UDC

539.3

Authors

Dorogov Yuriy Ivanovich
Branch of Moscow Power Engineering Institute (National Research University) (Volzhski, Russia)
e-mail: ydorogov@yandex.ru

Abstract

The process of loss of stability of an elastic rod with hinged ends and elastic support at the midspan is considered in the paper. The dependence of a form of a rod axis in the buckling process and the buckling force, which is the reason of a loss of stability of a rod, on the stiffness factor of the center support, is investigated. The critical value of the support stiffness factor is found. The form of a rod axis in the course of the loss of stability at this value varies from one sine half-wave to full-wave sine wave. It is supposed that an unloaded rod has the initial deflection. The problem of transversive-longitudinal bending of an elastic rod with hinged ends is considered. The rod is loaded by longitudinal compressive force and lateral force applied at midspan. The stable equilibrium for a bar in compression in dependence on the magnitude of the longitudinal compressive stress is investigated. Various configurations of the curved axis of a rod at different values of lateral load are considered. The process of brittle fracture of the center support at the elastic rod buckling is investigated. The material of a support is infinitely strong at compression. Strong under compression bearing material is destroyed under tension. The state of the material under tension is determined by the complete diagram of loading describing the stress dependence on the deformation from the beginning of stress up to final fracture. It is established, if the support is subjected to partial destruction and because of this is limited tensile strong, the critical load, at which the system loses stable equilibrium, in contrast to the elastic support, is defined as the load bearing capacity of the “rod – support” system. The bearing capacity of the system is less than the critical load determined for a rod with the elastic support.

Keywords

elastic rod, loss of stability, elastic support, buckling, buckling force, stiffness factor

References

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