This paper is concerned with the theoretical study of the collapse of oil well casing under various loading conditions. The analysis is based on a model of a cylindrical shell of infinite length subjected to an axial tension and an external pressure. It is found that when the thickness-radius ratio of the casing is sufficiently small, collapse of the casing may take place in a form of plastic buckling. Critical conditions for plastic buckling are derived based on the J2-incremental theory and the J2-deformation theory. Another type of collapse is caused by the realization of the ultimate strength of the material. Critical conditions in the second case of collapse are calculated based on a plane strain formulation associated with the J2-incremental theory. The theoretical results obtained in this paper correspond well with empirical formulas developed earlier by the API for the design of oil well casing.

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