• Title/Summary/Keyword: tangent modulus of elasticity

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Constitutive Relations of Concrete Including Elasticity, Damage, and Plasticity (탄성, 손상 및 소성을 고려한 콘크리트의 구성관계)

  • 변근주;이기성;김종우;이주영
    • Proceedings of the Korea Concrete Institute Conference
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    • 1993.10a
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    • pp.190-194
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    • 1993
  • This paper focuses on the development of the tangent modulus to describe the nonlinearity of concrete based on the continuum damage mechanics. This tangent modulus includes the effects of elasticity, damage and plasticity of concrete.

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A Review on the Tangent Modulus of Elasticity Associated With Partially Yielded Section of Steel Member Under Axially Compressed (강 압축부재의 단면 항복에 따른 접선탄성계수 고찰)

  • See, Sang Kwang
    • Journal of Korean Association for Spatial Structures
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    • v.18 no.1
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    • pp.127-134
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    • 2018
  • This study suggests the tangent modulus $E_t$ associated with partially yielded section of steel member under axially compressed. The provisions for column strength does not provide a information about failure mode of structural system. So, designers can not evaluate that a failure comes from member buckling or material yielding. The material of the axially compressed column under inelastic behavior reaches yielding point before the axial force renders the column bent. If axial members yields not by buckling effect but gradually yielding effect of material, the design code should accept related tangent modulus Et which is based on gradual yielding effect of material. This study provides the new effective tangent modulus $E_t$ derived in the case that residual stress is 30 percent and 50 percent of yielding stress respectively. The study considers idealized I section of steel which ignores web and general I section of steel with web respectively and makes conclude that tangent modulus $E_t$ with idealized I section of steel is rational.

Exploring Reliability of Wood-Plastic Composites: Stiffness and Flexural Strengths

  • Perhac, Diane G.;Young, Timothy M.;Guess, Frank M.;Leon, Ramon V.
    • International Journal of Reliability and Applications
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    • v.8 no.2
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    • pp.153-173
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    • 2007
  • Wood-plastic composites (WPC) are gaining market share in the building industry because of durability/maintenance advantages of WPC over traditional wood products and because of the removal of chromated copper arsenate (CCA) pressure-treated wood from the market. In order to ensure continued market share growth, WPC manufacturers need greater focus on reliability, quality, and cost. The reliability methods outlined in this paper can be used to improve the quality of WPC and lower manufacturing costs by reducing raw material inputs and minimizing WPC waste. Statistical methods are described for analyzing stiffness (tangent modulus of elasticity: MOE) and flexural strength (modulus of rupture: MOR) test results on sampled WPC panels. Descriptive statistics, graphs, and reliability plots from these test data are presented and interpreted. Sources of variability in the MOE and MOR of WPC are suggested. The methods outlined may directly benefit WPC manufacturers through a better understanding of strength and stiffness measures, which can lead to process improvements and, ultimately, a superior WPC product with improved reliability, thereby creating greater customer satisfaction.

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Prediction and Application of the Dynamic Modulus of Elasticity of Concrete Using the Wavelet Analysis (웨이블릿 해석을 이용한 콘크리트의 동탄성계수 추정 및 응용)

  • Jung, Beom-Seok
    • Journal of the Korea Concrete Institute
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    • v.22 no.6
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    • pp.843-850
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    • 2010
  • The dynamic modulus of elasticity of concrete can be determined nondestructively using impact echo test as prescribed in KS F 2437. The fundamental longitudinal frequency of the concrete cylinders with free-free boundary condition was estimated by the wavelet transform theory. The advantage of the wavelet transform over either a pure spectral or temporal decomposition of the signal is that the features of the pertinent signals can be characterized in the time-frequency plane. For the concrete mix design utilized in this study, no significant difference between the dynamic and the static moduli of elasticity was observed. This was contrary to the perceived general notion of having the dynamic modulus considerably higher than the static modulus. It has been shown that the modulus from static and dynamic by impact echo test are comparable to each other fairly well, when the effect of strain level was properly taken into account. In this experimental test, it was shown that the dynamic modulus is approximately equal to the tangent modulus at $1{\times}10^{-4}$ strain level.

The Estimation of Initial Elastic Modulus of Clay by Standard Consolidation Test (표준압밀시험에 의한 점토의 초기탄성계수 산정)

  • Kwon, Byenghae;Eam, Sunghoon
    • Journal of The Korean Society of Agricultural Engineers
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    • v.66 no.1
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    • pp.15-24
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    • 2024
  • Unlike artificially created homogeneous materials, the process of calculating the elastic modulus of natural soil involves the possibility of errors. Because the stress-strain behavior of soil is nonlinear, the secant modulus of elasticity is often used based on 1/2 of the stress at failure. Since soil has the property of changing its elastic modulus depending on the confining pressure, numerical analysis models that analyze its behavior inevitably include complex elements. The hyperbolic model, which relatively accurately simulates the behavior immediately after loading in soft ground, assumes that the stress-strain curve of the consolidated undrained triaxial test is hyperbolic and requires the slope of the tangent line at the starting point. However, the slope of the initial tangent in the stress-strain curve obtained from an actual triaxial test is difficult to have regularity according to changes in confining pressure. Additionally, due to the characteristics of a hyperbola, even small changes in related factors cause large changes in the hyperbola. Therefore, there is a lot of randomness in the process of calculating model parameters from the triaxial test results, which causes large differences in the results. Therefore, the method of calculating the initial elastic modulus by the consolidation test presented in this study is also used to verify the method by the triaxial test. It can be applied. However, since this study was applied to only one sample showing typical consolidation characteristics, it is necessary to check samples with various physical properties in the future.

Measurement Method of Broadband Dynamic Characteristics of Viscoelastic Material for Compliant Coating (유연벽면 점탄성 소재의 광대역 동특성 계측 기법)

  • Seoudi, Basel M.;Boiko, Andrey V.;Chun, Ho-Hwan;Lee, In-Won
    • Journal of the Society of Naval Architects of Korea
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    • v.45 no.1
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    • pp.73-80
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    • 2008
  • An improved method to measure the dynamic viscoelastic properties of elastomers is proposed. The method is based on the analysis of forced oscillation of a cylindrical sample loaded with inertial mass. No special equipment or instrumentation other than the ordinary vibration measurement apparatus is required. Typical measurement of the viscoelastic properties of a silicone rubber $Silastic^{(R)}$ S2 were measured over the wide frequency range from 10 Hz to 3 kHz under the action of wide region of deformation from $10^{-4}%$ to 5%. It was shown that modulus of elasticity and loss tangent fall on the single curves when the ratio of load mass to sample mass changed from 1 to 20.

Comparison of Limit Strength of Steel Cable-Stayed Bridges using Nonlinear Inelastic Displacement and Buckling Analyses (비선헝 비탄성 유한변위 해석 및 좌굴해석에 의한 강사장교의 극한강도 비교)

  • Kim Sung-Eock;Choi Dong-Ho;Ma Sang-Soo;Song Weon-Keun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.18 no.3
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    • pp.277-289
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    • 2005
  • The study examines the limit strength for steel cable-stayed bridges. A case studies have been performed in order to evaluate the limit strength lot steel cable-stayed bridges using nonlinear inelastic analysis approach and bifurcation point instability analysis approach, effective tangent modulus $(E_f)$ method. To realize it, a practical nonlinear inelastic analysis condoling the initial shape is developed. In the initial shape analysis, updated structural configuration is introduced instead of initial member forces for beam-column members at every iterative step. Geometric and material nonlinearities of beam-column members are accounted by using stability function, and by using CRC tangent modulus and parabolic function, respectively Besides, geometric nonlinearity of cable members is accounted by using secant value of equivalent modulus of elasticity. The load-displacement relationships obtained by the proposed method are compared well with those given by other approaches. The limit strengths evaluated by the proposed nonlinear inelastic analysis for the proposed cable-stayed bridges with tee dimensional configuration compared with those by the inelastic bifurcation point instability analyses.

Model on the Elastic Deflection of Temple of the Spectacle Frame (안경테 다리의 탄성변형에 관한 모델)

  • Kim, Dae-Soo
    • Journal of Korean Ophthalmic Optics Society
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    • v.12 no.1
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    • pp.41-51
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    • 2007
  • Differential equations and their solutions were formulated to describe the deflection of the tapered, nonuniform thickness and width's temple, clamped at one end while the perpendicular force is acting on the other end which is freely suspended. The model was derived based on laws of continuity at every point inside the elastic medium that the deflection, tangent slope, bending moment, shearing force must be continuous within the medium. The model is found to be in good agreement with measurements on the beta titanium temple with the correlation 0.992 and p=0.999(Chi test). Therefore it is possible to predict the effect of various temple parameters such as elastic modulus, thickness, width on the deflection of the temples being considered.

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A modified shear strength reduction finite element method for soil slope under wetting-drying cycles

  • Tu, Yiliang;Zhong, Zuliang;Luo, Weikun;Liu, Xinrong;Wang, Sui
    • Geomechanics and Engineering
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    • v.11 no.6
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    • pp.739-756
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    • 2016
  • The shear strength reduction finite element method (SSRFEM) is a powerful tool for slope stability analysis. The factor of safety (FOS) of the slope can be easily calculated only through reducing effective cohesion (c′) and tangent of effective friction angle ($tan{\varphi}^{\prime}$) in equal proportion. However, this method may not be applicable to soil slope under wetting-drying cycles (WDCs), because the influence of WDCs on c′ and $tan{\varphi}^{\prime}$ may be different. To research the method of estimating FOS of soil slopes under WDCs, this paper presents an experimental study firstly to investigate the effects of WDCs on the parameters of shear strength and stiffness. Twelve silty clay samples were subjected to different number of WDCs and then tested with triaxial test equipment. The test results show that WDCs have a degradation effect on shear strength (${\sigma}_1-{\sigma}_3)_f$, secant modulus of elasticity ($E_s$) and c′ while little influence on ${\varphi}^{\prime}$. Hence, conventional SSRFEM which reduces c′ and $tan{\varphi}^{\prime}$ in equal proportion cannot be adopted to compute the FOS of slope under conditions of WDCs. The SSRFEM should be modified. In detail, c′ is merely reduced among shear strength parameters, and elasticity modulus is reduced correspondingly. Besides, a new approach based on sudden substantial changes in the displacement of marked nodes is proposed to identify the slope failure in SSRFEM. Finally, the modified SSRFEM is applied to compute the FOS of a slope example.

A Characteristic of Deformation and Strength of Domestic Sands by Triaxial Compression Tests (삼축압축시험에 의한 국내 모래의 변형-강도 특성)

  • Park, Choon Sik;Kim, Jong Hwan;Park, Cheol Soo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.2
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    • pp.515-527
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    • 2014
  • This study conducted experiment for understanding engineering characteristics of domestic sands by examining standard sand and sand from Yokji Island and Nakdong River in terms of confining pressure, $K_0$, over consolidation and relative density factors through triaxial compression test. The test showed that deviator stress by strain positively changed as confining pressure and relative density grow while $K_0$ and over consolidation factors do not directly correlated with it. Angle of internal friction decreases as confining pressure increases which strengthens contact force between particles, and declines as relative density drops, whereas $K_0$ and over consolidation factors hardly affect the results. When it comes to volumetric strain, volume expansion decreases as confining pressure increase due to crushability and rearrangement of particles while $K_0$ and over consolidation shows same movement unconditionally, and relative density appears compressed as it grows at the beginning however it expands as axial strain increases. Modulus of elasticity ($E_{sec}$) by strain has tendency into convergence resulting in initial secant modulus of elasticity ($E_{ini}$) > secant modulus of elasticity($E_{sec}$) > tangent modulus of elasticity ($E_{tan}$). On the other hand, it grows as confining pressure and relative density increase while indicating similar modulus of elasticity ($E_{sec}$) regarding on $K_0$ and over consolidation. Slope of critical line (M) tended to decrease as confining pressure increases, follow same line according to $K_0$, confining pressure and relative density, and increase as relative density grows.