4, 4, pp. 545-564, 1956
The buckling problem of annular elements (which is the basic problem for tubes, tanks, etc.) is treated in this paper, the buckling force being due to a hooping around the element (by means of prestressed reinforcement). The problem is solved in the range of linear elasticity on the basis of the non-linear theory of thin bars; the solution is obtained in the form of elliptic integrals. It is shown that the form of the equilibrium in the undeformed state is stable, in principle, for any finite value of the stressing force. The (durably) deformed shape can be reached under the influence of an instantaneous forced deformation of finite value. This value tends to zero if the stressing force tends to infinity. The critical value of the prestressing force for which this "jump" is possible, is calculated. On the basis of the general theory approximate equations for the critical force are obtained, as well as the limit value of slenderness of the elements for different materials, such as concrete, cast iron, steel [Eqs. (3.9), (3.10) and the following]. It is also shown that the problem can be of considerable practical importance, especially for
prestressed metal elements.
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).
E. P. Popow, Nieliniejnyje zadaczi statiki tonkich stierzniej, Gostiechizdat, 1948.