I have just downloaded the flange calculator.
CalQlata Note: The above query was concerning a Slip-On Flange
There is no such thing as zero stress in any material at any time. Simply supporting or handling a material will induce stresses and all materials contain residual stresses from their manufacturing process. Therefore, SH, SR and ST can never be zero (theoretically).
Therefore, the calculations in ASME VIII are simple but accurate for the loads considered (internal pressure and bolting tension) and does not complicate matters by combining the dominant primary stresses; tangential (ST), hub (SH) and radial (SR) because they are not coincident. It also assumes that the clearances and tolerances applied to the manufacture of loose flanges are such that no locking or interference occurs at design temperature between the pipe and flange. Each of these stresses is treated as a Principle stress and therefore considered to be a design condition in the flange at each relevant location.
Slip-On flanges have no hub so SH is set to zero. This is not strictly true as the fillet weld at the back of the flange is effectively a hub in which stresses would be induced during bolting. But the moments in the fillet weld are so much smaller than would occur in a normal hub that its stresses are not considered to be a design factor.
ASME VIII therefore takes the commercial view that if the ring of a Slip-On flange is capable of supporting the tangential stresses from bolting (almost always the highest stresses), hub and radial stresses can be ignored.