Help me understand the API 650 seismic

[EfficientPuppy]

I am having a hard time understanding the results of some seismic calcs following API 650. I've asked around in my own sphere of my world through the years and no one has ever had an answer I've found satisfying, so I thought I'd throw this out into the universe and see what kind of response I get.
Lets consider two different tanks following API 650 code. the first is a 25' diameter 15' side shell, the second is a larger diameter with 80' dia x 15' side shell. I run the calcs for the 25' dia tank and get:

the center of action for Impulsive (Ringwall) = 5.25'​

the center of action for Convective (Ringwall) = 8.735​

the center of action for Impulsive (Slab) = 10.103'​

the center of action for Convective (Slab) = 10.397'​

No issues with these results as the heights are all inside the tank. However if I bump the diameter up quite a bit more to the 80' dia tank same height, I get:

the center of action for Impulsive (Ringwall) = 5.25'​

the center of action for Convective (Ringwall) = 7.231​

the center of action for Impulsive (Slab) = 32.887'​

the center of action for Convective (Slab) = 36.948'​

How does this actually work? Like are these results suggesting that there is a force that is acting 20' above the top of the tank? I've discussed this situation with several engineers over the years, each having their own explanation, from the distance being the result of some math and is not intended to be taken too literally, to that the distance is really a horizontal distance from the center to the force acting vertically on the slab. The prior one seems the more reasonable, but API is pretty clear in that it is measured from grade, implying a horizontal force.
I don't know. I've tried searching for papers giving the derivation of these formulas, or find explanations online for this to no avail. So I guess I'll create my own internet record. Anyone got a good explanation of what is happening here?

 

[HTURKAK]

I have calculated a bit different using hand calculator ;
Xis=32.7 ft Xcs=35.23
However we can say similar results both of them higher than H=15.0 ft.
The short answer to your question; ( My understanding),
- The “slab” moment, Ms, is overall TOTAL overturning moment on the foundation or supporting structure.The ringwall moment, Mrw,is the the moment calculated from the pressures on the walls but The “slab” or TOTAL moment covers the moment produced by the hydrodynamic impulsive and convective pressures acting on the circular base of the tank and walls .
- You should assume Xis and Xcs equivalent nominal height for slab moment calc. and would be higher than H if H/D≥ 0.4
- The “slab” moment is used when the tank is supported on raft - mat foundation or raft foundation supported on piles.
- When you look Table 5.21—Unfactored Downward Reactions on Foundations , Line item for SEISMIC , you will see
Seismic downward load at Shell= [4Mrw/D + 0.4 (Ws + Wrss)Av]/(Π D)
Seismic downward at Bottom = Varies linearly from 32Ms/(ΠD3) at the tank shell to zero at the center of the tank.

The long answer to this question is , you need to study and look some literature (Veletsos, A.S., 1984. Seismic response and design of liquid storage tanks,Veletsos, A.S. and Tang, Y., Dynamics of Vertically Excited Liquid Storage Tanks ) . You may read these doc.s at NISEE E-Library . You develop a model ( if you have an enhanced software say ANSYS, PLAXIS ..) and share you findings with this forum ? Why not?



He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock..

Luke 6:48

 

[JStephen]

The force on the shell produces a moment on the shell.
The force on the tank bottom produces an additional moment on the tank bottom.
You're taking both of those moments, adding together, and then dividing by the force on the shell, and what you find is the height that the shell force would need to be at, if it alone were producing that moment. So yes, that theoretical distance can be higher than the shell height.