When a casing buckles in three dimensions, torques, as well as bending moments, are developed. Since well casing is joined with threaded collars, it is necessary to know the magnitude of the twist of the casing to evaluate the risk of buckling failure. In this work, the strain energy for a three-dimensionally buckled column is developed and the differential equations of buckling are derived and solved for helical buckling, buckling caused by an applied moment, and combined end loading and torque.

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