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A refined finite element formulation for flexural and torsional buckling of beam–columns with finite rotations

Jian-Xin Gua, Siu-Lai Chanb

a College of Civil Engineering, Southeast University, Nanjing 210018, China

b Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong, China

Received 4 November 2003, Revised 28 December 2004, Accepted 28 December 2004


This paper describes a consistent formulation of a tangent stiffness matrix for the geometrically nonlinear analysis of the space beam–column elements allowing for axial–flexural, lateral–torsional and axial–torsional buckling. In the proposed formulation, three deformation matrices are derived for moderately large rotations in practical three-dimensional space frames subjected to axial force and moments. These matrices are functions of the element deformations and include the coupling among axial, lateral and torsional deformations. The proposed matrices are used together with linear and geometric stiffness matrices for beam elements to study the large deflection behavior of space frames which comprise members with negligible warping effects. Numerical examples show that the proposed element formulation is accurate and efficient in predicting the nonlinear behavior of space frames even when only a few elements are used to model a member.


Buckling; Flexural–torsional buckling; Second-order effects; Beam–columns; Elasticity; Bending; Torsion


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