Flexural-Torsional Buckling of Planar Frames

A method of analyzing flexural-torsional buckling frame failure is presented. The differential equations and equations of equilibrium and continuity at interior joints are derived by minimizing a total potential energy function for the structure. Although the paper is concerned with rectangular rigid frames, the equations are also applicable to single-span beams, continuous beams, and gabled frames. The differential equations are solved by numerical integration and the solution is used to set up a buckling determinant, which is evaluated for increasing estimates of the critical load until a value is found that makes the determinant zero. This value is the critical load for the structure. The effect of lateral bracing at the knees of a rigid frame on the flexural-torsional buckling load of the frame is investigated for three loading conditions: Lateral load at the top of the left column, transverse loads at third points of the beam section of the frame, and axial loads at the tops of the columns. The results are presented in graphical form.