A prestressing appts for a pressure vessel, esp. a nuclear reactor pressure vessel, consists of hoop tendons resting on shoes which bear in turn against the outer face of the pressure vessel. The tendons are stressed by a removable piston device or other type of apparatus. The seating face of the shoes on which the tendons bear has a smaller radius of curvature than the pressure vessel itself; the shoes are equipped with a device to prevent tilting in the circumferential direction. This arrangement of shoes and tendons prevents tilting of the shoes with consequent indeterminate application of the prestressing force predominantly along one or other side of the shoe.
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