A problem of prestressed concrete pressure vessels: Stress concentration adjacent to reinforced penetration under unidirectional stress

Present design philosophy for the advanced concept of the high temperature gas cooled reactor recommends easily removable and replaceable heat exchanger units which are enclosed within the prestressed concrete pressure vessel. This results in relatively large penetrations in the vessel wall becoming a prime requirement, because the openings required for heat exchanger withdrawal are of necessity much larger than those for the insertion of refuelling machines or control mechanisms.

The present paper deals with the simplest case likely to occur in practice, namely an individual circular opening in an infinitely wide slab of uniform thickness subjected to unidirectional stress in the plane of the slab. The theory presented assumes that the reinforcement to the penetration (i.e., the shutter tube) is bonded to the slab material and that both materials behave in a perfectly elastic manner. A further simplifying assumption made in the development of the theory is that the reinforcement material is concentrated along the edge of the opening in the slab. This to all intents and purposes is true for most practical values of reinforcement thickness. Allowance is made for the difference in elasticity between the materials of the slab and its reinforcement at the penetration.

The equations developed will apply equally well to a similar plane stress problem where there exists the combination of any two elastic materials bonded together at a circular opening. A part of the theory developed may be applied directly to the case of hydrostatic plane stress conditions in the slab in the region adjacent to such a circular reinforced penetration.