Characteristic Equation of Flexural Buckling of Columns in Two-bay Gable Frames for State of Free to Sway

In this paper flexural buckling load for tapered columns has been evaluated (in-plane buckling of frame). The studied issue is about two-bay frames. Their three bases are hinged, and sway is permitted. The analysis is based on the answer of the deformation differential equation of the column, imposing the boundary conditions at the tips of the columns, and the displacement compatibility equations at the nodes of the members. Therefore, a set of equations could be obtained. When the corresponding square matrix of the equations collection is available, the critical load will be calculated. The critical load is the minimum root of the characteristic equation. This equation is obtained by equating the determinate of that matrix to zero. The results of the analysis are compared with the other methods of other researchers in some examples. The comparison showed that the introduced method can calculate the critical load with a good accuracy. This method can be generalized for other frames made of tapered members.