Two-cell tank for design of liquid-containing concrete structures for earthquake forces

[SamGabO]

When dealing with a tank wherein you have to compute for your base shear, you have to consider the impulsive and convective force acting within the tank filled with fluid as well as the force acting on the wall. Considering that it is a two-cell tank wherein you have to compute the forces of the wall acting inside, assuming that the fluid will resist one another, would the formula for the base shear, V applying SRSS be sqrt((Pw+2Pi)^2+(2Pc)^2)?

Or would it be like the same equation on ACI 350.3-06 for Liquid Containing Structures and Commentary? V = sqrt((Pw+Pi)^2+Pc^2)??

I'm getting confused whether to double the value of both Pi and Pc when you're dealing with the wall inside a two-cell tank.

And does anyone have an idea what is the metric equation for 10.6.4 for Flexural Stress?

 

[JAE]

I think for the interior wall you might need to use the full value of the forces vs. 1/2 of Pc and Pi.

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[SamGabO]

Are you implying that when dealing with a two-cell tank your internal wall would be more critical than that of the external? I mean pressure at the internal wall due to the impulsive and convective force is greater than that of the external wall? Meaning to say that what I asked from my previous question, having the base shear, V at sqrt((Pw+2Pi)^2+(2Pc)^2) is more of a probable equation when dealing with the internal wall of a two-cell tank?

We've been looking for references with regards to dealing with two-cell tanks for liquid containing concrete structures for earthquake forces but unfortunately, we haven't found any sources for that matter, if you/anyone does have a work/reference in dealing with these kinds of tank, can someone tell us where to search/look for these references?

Thank you.

 

[JAE]

I'm not implying that the internal tank wall is more critical than the exterior - that would depend on the size of the tank, depth, earth forces on external walls, etc.

If you have an internal wall, it suggests to me that you could analyze each tank half separately, in a sense, and idealize the internal wall as participating in each tank separately.
Think of two separate tanks with a small gap between them. Once you determine the forces on that internal wall for both tanks, then you conceivably could combine the forces since you have ONE wall in reality.

However, having said that, note that it could be that the forces on the wall from each tank section may not be in phase with each other. ACI 350.3 mentions this early in the code with respect to convective and implusive forces not being in phase - thus the square root of the sum of squares.

You could theoretically have the two tanks be in or out of phase - thus a conservative approach would be to sum the two tank-half forces fully into that center wall.

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[JStephen]

It would make sense to assume the impulsive forces were in phase with each other and the convective forces were not. Differences in level would put them out of phase, for one thing.
The forces on the back side of a fluid container would just be a reduction in the hydrostatic loading. That being the case, for the design of lateral forces in that wall, I don't think seismic forces for both sides filled would ever be any higher than one side filled, one side empty (assuming that's a design condition in this case).

 

[JAE]

JStephen - good point about possible differences in level - I was assuming equal depth in both tanks.



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[bones206]

Would the interior wall be classified as a "special hydraulic structure" per ASCE 7-10, Section 15.6.4? If so, the stated code design basis seems to agree with what JStephen said:

15.6.4.1 Design Basis
Special hydraulic structures shall be designed for out-of-phase movement of the fluid. Unbalanced forces from the motion of the liquid must be applied simultaneously “in front of” and “behind” these elements.
Structures subject to hydrodynamic pressures induced by earthquakes shall be designed for rigid body and sloshing liquid forces and their own inertia force. The height of sloshing shall be determined and compared to the freeboard height of the structure. Interior elements, such as baffles or roof supports,
also shall be designed for the effects of unbalanced
forces and sloshing.

Although, I agree that the case of one cell full and one cell empty would likely govern the wall design.

 

[SamGabO]

@JAE,

Sir I have a question with one of your previous threads with regards to the Sanitary Durability Factor. I've been going through ACI 350-06 10.6.4 with regards to the value of fs, I don't know what is more 'permissible' and what to consider. Would it be more conservative to use the calculated value of fs from the equation at 10.6.4 or the maximum value fs,max?

"OK - I think we've figured it out -

Section 9.2.6 refers to fs and calls it the "permissible" stress in the bars. It then refers you to 10.6.4.

10.6.4 says the "calculated" stress must be less than the fs,max, which is ASSUMED BY ME to be the "permissible" stress. So I would use the permissible fs,max as my fs in the Sd equation, not the calculated fs.

The calculated fs is ONLY used to check against the fs,max and that's all.

So this makes more sense - but ACI sure isn't very clear in their wording."

This was from a previous post of yours.

Thank you in advance.

 

[JAE]

SamGabO,
We probably went through the same struggle in understanding that too!
The wording is a little convoluted.



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[SamGabO]

Have you gotten a hang with the code as per the fs,max and the overall use of Sd? Because IMO its much easier using the one from 350-01. Having an entire formula changed based on the flexure and how the wording is really taken into is quite confusing and convoluting. And sorry for being off topic since I am already bringing this one up, together with the equation for section 10.6.4, do you have an idea what the its counterpart in metric ? I'm just getting values of psi but maybe the equation changes when you're dealing with metric values. Thanks a bunch. Sorry for my bad english as well.