Out‐of‐Plane Buckling Formulas for Beam‐Columns/Tie‐Beams

This paper shows that the closed form expression for the elastic out‐of‐plane buckling of doubly symmetric beam‐columns under uniform moment can be expressed in form similar to that of beams by introducing a beam‐column parameter, $\eta ={\mathrm{4r}}_o^2/h^2$ in which $r_o$ is the radius of gyration about the centroid and h is the distance between flange centroids. The closed form solution is equally applicable to tie‐beams. For beam‐columns/tie‐beams under other loading conditions, accurate solutions are determined using the Rayleigh‐Ritz energy approach. Approximate formulas to predict the out‐of‐plane buckling capacities of the beam‐columns/tie‐beams under moment gradient, uniformly distributed load, and central concentrated load are presented. The proposed moment modification factor formulas furnish reasonably accurate predictions of the buckling capacities of beam‐columns/tie beams and may thus be adopted by code rules.