Stability of tapered I-Beams under torsional moments

Previous investigations on the buckling of torsionally loaded bars indicate that the critical loads depend upon the mechanical device that generates the end torque. By representing the torsional moment on an I-section as the combination of St. Venant and warping torsions, this study presents a finite element model for buckling analysis of tapered I-beams subjected to torsional moments. Regarding a tapered I-beam as the formation of three tapered narrow beams (the top flange, web, and the bottom flange), one can directly express the total potential energy equation of the tapered I-beam by summing up all the potential energy equations of these narrow beams based on Yang et al.'s well-developed potential equation of a tapered solid beam. As a result, the linear elastic and geometric stiffness matrices of a torsionally loaded I-beam element with tapered cross-section can be established from the total potential energy derived herein. It is worthy mentioning that the second-order effects of warping moments and non-uniform torsions have been included in the present geometric stiffness matrix. By buckling analysis, the numerical examples indicate that the warping and St. Venant torsions may significantly affect the flexural buckling resistance of tapered I-beams against torsional loadings. Besides, the critical loads of the tapered I-beams with higher warping rigidity would be reduced by the instability effect of warping moments.