A set of accurate buckling equations recently developed by the authors is used to compute the buckling loads of axially compressed circular cylindrical shells subject to “relaxed,” incremental boundary conditions. Over a large range of values of the length to radius ratio, L/R, the buckling loads are essentially 1/2 of the classical value, as has been found by many previous investigators using the simplified Donnell buckling equations. However, it is shown that as L/R → 0 or as L/R → ∞, the buckling loads approach zero, in contrast to the behavior predicted by the Donnell equations. The correct behavior as L/R → 0, first discovered by Koiter, may be interpreted as the buckling of a ring-beam constrained between two rigid, concentric, frictionless cylinders. The behavior as L/R → ∞ simply represents Euler column buckling.

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