Dear canercaner,

Eq 3-42 calculates the seismic uplift force PS; the formula belongs to 3.8.9 Design load, which is under Sec. 3.8 Anchorage.
The anchorage criteria is under 3.8.1 General, 3.8.1.1 Required anchorage that stipulates For ground-supported flat-bottom reservoirs and standpipes, mechanical anchorage shall be provided when the wind or seismic loads exceed the limits for self-anchored tanks. Mechanical anchorage shall always be provided for elevated tanks.

Under 13.5.4.1 Resistance to overturning provisions, the resisting force is adequate for tank stability and the tank may be selfanchored, provided the following requirements are met:
1. The overturning ratio J determined by Eq 13-36 is less than 1.54. The maximum width of annulus for determining the resisting force is 3.5 percent of the tank diameter D
2. The shell compression satisfies Sec. 13.5.4.2
3. The required thickness of the bottom annulus tb does not exceed the thickness of the bottom shell ring per Sec. 13.5.4.1.2
4. Piping flexibility requirements of Sec. 13.6 are satisfied

Paragraph 13.5.4.1 Resistance to overturning details that for J < 0.785, there is no shell uplift because of the overturning moment and the tank is self-anchored. For 0.785 < J < 1.54, there is shell uplift, but the tank is stable, provided the shell compression requirements of Sec. 13.5.4.2 are satisfied.

So it is true that Paragraph 13.5.4.1 considers that in case 0.785< J < 1.54 it is expected an partial uplift under seismic events which may be acceptable if all 4 stability conditions are satisfied. And I guess that for such case using common language we may say that, even the tank is stable, it is not self anchored while 3.8.1 says that anchorage is required when tank is not self- anchored (does not mention stability as anchorage criterion).

Is this the conflict you are considering in your post?

If yes, I would add that it is rather a matter of terminology because the conflict may be consider solved by definitions given in the same standard- just my opinion, of course!
By 13.1.2 Definitions, definition no 7, Self-anchored tanks are Tanks that rely on the inherent stability of the selfweight of the tank and contents to resist overturning forces.. That means the Self-anchored criterion is "stability"/"to resist overturning" rather than "no partial shell uplift".

I would add that the assumptions made for case 0.785 < J < 1.54 (a model with seismic plastic hinges developed in tank bottom, partial shell uplift, etc) and the related overturning resistance calculation are available in an excellent book, "Aboveground Storage Tanks" by Phillip Myers.

Bets regards.