Lateral-torsional buckling of compressed and highly variable cross section beams

In the critical state of a beam under central compression a flexural-torsional equilibrium shape becomes possible in addition to the fundamental straight equilibrium shape and the Euler bending. Particularly, torsional configuration takes place in all cases where the line of shear centres does not correspond with the line of centres of mass. This condition is obtained here about a z-axis highly variable section beam; with the assumptions that shear centres are aligned and line of centres is bound to not deform. For the purpose, let us evaluate an open thin wall C-cross section with flanges width and web height linearly variables along z-axis in order to have shear centres axis approximately aligned with gravity centres axis. Thus, differential equations that govern the problem are obtained. Because of the section variability, the numerical integration of differential equations that gives the true critical load is complex and lengthy. For this reason, it is given an energetic formulation of the problem by the theorem of minimum total potential energy (Ritz-Rayleigh method). It is expected an experimental validation that proposes the model studied.