Operation of the steel rod when buckling under the action of compression loads.

The paper studies the behavior of a pivotally supported rod, the ends of which are fixed in the longitudinal direction under the action of a compressive load. The stability of a centrally compressed rod with an incompressible axis is considered if transverse reactions occur during buckling that are proportional to its deflections. It is assumed that these reactions are distributed along a vertical axis parallel to the axis of the rod and are determined by the coordinates in three-dimensional space x, y, and z. The equations are used, taking into account which it is possible to study the buckling of the rod in the case when the axis around which the cross sections rotate during the buckling does not shift. The condition is assumed that if the compressive force differs little from the critical load, then the resulting curved form of the rod equilibrium differs little from the rectilinear one, and the usual approximate expressions can be used to express the curvature. It is shown that in this case, the buckling of the rod in the planes of symmetry does not depend on torsion. When studying the stability of the rod under the action of end forces, it is shown that even in the first approximation, the results are close to the exact solution of F. S. Yasinsky. The stability of the supported rod is analyzed when the intensity of the longitudinal compressive load changes according to a linear law. The author believes that buckling occurs at a non-deformable surface. [ABSTRACT FROM AUTHOR]