Annex V top stiffener area calculation

[Hasay]

Hey everyone, i am designing storage tank under external pressure with dome roof. Api 650 provides two formulas for the calculation of required area of top stiffener, one in self supported dome section and other in end stiffener section. Can anyone tell me the purpose of both formulae. TIA

 

[JStephen]

For the area based on roof design, it should be treating the area as a tension ring due to compression in the roof trying to push it outward.
For the area based on shell design, it would be treating it as a compression ring due to shell pushing inward on it.
I assume the first area increases according to tank diameter, with no regard to shell height, while the second would be based on diameter and shell height.
Some of these factors may come out pretty negligible in specific cases.