Evaluation of Non-sway Flexural Buckling of One-bay Gabled Frames by Solving Characteristic Equation

Flexural buckling is one of the buckling limit states in columns, which have at least one symmetric axis. Due to the lack of analytical solution for the differential equation of deformation of a non-prismatic column, its flexural buckling load has been determined by numerical methods, resulting in approximate solutions. This research aims at the analytical evaluation of non-sway in-plane flexural buckling of one-bay industrial structures known as gabled frames with web-tapered members. All the two bases of the columns were hinged or fixed and the members followed Euler-Bernoulli beam theory. First, the differential equation of the deflected column and the suitable free body diagrams were considered. The equilibrium and differential equations were simultaneously used in the elastic flexural energy. By equating the external work on the structure with its internal elastic flexural energy, the characteristic equation (for critical load) is achieved and required graphs can be drawn. Design graphs are plotted for effective length coefficient. In each Cartesian coordinate system the vertical axis belongs to the values of effective length coefficient and the horizontal axis belongs to the values of "s/l" (the oblique beam length divided by the column length). Finally, some examples are solved with the proposed and approximate methods. In proposed method the effective length coefficient can be determined only with having two geometrical parameters of a gabled frame, using the relevant graph and short calculations. Accurate results and simple use of the drawn graphs are among the benefits of the introduced method.