Abstract
This paper is dealt with the in-plane elastic buckling of the circular ring which is supported by uniformly distributed springs in tangential directions and subjected to three types of external pressure. The acting directions of three types of loads after buckling are constant, normal to the surface and centripetal, respectively. The main conclusions are as follows. 1) The buckling mode is of a cos nθ type for the normal displacement, sin nθ for tangential displacement, and also sin riff for the rotation of section unless coupling terms between shear and others exist. 2) The effect of stretching strain on the buckling load is negligible small on the order of EI≪EAγ^2. 3) The values of buckling load are expressed in simple formula ignoring the stretching strain, and the effect of shear deformation and coupling rigidity between shear and bending is made clear. 4) A pracical procedure to obtain the buckling load is presented. 5) For free rings without tangential support, the buckling load subjected to the pressure of constant direction is not the well known result, p_α=4EI/γ^3, but zero accompanying the mode of rigid body rotation.
