• Structural Engineering and Mechanics
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• 제59권3호
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• pp.527-537
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• 2016

We describe a stress analysis of a single leaf flexure under torsion in which the warping effect is considered. The theoretical equations for the warping normal stress (${\sigma}_{xx}$) and shear stresses (${\tau}_{xz}$ and ${\tau}_{xy}$) are derived by applying the warping function of a rectangular cross-sectional beam and the twist angle equation that includes the warping torsion. The results are compared with those of the non-warping case and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory of warping stress results and the FEA results are lower than 4%. This indicates that the proposed theoretical stress analysis with warping is accurate in the torsion analysis of a single leaf flexure.

• 한국정밀공학회지
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• 제3권4호
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• pp.53-63
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• 1986

In this study, the stress distribution of rectangular bar under torsion, when warping of both ends is free or constrained, is investigated. Method of separation of variable and Fourier Series are used for the theoretical analysis, and 3dimensional photoelastic stress-freezing method for experimental analysis. The main results are as follows; 1) In the case of warping-constrained rectangular bar, the normal stresses are negligible because they are less then 0.5% of the shear stresses. The maximum normal stress is placed on the point of y=0.61 b when b/a=1 and it gradually moves to the corner y=b when the value of b/a is increased. 2) According to increase of the value of b/a, on the crossection, the maximum shear stress is placed on the middle point of the long side (x=${\pm}a$, y=0) when warping of both ends is free but the middle of the short side (x=0, y=${\pm} b$) when warping is constrained. The stress distribution is straight line when warping is constrained, namely, the stress distribution is proportional to the distance from the axis of centroid, but parabolic when warping is free. 3) The values of the combined stress of warping-constrained bar, if the influence of the loaded point is neglected, are generally smaller than those of warping-free.

• Structural Engineering and Mechanics
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• 제22권5호
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• pp.599-611
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• 2006

The theory with hierarchical warping functions had been used to analyze composite thin-walled structure, laminated beam and had good results. In the present paper, a series of hierarchical warping functions are developed to analyze the cylindrical bending problems of composite lamina. These warping functions which refine through-the-thickness variation of displacements were composed of basic and corrective functions by taking into account of anisotropic, material discontinues, and transverse shear and normal strain. Then the hierarchical finite element method was used to form a numerical algorithm. The distribution of the displacements, in-plane stresses, transverse shear stresses and transverse normal stress for composite laminate were analyzed with the present model. The results show that the present model has precise mechanical response compared with the first deformation transverse theory and the corrective order affects the accuracy of result.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.435-442
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• 2002

In a multicell box structure, distortional warping normal stress due to warping of cross section and transverse bending normal stress of walls due to distortion of cross section may consider as significant stresses unless distortion of box section is appropriately restricted. Nevertheless, during the past decades, no evaluation of distortional warping and transverse bending resistances for the multicell box section has been performed owing to geometric complexity and Insufficient information with respect to the distortion of multicell box section. The objective of present study is to evaluate the distortional warping and transverse bending resistances for the distortion of multicell box section and to validate the resistances through box girder analyses using multicell box beam element developed and conventional shell element. This developed box beam element has nine degrees of freedom per node including the effect of distortion.

• 한국자동차공학회논문집
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• 제13권3호
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• pp.146-153
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• 2005

Structural design of the torsion beam rear suspension is investigated by calculating warping of the torsion beam. Since the longitudinal displacement in the cross section of the torsion beam due to torsional moment causes normal stress across the beam restrained from outside at both ends, the profile of torsion beam needs to be designed considering the warping. Warping function of the beam is derived with the parameters of cross section fur the arbitrary shapes of torsion beam profiles assuming thin-walled open section. From comparing the warping calculated for two different beam profiles, the design method for the torsion beam in the view point of low stress is discussed. It is shown that the gusset used to reinforce the torsion beam can be optimized in accordance with warping shape. The method to fix the end point of the gusset is proposed to minimize the stress concentrated on the end point of the gusset produced during torsional moment. The result from finite element analysis shows the stress is minimized when the height of gusset end point is coincident with the point where warping of the beam is minimized.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 봄 학술발표회 논문집
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• pp.335-342
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• 1999

It is well known that l-girders are weak in torsion and it might be more economical to use a box girder, which has great torsional rigidity. The use of box beams does, however, present a potential problem in that cross-sectional distortions can induce large warping normal stresses and transverse bending stress. Accordingly a sufficient number of diaphragms are provided to make the distortional effects minimal. In engineering practice, diaphragms are spaced in 5m intervals without reasonable basis. It is considered to be noneconomical design to the almost design engineers, and it may produce the unsafe structural systems in special cases such as curved bridges with large initial curvature. These problems have not been solved for the lack of adequate tools of structural analysis. In this study, on the basis of the parametric studies, the design formulas for the distortional warping stress and the reasonable diaphragm spacing of box girder were presented.

• 한국강구조학회 논문집
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• 제18권2호
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• pp.203-211
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• 2006

본 논문에서는 집중 비틂모멘트와 등분포 비틂모멘트가 작용하는 박벽개보의 뒴구속에 대한 영향을 고려할 수 있는 새로운 유효비틀림계수를 제시한다. 상용 유한요소 프로그램의 알고리즘을 바꾸지 않고 순수 비틀림계수 대신에 제안된 비틀림계수를 직접 사용할 수 있다. 유도된 비틀림계수는 순수 비틀림과 뒴 비틀림에 의한 영향을 고려하며 순수 비틀림계수에 보정계수를 곱하여 산정한다. 순수 비틀림의 경우 유도된 계수는 순수 비틀림계수와 일치하게 나타났다. 순수 비틀림을 이용하여 본 연구에서 유도한 유효 비틀림계수는 Elhelbawey 등이 제안한 비틀림계수와 차이를 보여주고 있다. 또한, 유효 비틀림계수를 사용하여 구한 최대비틀림각을 이용하여 부재 내 에 발생하는 전단응력과 다른 연구자의 결과들과 비교, 검토한다.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2003년도 추계학술대회 논문집(II)
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• pp.522-530
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• 2003

Generally, diaphragms are installed in the box girder to prevent or decrease the distortion of the cross section. In engineering practice, diaphragms are spaced in 5m intervals without reasonable basis. the usual diaphragm type is solid-plate type. It is considered to be noneconomical design to the almost design engineers. In this paper, the parametric study was performed to present the design proposal about the diaphragm stiffness and spacing only in the single cell box girder. For that, the distortional warping normal stress, bending normal stress and transverse bending normal stress were analyzed using finite element program 'SMB' for the accurate structural analysis.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.133-144
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• 2003

Generally, diaphragms are installed in the box girder to prevent or decrease the distortion of tile cross section. In engineering practice, diaphragms are spaced in 5m intervals without reasonable basis. ANd the usual diaphragm type is solid-plate type. It is considered to be noneconomical design to the almost design engineers. In this paper, the parametric study was performed to present the design proposal about the diaphragm stiffness and spacing only in tire single cell box girder. For that, the distortional warping normal stress, bending normal stress and transverse bending normal stress were analyzed using finite element program 'SMB' for the accurate structural analysis.

• 한국강구조학회 논문집
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• 제16권1호통권68호
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• pp.51-60
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• 2004

본 논문에서는 냉간성형 ㄷ 형강보에 대해 국부좌굴을 고려한 휨해석을 하였다. 유한요소법을 이용하여 주어진 하중 상태에서의 응력을 구한후 국부좌굴 효과를 고려하기 위해규준에서 주어진 유효폭 개념을 이용하여 유효 단면적을 결정하였으며, 결정된 유효 단면적으로부터 응력을 계산 하였다. x축에 대한 휨응력 뿐 아니라 y축에 대한 휨응력과 뒤틀림 응력값을 고려하였으며, 이를 하중이 전단중심에 작용하는 경우와 도심에 작용하는 두가지의 경우에 대하여 연구를 수행하였다. 연구 결과는 하중-처짐 곡선으로 나타내었다.