Seismic Parameter, Xis, issue in Appendix E

[HTCivil]

The problem I'm facing is in regard to equation E.6.1.2.2-1 which gives the height from the bottom of the tank shell to the center of action of the lateral seismic force related to the impulsive liquid force for the slab (pile cap) moment, Xis. When I calculate this distance, I get a value that is larger than the liquid level. Also, I noticed that when I vary the liquid level in the equation while holding the tank diameter constant, the stability factor, J, decreases (the tank becomes more stable) with an increase in liquid level where I would assume the opposite to be true.

The values I am using for the equation are:

D = 127 ft
H = 44.5 ft

The value I calculate using E.6.1.2.2-1 for Xis:

Xis = 50.21 ft. > H
&
J = 3.11 ---> unstable

This is also greater than the height of the tank which is 49.5 ft.

Arbitrarily setting H = 60 ft (the tank is now more slender and should become less stable)

Xis = 50.37
J = 2.78 ---> more stable than before

Please advise.

 

[JStephen]

The height for impulsive loading on the shell only represents the centroid of the pressures on the shell, and should never be higher than the shell itself.

The height for the impulsive loading for the slab moment is the combination of moment due to pressures on both the bottom and the shell, but is only divided by the horizontal force to get the equivalent height, and can in fact be higher than the shell height. The equations could have been formulated differently to make this less confusing.

On the other item, I'll have to look at it when I have more time. Stability should be reduced with a higher tank. Make sure you're using the right equations and right factors in there.

 

[HTCivil]

"The height for the impulsive loading...can in fact be higher than the shell height."

I do not understand how the line of action of a mass that is at the bottom of the tank could be higher than the shell height. Please explain more so that I may understand. Values obtained for Xi and J when using a ring wall foundation are consistent with my understaning of the physics involved.

 

[IFRs]

Stability may increase for his tank - it is much larger than tall so an increase in liquid height may add to the overturning resistance more than it increases the overturning moment untill some height at which the opposite happens. Typical run-on engineer sentence but I hope there is some glimmer of intelligence somewhere therein.

 

[HTCivil]

There is certainly intelligence there and when I looked at very high values of liquid levels (ie. 100, 120), stability started to become worse. I would have to consider added tank weights to really put that issue to rest. My original question is still unsettled about why the seismic force for the impulsive mass of fluid is applied above the tank shell. This basically is resulting in an unstable J when the tank would be structurally stable if I were to use a ring foundation. (I am not using a ring foundation because the soil is terrible, fyi, but this should be irrelevent, in my limited understanding.)

 

[JStephen]

It sounds as though you are using the slab moment to evaluate tank stability. The slab moment is used for foundation design only. The tank stability is always evaluated with the ringwall moment, never the slab moment.

 

[HTCivil]

When I said "tank stability" I was referring to the anchorage ratio, J, which is a measurement of tank stability. J is a function of (among other things) overturning moment which includes moments caused by convective and impulsive portions of the fluid. The lines of action of the forces associated with the convective and impulsive fluids vary considerably depending on which type of foundation I am using (please see attachment). My goal is to avoid using mechanical anchorage, but when I use the parameters associated with a slab foundation, the tank becomes unstable under seismic loads, i.e. the anchorage ratio becomes larger than 1.54. I am attempting to understand this issue so that I may move forward with a general understanding of the code. Please bear with me.

 

[HTCivil]

I see now, you were right, I was using slab moment to evaluate tank stability by pluging in slab moment to the anchorage ratio J equation. Are you saying that if I am using a slab foundation I would still calc out Mrw and use it to evaluate J? If that is the case then my issue goes away.

 

[JStephen]

Yes, for evaluating stability of the tank for anchorage and shell compression, the ringwall moment is used, which is the moment applied by the shell itself. The additional moment due to pressures on the floor is only required to design or evaluate slab-type foundations.

 

[HTCivil]

Thank you for clearing that up for me. I am still curious about the equivalent height for the impulsive line of action for slab that acounts for the vertical pressure on the slab in addition to the horizontal pressure on the side of the tank walls. What moment would you use to design a ring foundation? Why is it that you consider only the ringwall moment to determine stability if the slab moment is in fact being transfered to the foundation? If it is transfered to the foundation, and the tank is not anchored, would it not also try to turn the tank over?

 

[IFRs]

Sir - I may be out in left field here, but read on and feel free to disparage as needed.

The "ringwall moment" is used for the tank stability and anchorage because the interior of the tank has no strength - all the overturning resistance is at the shell. So, a ring analysis is appropriate.

When designing a ringwall foundation we use the ringwall moment. Because it is a ring, it does not directly resist forces and moments inside the tank shell.


When designing an slab foundation we use the slab moment. Because it is a slab, it must directly resist forces and moments inside the tank shell.

 

[JStephen]

Pressure variations across the bottom plate of the tank are just transferred to the subgrade, and do not affect the tank shell. If the entire floor were somehow suspended off the foundation, then those pressure variations would need to be considered as well.