The conventional formulas for bolted-flange design, given in the ASME Unfired Pressure Vessel Code, provide for stresses due to initial bolt tightening and the axial force of internal pressure. Additional forces tending to loosen a joint are created by unequal radial expansion or barreling of the flange and shell, due to temperature differences or pressure, and by unequally warped flanges. Formulas have been developed for the extra bolt loads required to overcome these effects and applied to a heat-exchanger joint in a catalytic reforming unit. The margin of safety against leakage is increased by using soft gaskets that can re-expand after being compressed, and by retightening bolts after operating temperatures and pressures are reached. Joints designed to resist initial bolting and hydrostatic forces only are likely to leak because of barreling effects or warped flanges.

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