End Effects of Thin-Walled Beams with General Quadrilateral Cross Sections

일반 사각 단면 형상을 갖는 박판보의 끝단효과에 관한 연구

Kim, Jin-Hong;Kim, Yun-Yeong

  • Published : 2000.09.01


End effects due to sectional deformations of thin-walled beams with closed cross section are analysed by a one-dimensional theory. In particular, end effects associated with warping (out of plane m otion) and distortion (in plane motion) are investigated. The exact solutions as a vector form are newly derived to reveal slowly-decaying nature of the end effects in a thin-walled beam loaded by a couple. Several examples of thin-walled beams under various loading conditions indicate that the local end effect zone due to warping and distortion is approximately ten times the typical beam width.


Thin-Walled Beam;Quadrilateral Cross Section;Distortion;Warping;End Effects


  1. Oden, J. T., 1967, Mechanics of Elastic Structures, McGraw-Hill, New York
  2. SDRC, 1993, I-DEAS FEM User's Guide, Structural Dynamics Research Corporation, Milford
  3. Steele, C. R. and Balch, C. D., 1988, Shells of Revolution With Axlsymmetrics Loadings, Stanford University Lecture Note
  4. Paavola, J., 1992, 'A Finite Element Technique for Thin-Walled Girders,' Computers & Structures, Vol. 44, (1/2), pp. 159-175
  5. Balch, C. D. and Steele, C. R., 1987, 'Asymptotic Solutions for Warping and Distortion of Thin-Walled Box Beams,' ASME Journal of Applied mechanics, Vol. 54, pp. 165-173
  6. Gjelsvik, A., 1981, The Theory of Thin Walled Bars, Jhon Wiley & Sons, New York
  7. Steel, C. R. and Balch, C. D., 1970. Shells of Revolution With Axisymmetric Loading, McGraw-Hil 3rd ed., New York
  8. Boswell, L. F. and Zhang, S. H., 1985, 'An Experimental Investigation of the Behavior of Thin-Walled Box Beams,' Thin-Walled Structures, Vol. 3, pp. 35-65
  9. Boswell, L. F. and Zhang, S. H., 1983, 'A Box Beam Finite Element for the Elastic Analysis of Thin-Walled Structures,' Thin-Walled Structures, Vol. 1, pp. 353-383
  10. Mikkola, M. J. and Paavola, J., 'Finite Element Analysis of Box Girders,' Journal of the Structural Division, ASCE, Vol. 106, (ST6), pp. 1343-1357
  11. Kim, J. H. and Kim, Y. Y., 1999, 'Analysis of Thin-Walled Closed Beams with General Quadrilateral Cross Sections,' ASME Journal of Applied Mechanics, Vol. 66, No. 4, pp. 904-912
  12. Kim, Y. Y. and Kim, J. H., 1999, 'Thin-Walled Closed Box Beam Element for Static and Dynamic Analysis,' International Journal for Numerical Methods in Engineering, Vol. 45, pp. 473-490<473::AID-NME603>3.0.CO;2-B
  13. 양웅필, 신효철, 1996, '임의 형상의 단면을 갖는 박판보의 유한요소해석,' 대한기계학회논문집, 제20권, 제1호, pp. 100-144
  14. 김윤영, 김진흥, 송상헌, 1998, '버틀림을 받는 직사각 폐단면 박판보 유한요소 개발,' 대한기계학회논문집, 제22권, 제6호 pp. 947-954
  15. Vlasov, V. Z., 1961, Israel Program for Scientific Translations(2nd ed.),Thin Walled Elastic Beams, Jerusalem
  16. 김윤영, 김진흥, 강정훈, 임흥재, 1995, '박스보 T형 조인트의 강성 평가에 관한 연구,' 한국자동차공학회 논문집, 제3권 제4호, pp. 68-77
  17. Timoshenko, S. P. and Gere, J. M., 1963, Theory of Elastic Stability, McGraw-Hill, 2nd ed.