• Structural Engineering and Mechanics
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• v.59 no.3
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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.

• Journal of the Korean Society for Precision Engineering
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• v.3 no.4
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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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• v.22 no.5
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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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.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.3
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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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.

• Journal of Korean Society of Steel Construction
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• v.18 no.2
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• pp.203-211
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• 2006

This paper presents a new, effective torsional constant for thin-waled open beams under concentrated and uniformly distributed torques. The proposed constant can be used directly, instead of the St. Venant torsional constant, for any generic comemrcial finite-element program, without modifying the algorithm. The derived torsional constant accounts for both the pure torsion and the warping torsion, and is equal to the St. Venant torsion constant times a correction factor. It is also shown, in the case of the St. Venant torsion, that the derived constant is identical to the torsional constant. The derived effective torsional constant is different from the one given by Elhelbawey et al. The pure torsional shear stress, the warping shear stress, and the warping normal stress were also determine d, using the maximum twisting angle. The accuracy of the proposed torsional constant was validated by comparing the numerical results with the closed-form solutions or other numerical results available in the literature.

• Proceedings of the KSR Conference
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• 2003.10b
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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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.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.51-60
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• 2004

The stress analysis of cold-formed channel section steel beams under transverse load was conducted. The local buckling effect was included in the analysis using effective area concept. The proposed analytical model is capable of predicting accurate normal stress in the beam due to various behaviors including biaxial bending and warping. It was found to be appropriate for predicting stresses as well as deflection in the beam. A finite element model was developed to solve the analytical model.