Abstract
Thin rings and arches (high or low) are often used as structural elements and, when loaded in their plane and in a normal direction, are subject to instability. This chapter presents the analyses of thin circular rings, high circular arches, and low arches. In addition, the analysis of a low half-sine arch, loaded by a half-sine distributed load, resting on an elastic foundation, and pinned at both ends is discussed. This is an interesting model because, depending on the values of the rise parameter and the modulus of the foundation, it exhibits the possibilities of limit point stability (top-of-the-knee buckling), snapthrough buckling through unstable bifurcation, and classical stable bifurcation buckling. For all cases, it is assumed that the behavior of the material is linearly elastic.
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