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Buckling of Thin-Walled Circular Cylinders (NASA SP-8007)

Structural components are said to be unstable under static loading when infinitesimal load increases or other small disturbances will induce the structure to change from one equilibrium configuration to another of a different character. For some structures and loadings the two configurations may differ slightly and large changes of shape develop gradually with an increase of load. In this case, the initial buckling load merely indicates when a change in the character of the deformations will occur. Generally, a more significant load is the ultimate load of the structure which may be reached either when the material fails plastically or when the structure collapses. In other instances the two equilibrium configurations differ greatly and the transition from one to the other is extremely rapid. The structure usually loses its capacity to sustain further load increases orjt undergoes large deformations that render it unsafe for continued use. 

The primary design problem is the prevention of the buckling that leads to undesirable configurations - in particular, collapse. The magnitude of the critical static load of a structure generally depends on its geometric proportions, the manner in which it is stiffened and in which it is supported, the bending and extensional stiffnesses of its various components, or other reasonably well-defined characteristics. For thin-walled shell structures, less certain characteristics, such as small deviations of the structure from its nominal unloaded shape, may also have quite important effects on the load at
which buckling will occur. Other factors that affect buckling, such as cutouts, nonuniform stiffnesses, and variation of loading with time, are not  considered in this monograph.

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