Elastic Flexural Buckling Load for Tapered Columns in Gabled Frames sway is permitted with Finite Differences and Virtual Work Methods

In this paper flexural buckling load for tapered columns has been evaluated (in-plane buckling of frame). The studied issue is a one-bay frame, its two bases are hinged or rigid, and sway is permitted. The analysis is done by finite differences and virtual work methods. First the length column divided into "n" pieces and the deformation differential equation is approximated in form of finite differences. In this process "n-1" linear equations are obtained which are composed of "n" variables. The variables are the lateral displacement of specified points on the length of the column. For the continuation of the problem an equation is required. It can be gained by the virtual work and consideration of the displacement boundary condition in the top of the column. When the corresponding square matrix of the equations collection is available the critical load will be calculated. The equation obtained by equating the determinate of that matrix to zero has "n" roots. The minimum root is the critical load. 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.