), which indicates discontinuity and surface condition of rock mass in Hoek-Brown criterion. Though comparisons with results of nine drilled shafts's load tests, it is found that the load-transfer curve by this study is in good agreement with the general trend observed by in situ measurements, and thus represents a significant improvement in the prediction of bearing capacity of drilled shaft.

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Development of the Hybrid Vibration Isolator for Large Superprecision Stage (대형 초정밀 스테이지용 복합 아이솔레이터 개발)

  • Kim, Won-Kyum;Jung, Soon-Chul;Chang, Seung-Hwan;Lee, Jae-Eung;Shin, Dong-Su;Lee, Jae-Jung
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2006.05a
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    • pp.1404-1408
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    • 2006
  • In this paper, a hybrid-type vibration isolator which has air chamber(spring) and viscous damper in series is developed. The developed vibration isolator is designed to perform 3 following functions : spring function for normal operating conditions, damping function to reduce an impact for sudden move of upper beam, and finally leveling function. Based on the given natural frequency and damping factor, the design procedure is proposed. The performance of the developed isolator is tested by measuring stiffness and damping.

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