Nonlinear analysis of thin walled bars of open cross-section

Abstract Energy equations governing the goemetrically nonlinear behaviour of thin walled bars of open cross-section when subjected to axial, flexural and torsional displacements, are derived. The equations are based on the assumption of small displacements and linear elastic material behaviour. Shear deformations due to nonuniform bending, and distortion of the cross-section are not included in the analysis. Solutions of the governing nonlinear equations are obtained by the finite element method, making use of linearised mid-increment stiffness matrices. The results of the geometrically nonlinear analysis are combined with an approximate failure criterion to predict the failure loads of I beams having initial imperfections. The predicted failure loads are compared, and show satisfactory agreement, with existing experimental results.

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