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

• Published in: Journal of mechanics 2012-03, Vol.28 (1), p.97-106
• Main Authors: Yau, J. D., Kuo, S.-R.
• Format: Article
• Language: English
• Subjects: Analysis; Finite element method; H beams; I beams; Load; Materials science; Mechanics; Nonlinearity; Stiffness; Stiffness matrix; Studies; Warpage; Warping
• ISSN: 1727-7191; 1811-8216
• DOI: 10.1017/jmech.2012.10

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.