Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method

Abstract

The finite difference method has been used to solve the differential equation for the critical loading associated with a specific lateral-torsional buckling test configuration. The linear elastic analysis is valid for thin-walled composite doubly symmetric I-beams made from mid-plane symmetric, fibre-reinforced laminated panels. Here, the test configuration has an I-beam with specially orthotropic panels. It is subjected to three-point bending, and supported at each end such that the only degree of freedom is rotation about the major axis of the beam. For the modelling case where the central load is applied at the shear centre (centroid) of the cross-section there is a favourable comparison between the finite difference results and those results presented by Timoshenko and Gere (1961, Theory of Elastic Stability 2nd edn, McGraw-Hill, New York), which were originally generated for isotropic beams. A favourable comparison has also been found between the finite difference analysis and experimental evidence using an E-glass fibre-reinforced polymeric pultruded I-beam, where the central load is now applied to the top compression flange. The various theoretical models presented in the paper are used to show that the critical loading for buckling in real composite I-beams will be strongly dependent on both the support boundary conditions and the height of the loading relative to the centroid (shear centre).