Few years ago I tried to understand API 650 seismic section basis.
For self-anchored tanks, the bases are related to a "double-hinged model" of the annular bottom. It may be understood as a limit of the theoretical collapse (by developing two plastic hinges) of the lifted part of the bottom.
The point is this "state" of the bottom is not really seen as a response to a set of the seismic accelerations and has no connection to a particular design spectrum or seismic event. It is a limit state for a calculation focused on tank overturning (and an increased compression in a part of shell) under a design seismic event. Doesn't means plastic double hinges would appear in bottom for the design seismic event.

For me the intention of API 650 "yu" calculation appears strange because was linked directly with "double hinged model" rather to a design seismic event. IMO, event the intention failed; I was able to reconstruct, formula by formula, the results of Appendix E but not "yu".

So "yu" can be understood as the maximum displacement of shell before the theoretical collapse of the bottom will occur (interpretation that explains why there is no need to be multiplied by 1.4Cd).
In API 650 "yu" is just wrong calculated within the "double hinged model" and a corrected formula should give results reduced by a factor more than 2. I mean the coefficient in formula doesn't meet even the theory! And I guess (with no evidence) that the table giving displacements was a tentative to offer more acceptable results adjusting results of a "theory"/formula which is just unrealistic.

Now, trying to say something about your question... which is the relevance to calculate piping attached to a tank when the bottom is ready to develop plastic double-hinges, in an unpredictable seismic event? Or which is the relevance to use as imposed displacement for piping the tabulated values based or not on "yu", anyway based on obscure criteria?
Frankly, I don't know.