Expansion Bellows Meridional Membrane Stress Equation S3

[ENG2194]

Im having a hard time imaging the location and means of this stress in a U shaped convolution. Is this stress not the same as the longitudinal stress of an annulus pressure vessel with the same OD as the expansion joint, ID = OD-2*w, and a wall thickness equal to ply thickness? If not please explain how this S3 stress equation was developed. Visuals are always a plus. Thanks

 

[flexy]

You can envision the S3 stress as the stress in the bellows sidewall that is resisting internal pressure force that is trying to blow the crown off of the convolution.