Calculation of Centrally Loaded Thin-Walled Columns Above the Buckling Limit

When thin-walled columns formed from flanged sheet, such as used in airplane construction, are subjected to axial load, their behavior at failure varies according to the slenderness ratio. On long columns the axis deflects laterally while the cross section form is maintained; buckling results. The respective breaking load in the elastic range is computed by Euler's formula and for the plastic range by the Engesser- Karman formula. Its magnitude is essentially dependent upon the length. On intermediate length columns, especially where open sections are concerned, the cross section is distorted while the cross section form is preserved; twisting failure results. The buckling load in twisting is calculated according to Wagner and Kappus. On short columns the straight walls of low-bending resistance that form the column are deflected at the same time that the cross section form changes - buckling occurs without immediate failure. Then the buckling load of the total section computable from the buckling loads of the section walls is not the ultimate load; quite often, especially on thin-walled sections, it lies considerably higher and is secured by tests. Both loads, the buckling and the ultimate load are only in a small measure dependent upon length. The present report is an attempt to theoretically investigate the behavior of such short, thin-walled columns above the buckling load with the conventional calculating methods