• Journal of the Korea Concrete Institute
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• v.16 no.3 s.81
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• pp.375-382
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• 2004

The compressive strength of concrete is used as the most basic and important material Property when reinforced concrete structures are designed. It has become a problem to use this value, however, because the control specimen sizes and shapes are different from every country. In this study, the effect of specimen sizes and shapes on compressive strength of concrete specimens was experimentally investigated based on fracture mechanics. Experiments for the Mode I failure was carried out by using cylinder, cube, and prism specimens. The test results are curve fitted using least square method(LSM) to obtain the new parameters for the modified size effect law(MSEL). The analysis results show that the effect of specimen sizes and shapes on ultimate strength is apparent. In addition, correlations between compressive strengths with size, shape, and casting direction of the specimen are investigated. For cubes and prisms the effect of placing direction on the compressive strength was investigated.

• Advances in nano research
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• v.12 no.5
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• Advances in nano research
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• v.12 no.1
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• pp.101-115
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• 2022

Some researchers pointed out that the nonlocal cantilever models do not predict the dynamic softening behavior for nanostructures (including nanobeams) with clamped-free (CF) ends. In contrast, some indicate that the nonlocal cantilever models can capture the stiffness softening characteristics. There are substantial differences on this issue between them. The vibration analysis of porosity-dependent functionally graded nanoscale tubes with variable boundary conditions is investigated in this study. Using a modified power-law model, the tube's porosity-dependent material coefficients are graded in the radial direction. The theory of nonlocal strain gradients is used. Hamilton's principle is used to derive the size-dependent governing equations for simply-supported (S), clamped (C) and clamped-simply supported (CS). Following the solution of these equations by the extended differential quadrature technique, the effect of various factors on vibration issues was investigated further. It can be shown that these factors have a considerable effect on the vibration characteristics. It also can be found that our numerical results can capture the unexpected softening phenomena for cantilever tubes.

• Steel and Composite Structures
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• v.48 no.4
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• pp.443-459
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• 2023

This paper investigates the stability of a bi-directional functionally graded (BD-FG) cylindrical beam made of imperfect concrete, taking into account size-dependency and the effect of geometry on its stability behavior. Both buckling and dynamic behavior are analyzed using the modified coupled stress theory and the classical beam theory. The BD-FG structure is created by using porosity-dependent FG concrete, with changing porosity voids and material distributions along the pipe radius, as well as uniform and nonuniform radius functions that vary along the beam length. Energy principles are used to generate partial differential equations (PDE) for stability analysis, which are then solved numerically. This study sheds light on the complex behavior of BD-FG structures, and the results can be useful for the design of stable cylindrical microstructures.

• Proceedings of the Korea Concrete Institute Conference
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• 1993.04a
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• pp.124-129
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• 1993

In this study, a simple and accurate model equation for prediction of shear strength of reinforce concrete beams without web, reinforcement is proposed based on basic shear transfer mechanism and modified Bazant's size effect law. The proposed equation includes the effects of concrete strength, longitudinal steel ratio, shear span to depth ratio and effective depth. Comparisons with published experimental data indicate that the proposed equation estimates properly the effects of these factors. Among many equations, ACI code equation, Zsutty's equation and Bazant's equation are selected for comparison. As the result, the accuracy of the proposed equation is better than that of any other equations.

• Advances in nano research
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• v.8 no.4
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• pp.283-292
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• 2020

In the present research, differential quadrature (DQ) method has been utilized for investigating free vibrations of porous functionally graded (FG) micro/nano beams in thermal environments. The exact location of neutral axis in FG material has been assumed where the material properties are described via porosity-dependent power-law functions. A scale factor related to couple stresses has been employed for describing size effect. The formulation of scale-dependent beam has been presented based upon a refined beam theory needless of shear correction factors. The governing equations and the associated boundary conditions have been established via Hamilton's rule and then they are solved implementing DQ method. Several graphs are provided which emphasis on the role of porosity dispersion type, porosity volume, temperature variation, scale factor and FG material index on free vibrational behavior of small scale beams.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Smart Structures and Systems
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• v.20 no.6
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• pp.709-728
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• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Progress in Medical Physics
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• v.14 no.4
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• pp.234-239
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• 2003

We examined the variation of percent depth dose (PDD) curves for 10 MV X-rays in the presence of magnetic fields. The EGS4 Monte Carlo code was applied and modified to take account of the effect of electron deflection under magnetic field was used. We defined and tested DI (dose improvement) and DR (dose reduction) to describe variation of PDD curves under various magnetic fields. For a magnetic field of 3 T applied at the depth region of 5-10 cm and field size of 10${\times}$10 $\textrm{cm}^2$, the DI is 1.56 (56% improvement) and DR is 0.68 (32% reduction). We explained the results from the Lorentz law and the concept of electron equilibrium. We suggested that the dose optimization in radiotherapy can be achieved from using the characteristics of dose distributions under magnetic fields.

• Magazine of the Korea Concrete Institute
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• v.11 no.1
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• pp.173-181
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• 1999

To deepen the understanding of shear behaviour in beams without transverse reinforcement, the relative importance of five contributing factors to concrete shear resistance($v_c$), which are i)flexural compression zone, ii)friction at crack faces, iii)dowel action, iv)arch action and recently identified, v)residual tensile stresses across cracks, was explained physically using two analytical methods based on the truss concept. One is called "Modified Compression Field Theory(MCFT)" considering ii) and v) explicitly, and the other "Crack Friction Truss Model(CFTM)" more dominantly ii) in determining concrete resistance. To verify their effectiveness, the predictions using MCFT and CFTM were also made for twenty KAIST beam tests($f'_c$=53.7Mpa), designated more likely to the development of the size effect law based on the fracture mechanics concept. Experimental findings with varying of a/d, longitudinal reinforcement ratios, and obtained from MCFT enabled additional explanations for some phenomena which were difficult to measure in tests. However, MCFT seemed somewhat conservative for beams with higher longitudinal reinforcement, while somewhat unsafe for beams with larger depths. More tests are necessary leading to firm conclusions in these areas.