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TECHNICAL PAPERS

Thin-Walled Multicell Beam Analysis for Coupled Torsion, Distortion, and Warping Deformations

[+] Author and Article Information
J. H. Kim, Y. Y. Kim

School of Mechanical and Aerospace Engineering and Institute of Advanced Machinery and Design, Seoul National University, Kwanak-Gu, Shinlim-Dong, San 56-1, Seoul 151-742, Korea

J. Appl. Mech 68(2), 260-269 (Oct 04, 2000) (10 pages) doi:10.1115/1.1357166 History: Received February 08, 2000; Revised October 04, 2000
Copyright © 2001 by ASME
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References

Timoshenko, S. P., and Gere, J. M., 1963, Theory of Elastic Stability, 2nd ed, McGraw-Hill, New York.
Vlasov, V. Z., 1961, Thin Walled Elastic Beams, Israel Program for Scientific Translations, Jerusalem.
Křı́stek,  V., 1970, “Tapered Box Girders of Deformable Cross Section,” J. Struct. Div. ASCE, 96, No. ST8, Proc. Paper7489, pp. 1761–1793.
Wright,  R. N., Abdel-Samad,  S. R., and Robinson,  A. R., 1968, “BEF Analogy for Analysis of Box Girders,” J. Struct. Div. ASCE, 94, No. St7, pp. 1719–1743.
Boswell,  L. F., and Zhang,  S. H., 1984, “The Effect of Distortion in Thin-Walled Box-Spine Beams,” Int. J. Solids Struct., 20, No. 9–10, pp. 845–862.
Balch,  C. D., and Steele,  C. R., 1987, “Asymptotic Solutions for Warping and Distortion of Thin-Walled Box Beams,” ASME J. Appl. Mech., 54, pp. 165–173.
Hsu,  Y. T., Fu,  S. S., and Schelling,  D. R., 1995, “EBEF Method for Distortional Analysis of Steel Box Girder Bridges,” J. Struct. Div. ASCE, 121, No. 3, pp. 557–566.
Kim,  J. H., and Kim,  Y. Y., 1999, “Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections,” ASME J. Appl. Mech., 66, pp. 904–912.
Kim,  J. H., and Kim,  Y. Y., 2000, “One-Dimensional Analysis of Thin-Walled Closed Beams Having General Cross Sections,” Int. J. Numer. Methods Eng., 49, pp. 653–668.
Jönsson,  J., 1999, “Distortional Warping Functions and Shear Distributions in Thin-Walled Beams,” Thin-Walled Struct., 33, pp. 245–268.
Razaqpur,  A. G., and Li,  H., 1991, “Thin-Walled Multicell Box-Girder Finite Element,” J. Struc. Eng. ASCE, 117, No. 10, pp. 2953–2971.
Razaqpur,  A. G., and Li,  H., 1994, “Refined Analysis of Curved Thin-Walled Multicell Box-Girders,” Comput. Struct., 53, No. 1, pp. 131–142.
Kim,  Y. Y., and Kim,  J. H., 1999, “Thin-Walled Closed Box Beam Element for Static and Dynamic Analysis,” Int. J. Numer. Methods Eng., 45, pp. 473–490.
Gjelsvik, A., 1981, The Theory of Thin Walled Bars, John Wiley and Sons, New York.
SDRC, 1993, I-DEAS FEM Users’ Guide, Structural Dynamics Research Corporation, Milford.

Figures

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A typical two-cell box beam
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Two independent preliminary distortion modes. These modes do not satisfy the rotation continuity and moment equilibrium at corners.
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Two independent distortion modes satisfying the rotation continuity and moment equilibrium at corners
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Shear flows of three adjacent cells J−1,J,J+1 of a multicell cross section associated with distortion and distortional warping
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Two distortional warping functions corresponding to the distortion functions shown in Fig. 6. Numbers denote the relative magnitudes of axial warping displacements.
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A two-cell box beam subjected to (a) a couple and (b) a set of three concentrated loads
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The vertical displacements uy along corner A. The results (a) and (b) correspond to the loading cases shown in Figs. 9(a) and (b), respectively. The number of the present beam finite elements is denoted by Ne.
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The distribution of the transverse bending stress σss at z=175 mm and n=t/2. The present results (solid lines) are compared with the finite element results (dotted lines) by IDEAS.
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Displacements at an arbitrary point of a thin-walled beam    
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Section deformations of a rectangular box beam for (a) warping, (b) rotation and (c) distortion. Dotted lines denote the deformed shapes. In this case, no distinction between torsional and distortional warping deformations is needed as they are identical.
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(a) A corner at which two walls meet and (b) a corner at which three walls meet
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The vertical displacement uy along corner A of a trapezoidal two-cell box beam under a couple (beam length=200 mm)
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The horizontal displacement ux along corner A in an unsymmetric two-cell beam under a couple (beam length=200 mm)
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(a) The fourth and (b) the seventh distortional eigenmodes of a two-cell box beam with a freely supported condition

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