Non-sway In-plane Buckling of Columns in Gable Frames with Virtual Work and Finite Differences Methods

In this paper, non -sway flexural buckling for non-prismatic columns is analyzed. The studied structures are one-bay gable frames, which are evaluated for in-plane buckling, and their two bases are hinged or rigid using virtual work and finite difference methods. First, the length of the column is divided into "n" parts. Then the deformation differential equations of these parts are converted into finite difference forms. Thus "n-1" linear equations with "n" variables are obtained. These variables are the lateral displacements of the specified points on the length of the column. Now, an equation is required to complete the system of linear equations.  It can be obtained by employing the virtual work method. The equations’ system corresponds to a matrix equation in which the coefficient matrix is a square matrix. By letting the determinant of this matrix be equal to zero, an n-degree linear equation is produced. The buckling load is the minimum root of this equation. The results are shown in dimensionless charts. To verify the results, some examples are solved with the introduced method and other methods. The comparison shows that the buckling load can be easily calculated using the introduced method with a good accuracy.