Elastic Stability of Tapered I-Beams

In this paper, the differential equation for the nonuniform torsion of tapered I-beams is derived by analyzing the deformations of the flanges, and this equation is used to study the elastic flexural-torsional buckling of simply supported tapered I-beams. For constant flange beams which are tapered in depth, it is found that the changes in the torsional stiffness with the degree of taper are small, and that consequently the elastic critical loads do not vary greatly. The elastic critical loads of constant depth beams which have tapered flanges decrease significantly as the degree of taper increases. Torsion tests were carried out on tapered depth cantilevers and the results of these were in close agreement with the theoretical predictions. Buckling tests were carried out on simply supported I-beams which were tapered in flange width, thickness or web depth, and the experimental critical loads confirmed the theoretical predictions.