Dear Champ58 (Mechanical),
API 650 5.10.5 is for self-Supporting Cone Roofs and the mentioned compression area Ac=(p*D**2)/(8Fa tanθ) .Notice that ,The load term p includes only external pressure+ gravity loads.
Appendix F is for small internal pressure. and the loading at F.5.1 formula contains only internal pressure .
Apparently , there is confusion for the interpretation of App F and 5.10.5 .If this is a real question, In order to get more valuable comments, please share the dimensions of the tank, internal pressure, roof type, shell wt...etc