Large deflection analysis of a thin walled channel section cantilever beam

Abstract

For a special application the large deflection behaviour of thin walled channel section beams made of thin sheet steel has been investigated. The experiments consisted of cantilever bending tests with the beam loaded through the shear centre and through the centroid. When loaded through the shear centre the beam buckling took place in the compression flange at the root of the cantilever. When loaded through the centroid however, it was noted that the compression flange buckled at a fixed distance from the fixed end. The general theory of thin walled beams developed by Vlasov was applied to the problem and indicated that the maximum compression stress at the edge of the flange would be at some distance from the fixed end. The value of the maximum compression stress obtained by the general linear theory was small and its position did not coincide with the experimental position. The Vlasov analysis has been modified to include the increase in the twisting moment due to the lateral deformation of the beam along its length. Good agreement between the modified theory and experiment both for the position of the maximum compressive stress and for the twist of the cantilever at three points along its length. Because of the very low torsional stiffness of thin walled channel sections, the small deflection theory is only applicable for small bending loads applied through the centroid and the modified theory should be used for practical loading cases.