• Title/Summary/Keyword: rectangular beam

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Exact Solutions for Vibration and Buckling of Rectangular Plates Loaded at Two Simply-Supported Opposite Edges by In-Plane Moments, Free along the Other Two Edges (면내(面內) 모멘트를 받는 단순지지된 두 모서리와 자유경계인 나머지 두 모서리를 갖는 직사각형 판의 진동과 좌굴의 엄밀해)

  • Shim, Hyun-Ju;Woo, Ha-Young;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.6 no.4 s.22
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    • pp.81-92
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    • 2006
  • This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

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Fabrication of 2D Bravais Nano Pattern and Growth of ZnO Nano Rods with Photonic Crystal Effect (2차원 Bravais Lattice를 가지는 나노 패턴 제조 및 광결정 효과를 가지는 ZnO 나노 기둥 성장)

  • Kim, Tae-Un;Moon, Jong-Ha;Kim, Seon-Hoon;Kim, Doo-Gun;Kim, Jin-Hyeok
    • Korean Journal of Materials Research
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    • v.21 no.12
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    • pp.697-702
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    • 2011
  • Two-dimensional (2D) nano patterns including a two-dimensional Bravais lattice were fabricated by laser interference lithography using a two step exposure process. After the first exposure, the substrate itself was rotated by a certain angle, $90^{\circ}$ for a square or rectangular lattice, $75^{\circ}$ for an oblique lattice, and $60^{\circ}$ for a hexagonal lattice, and the $90^{\circ}$ and laser incident angle changed for rectangular and the $45^{\circ}$ and laser incident angle changed for a centered rectangular; we then carried out a second exposure process to form 2D bravais lattices. The band structure of five different 2D nano patterns was simulated by a beam propagation program. The presence of the band-gap effect was shown in an oblique and hexagonal structure. The oblique latticed ZnO nano-photonic crystal array had a pseudo-bandgap at a frequency of 0.337-0.375, 0.575-0.596 and 0.858-0.870. The hexagonal latticed ZnO nano-crystallite array had a pseudo-bandgap at a frequency of 0.335-0.384 and 0.585-0.645. The ZnO nano structure with an oblique and hexagonal structure was grown through the patterned opening window area by a hydrothermal method. The morphology of 2D nano patterns and ZnO nano structures were investigated by atomic force microscopy and scanning electron microscopy. The diameter of the opening window was approximately 250 nm. The height and width of ZnO nano-photonic crystals were 380 nm and 250 nm, respectively.

An Experimental Study on the Ultimate Strength and Deformation Capacity of Composite Beams with Eccentric Web Openings (편심유공합성보의 종국내력 및 변형능력에 관한 실험적 연구)

  • Choi, San Ho;Seo, Seong Yeon
    • Journal of Korean Society of Steel Construction
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    • v.12 no.5 s.48
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    • pp.595-604
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    • 2000
  • Web openings of large beams provide space for wiring, piping, and duct work to provide for proper drainage, pipes and duct must be slightly sloped with the attendant result that all web openings can not be centered on the centroidal axes of the beams. Test specimens are made for opening-depth to beam-depth ratio of 0.5 and for eccentricities of the opening center line of 10% from middepth of the beam because of the proximity of the opening edge to the flange. In this paper, available test results and theories relating to the strength of composite beams having eccentric rectangular openings are surveyed and experiments were carried out to examine the structural behaviors. In all the tests in this paper good agreement is demonstrated with maximum loads measured in tests, and observed failure modes Furthermore, compared with analytical values and experimental values of interaction diagram between moment and shear capacity were safed as it is scattered with outer part of the analytical values.

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Analysis of Laminated Composite Stiffened Plates with arbitrary orientation stiffener (임의방향 보강재를 가지는 복합적층 보강판의 해석)

  • Yhim, Sung-Soon;Chang, Suk-Yoon;Park, Dae-Yong
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.8 no.2
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    • pp.147-158
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    • 2004
  • For stiffened plates composed of composite materials, many researchers have used a finite element method which connected isoparametric plate elements and beam elements. However, the finite element method is difficult to reflect local behavior of stiffener because beam elements are transferred stiffness for nodal point of plate elements, especially the application is limited in case of laminated composite structures. In this paper, for analysis of laminated composite stiffened plates, 3D shell elements for stiffener and plate are employed. Reissner-Mindlin's first order shear deformation theory is considered in this study. But when thickness will be thin, isoparamatric plate bending element based on the theory of Reissner-Mindlin is generated by transverse shear locking. To eliminate the shear locking and virtual zero energy mode, the substitute shear strain field is used. A deflection distribution is investigated for simple supported rectangular and skew stiffened laminated composite plates with arbitrary orientation stiffener as not only variation of slenderness and aspect ratio of the plate but also variation of skew angle of skew stiffened plates.

Development of DCOC Algorithm Considering the Variation of Effective Depth in the Optimum Design of PRC Continuous Beam (PRC연속보 최적설계에서 단면의 유효깊이 변화를 고려한 DCOC알고리즘 개발)

  • 조홍동;한상훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.2
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    • pp.281-291
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    • 2002
  • This paper describes the minimum cost design of prestressed reinforced concrete (PRC) hem with rectangular section. The cost of construction as objective function which includes the costs of concrete, prestressing steel, non prestressing steel, and formwork is minimized. The design constraints include limits on the minimum deflection, flexural and shear strengths, in addition to ductility requirements, and upper-Lower bounds on design variables as stipulated by the specification. The optimization is carried out using the methods based on discretized continuum-type optimality criteria(DCOC). Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables - effective depth, eccentricity of prestressing steel and non prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. In this paper the effective depth is considered to be freely-varying and one uniform for the entire multispan beam respectively. Also the maximum eccentricity of prestressing force is considered in every span. In order to show the applicability and efficiency of the derived algorithm, several numerical examples of PRC continuous beams are solved.

Shear Behavior of Reinforced Concrete Beams Strengthened with CFRP Strips (탄소섬유판 (CFRP Strip)으로 보강된 철근콘크리트 부재의 전단거동)

  • Lim, Dong-Hwan;Nam, Min-Hee
    • Journal of the Korea Concrete Institute
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    • v.20 no.3
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    • pp.299-305
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    • 2008
  • The main goal of this study was to examine the shear behavior of reinforced concrete beams strengthened with CFRP strups. Seven rectangular beams were tested. The test variables were the configuration types, spacing length of CFRP strips and the amount of reinforced stirrups bars. From this experimental study, the shear capacity of beams strengthened with CFRP increased significantly compared to the beam without CFRP strip. Maximum increase of ultimate shear strength was found about 100% more than that of the beam without a CFRP strip and the CFRP strips attached in the shear region can resist the occurrence of the initial shear cracks and the propagation of major shear cracks. In this test, most of the shear strengthened beams failed suddenly due to the debonding of CFRP strips. A calculation of the shear strength of reinforced beams strengthened with CFRP strips based on the effective stresses was conducted and the comparisons were made with the test results.

Minimum Cost Design of Reinforced Concrete Beam Using DCOC (DCOC를 이용한 철근 콘크리트보의 최소경비설계)

  • 조홍동;한상훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.13 no.4
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    • pp.417-425
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    • 2000
  • This paper describes the application of discretized continuum-type optimality criteria(DCOC) and the development of optimum design program for the reinforced concrete continuous beams with rectangular cross-section. The cost of construction as objective function which includes the costs of concrete, reinforcing steel and formwork is minimized. The design constraints include limits on the maximum deflection, flexural and shear strengths, in addition to ductility requirements, and upper and lower bounds on design variables as stipulated by the design Code. Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables-effective depth, and steel ratio. The self-weight of the beam is included in the equilibrium equation of the real system. An iterative procedure and computer program for updating the design variables are developed. Two numerical examples of reinforced concrete continuous beams are presented to show the applicability and efficiency of the DCOC-based technique.

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Experimental Study of Coupled Shearwalls with different Coupling Member (인방보의 형태에 따른 개구부가 있는 전단벽의 거동 특성에 대한 실험적 연구)

  • Bae, Baek-Il;Choi, Hyun-Ki;Choi, Yoon-Chel;Choi, Chang-Sik
    • Proceedings of the Korea Concrete Institute Conference
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    • 2008.04a
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    • pp.37-40
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    • 2008
  • Many engineers find the way of improving the old building's structural behavior in the remodeling project which is performed using artificial openings for merging two houses. This test was performed to verify the characteristics of coupling beams according to the shape of the openings. One of test specimen has rectangle shape and the other was made by the circle shaped opening and one has coupling member only as slabs. Additionally, three specimens which have openings have 23% ratio in opening area to total wall area. Consequently, solid type which have no opening area shows shear failure. In the case of CW-RBS which have rectangular shaped opening, cracks are developed in coupling beam significantly. And CW-CS which has circular opening failed in shear showing development of diagonal cracks at wall toes and wall mid-height. It is thought that degradation of the wall strength is under the control of the opening shape and coupling beam-wall connection area.

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Thrust Characteristics of a Laser-Assisted Pulsed Plasma Thruster

  • Masatoshi Kawakami;Hideyuki Horisawa;Kim, Itsuro ura
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.294-299
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    • 2004
  • An assessment of a novel laser-electric hybrid propulsion system was conducted, in which a laser-induced plasma was induced through laser beam irradiation onto a solid target and accelerated by electrical means instead of direct acceleration only by using a laser beam. A fundamental study of newly developed rectangular laser-assisted pulsed-plasma thruster (PPT) was conducted. On discharge characteristics and thrust performances with increased peak current compared to our previous study to increase effects of electromagnetic forces on plasma acceleration. Maximum peak current increased for our early study by increasing electromagnetic effects in a laser assisted PPT. At 8.65 J discharge energy, the maximum current reached about 8000 A. Plasma behaviors emitted from a thruster in various cases were observed with an ICCD camera. It was shown that the plasma behaviors were almost identical between low and high voltage cases in initial several hundred nanoseconds, however, plasma emission with longer duration was observed in higher voltage cases. Canted current sheet structures were also observed in the higher voltage cases using a larger capacitor. With a newly developed torsion-balance type thrust stand, thrust performances of laser assisted PPT could be estimated. The impulse bit and specific impulse linearly increased. On the other hand, coupling coefficient and the thrust efficiency did not increase linearly. The coupling coefficient decreased with energy showing maximum value (20.8 ?Nsec/J) at 0 J, or in a pure laser ablation cases. Thrust efficiency first decreased with energy from 0 to 1.4 J and then increased linearly with energy from 1.4 J to 8.6 J. At 8.65 J operation, impulse bit of 38.1 ?Nsec, specific impulse of 3791 sec, thrust efficiency of 8 %, and coupling coefficient of 4.3 ?Nsec/J were obtained.

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A Study on the Supporting Method of the Nemok-dori (내목도리 지지 방식에 관한 연구)

  • Heo, Kyoung-Do;Chung, Myung-Sup
    • Journal of the Architectural Institute of Korea Planning & Design
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    • v.36 no.3
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    • pp.69-78
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    • 2020
  • This study is designed to find out the role and relation of the Nemok-dori support members in order to clearly specify the structure of the Dapogye architecture which adopts the Nemok-dori. The dori at the eaves in the Dapogye architecture was expanded to include Oemok-dori, Jusim-dori and Nemok-dori in cooperation with the bracket. The Oemok-dori is used to lengthen the eaves and the Jusim-dori makes the reasonable transfer of loads while the Namok-dori contributes to the stability of the building through the balancing of the bracket. Nemok-dori is located higher than Oemok-dori or Jusim-dori, depending on the slope of Jangyeon and the distance of Chulmok. But as it is not directly supported by bracket or beam, it needs an independent support. The vertical support of Nemok-dori is selectively involved with Cheomcha, lower Jangyeo, support Wall and upper Jangyeo. As the time went by, the vertical height increased, thus making the omitted members less. The horizontal support of Nemok-dori is made in various ways. There are also special cases such as the Nemok-dori □ type chain structure for small rectangular buildings, the 'Nemok-dori = Jung-dori' type for the buildings having small sides and the 'Nemok-dori = Meongechangbang' type appearing on the lower part of the Bankanmulrim type middle height buildings. The horizontal support of Nemok-dori usually uses either the support of the Toeryang type member, the support of beam directed Hwaban or the support through overlaying of internal Jegong. As the time went by and the number and distance of Chulmok increased, the multiple support structures acted together rather than as one support structure. Nemok-dori got stabilized as it has both the vertical and horizontal supports and this support structure also has he role of decoration.