Thermal Buckling and Snapping of a Circular Ring

An analysis is made of the thermal buckling of flat rings and of shallow conical rings which are subjected to an axisymmetric temperature distribution. It is found that flat rings can buckle when there is a radial temperature variation only. Conical rings are subject to instability and snapping in the presence of either an axial temperature variation alone, or a combined axial and radial temperature variation, of the proper magnitude. Expressions are developed which give the temperatures at which buckling and snapping take place, as well as the temperature over-lap in a full thermostatic cycle of increasing and decreasing temperatures. Bimetallic conical rings at uniform temperature are examined, and snapping temperatures are determined for this type element.