Stateczność Prętów o Skokowo Zmiennym Przekroju Ściskanych Siłą Śledzącą

The stability analysis for the above bar (which is a cantilever bar) is done by introducing in the Lagrange equations a two-parameter family of elastic lines composed of two joined segments, the total number of boundary conditions being eight. After formulating the kinetic criterion, the tangential force is obtained in function of the location of the section jump and the ratio of moments of inertia.
The influence of the ratio of masses and moments of inertia of both parts of the bar on the magnitude of the critical force proves to be insignificant especially for J1/J2 < 1,0. An optimization analysis proves the possibility of saving about 6 per cent of the weight if a constant section bar is replaced by a sectionally constant section.