Shear Buckling of Bars

It is shown that a perfectly straight bar, subjected to a state of uniform shear stress, will buckle, in a manner similar to a column under compression, if the shear stress exceeds a certain critical value. The buckling equations are obtained by the Newtonian approach and also by the application of the principle of minimum potential energy. In order to provide additional insight into this buckling mechanism, a simple model is introduced and analyzed.