Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T03:10:20.746Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

Published online by Cambridge University Press:  22 March 2012

J. D. Yau  and
S.-R. Kuo
J. D. Yau*
Affiliation:
Department of Architecture, Department of Transportation Management, Tamkang University, New Taipei City, Taiwan 25137, R.O.C.
S.-R. Kuo
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C
*
*corresponding author ([email protected])
Get access

Abstract

Using conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yang et al.'s simplified geometric stiffness matrix [kg]12×12 of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14 of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14 matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14 matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Keywords

Geometric nonlinear analysisRigid beamThin-walled beamWarping
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 97 - 106
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Johnston, B. G., “Lateral Buckling of I-section Columns with Eccentric Loads in Plane of Web,” Journal of Applied Mechanics, 20, p. 180 (1941).Google Scholar
2. Bleich, F., Buckling Strength of Metal Structures, McGraw-Hill, New York (1952).Google Scholar
3. Chen, W. F. and Atsuta, T., “Theory of Beam-Columns,” 2, Space Behavior and Design, McGraw-Hill, New York (1977).Google Scholar
4. Timoshenko, S. P. and Gere, J. M., Theory of Elastic Stability, 2nd Ed., McGraw-Hill, New York (1961).Google Scholar
5. McGuire, W., Steel Structures, Prentice-Hall, New Jersey (1968).Google Scholar
6. Kitipornchai, S. and Trahair, N. S., “Elastic Stability of Tapered I-beams,” ASCE Journal of Structural Division, 98, pp. 713–728 (1972).Google Scholar
7. Kitipornchai, S. and Trahair, N. S., “Elastic Behavior of Tapered Monosymmetric I-beams,” ASCE Journal of Structural Division, 101, pp. 1661–1678 (1975).Google Scholar
8. Trahair, N. S., Flexural-Torsional Buckling of Structures, E & FN Spon, London, UK (1993).CrossRefGoogle Scholar
9. Vlasov, V. Z., Thin-Walled Elastic Beams, 2nd Ed., Moscow, English translation, Jerusalem: Israel Program for Scientific Translation (1961).Google Scholar
10. Yang, Y. B. and Kuo, S. R., Theory & Analysis of Nonlinear Framed Structures, Prentice Hall, Singapore (1994).Google Scholar
11. Yang, Y. B. and McGuire, W., “Stiffness Matrix for Geometric Nonlinear Analysis,” ASCE Journal of Structural Engineering, 112, pp. 853–877 (1986).Google Scholar
12. Yang, Y. B. and McGuire, W., “Joint Rotation and Geometric Nonlinear Analysis,” ASCE Journal of Structural Engineering, 112, pp. 879–905 (1986).Google Scholar
13. Yang, Y. B. and Chiou, H. T., “Rigid Body Motion Test for Nonlinear Analysis with Beam Elements,” ASCE Journal of Engineering Mechanics, 113, pp. 1404–1419 (1987).Google Scholar
14. Yang, Y. B., Chang, J. T., and Yau, J. D., “A Simple Nonlinear Triangular Plate Element and Strategies of Computation for Nonlinear Analysis,” Computer Methods in Applied Mechanics and Engineering, 178, pp. 307–321 (1999).CrossRefGoogle Scholar
15. Yang, Y. B., Kuo, S. R. and Wu, Y. S., “Incrementally Small-Deformation Theory for Nonlinear Analysis of Structural Frames,” Engineering Structures, 24, pp. 783–798 (2002).Google Scholar
16. Yang, Y. B., Lin, S. P. and Leu, L. J., “Solution Strategy and Rigid Element for Nonlinear Analysis of Elastic Structures Based on Updated Lagrangian Formulation,” Engineering Structures, 29, pp. 1189–1200 (2007).Google Scholar
17. Yang, Y. B., Lin, S. P. and Chen, C.S., “Rigid Body Concept for Geometric Nonlinear Analysis of 3D Frames, Plates and Shells Based on the Updated Lagrangian Formulation,” Computer Methods in Applied Mechanics and Engineering, 196, pp. 1178–1192 (2007).Google Scholar
18. Kwak, H. G., Kim, D. Y. and Lee, H. W., “Effect of Warping in Geometric Nonlinear Analysis of Spatial Beams,” Journal of Constructional Steel Research, 57, pp. 729–751 (2001).Google Scholar
19. Lin, W. Y. and Hsiao, K. M., “Co-Rotational Formulation for Geometric Nonlinear Analysis of Doubly Symmetric Thin-Walled Beams,” Computer Methods in Applied Mechanics and Engineering, 190, pp. 6023–6052 (2001).CrossRefGoogle Scholar
20. Lin, W. Y. and Hsiao, K. M., “More General Expression for the Torsional Warping of a Thin-Walled Open Section Beam,” International Journal of Mechanical Science, 45, pp. 831–849 (2003).CrossRefGoogle Scholar
21. Chen, H. H., Lin, W. Y. and Hsiao, K. M., “Co-Rotational Finite Element Formulation for Thin-Walled Beams with Generic Open Section,” Computer Methods in Applied Mechanics and Engineering, 195, pp. 2334–2370 (2006).Google Scholar
22. Chen, H. H. and Hsiao, K. M., “Coupled Axial–Torsional Vibration of Thin Walled Z-Section Beam Induced by Boundary Conditions,” Thin-Walled Structures, 45, pp. 573–583 (2007).Google Scholar
23. Chen, H. H. and Hsiao, K. M., “Quadruply Coupled Linear Free Vibrations of Thin-Walled Beams with Generic Open Section, Engineering Structure, 30, pp. 1319–1334 (2008).CrossRefGoogle Scholar
24. Yang, Y. B., Kuo, S. R. and Cherng, Y. D., “Curved Beam Elements for Nonlinear Analysis,” ASCE Journal of Engineering Mechanics, 115, pp. 840–855 (1989).Google Scholar
25. Yang, Y. B. and Yau, J. D., “Stability of Beams with Tapered I-sections,” ASCE Journal of Engineering Mechanics, 113, pp. 1337–1357 (1987).Google Scholar
26. Yau, J. D., “Stability of Tapered I-Beams Under Torsional Moments,” Finite Element Analysis and Design, 42, pp. 914–927 (2006).Google Scholar
27. Yau, J. D., “Elastic Stability of I-Columns Subjected to Compressions and Bi-moments,” Journal of Chinese Institute Engineers, 30, pp. 569–578 (2007).Google Scholar
28. McGuire, W. and Gallagher, R. H., Matrix Structural Analysis, John Wiley & Sons Inc., New York (1979).Google Scholar
29. Yang, Y. B. and Shieh, M. S., “Solution Method for Nonlinear Problems with Multiple Critical Points,” Journal of AIAA, 28, pp. 2110–2116 (1990).Google Scholar
30. Izzuddin, B. A. and Smith, D. L., “Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. I: Formulation and Implementation, Journal of Structural Engineering, ASCE, 122, pp. 905–914 (1996).CrossRefGoogle Scholar
31. Izzuddin, B. A. and Smith, D. L., “Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. II: Verification and Application,” ASCE Journal of Structural Engineering, 122, pp. 915–925 (1996).CrossRefGoogle Scholar
32. Yau, J. D., “An Iterative Approach for Linear Torsion Analysis of Web-tapered I-Beams Using Uniform I-beam Element, International Journal of Structural Stability and Dynamics, 8, pp. 521–529 (2008).Google Scholar
33. Andrade, A. and Camotim, D., “Lateral–Torsional Buckling of Singly Symmetric Tapered Beams: Theory and Applications, ASCE Journal of Engineering Mechanics, 131, pp. 586–597 (2005).Google Scholar