Anchorage Ratio for Rectangular Tank

[rohit307]

*** Long Post Alert***
I am new to the Tank industry but been involved in structural engineering for 12+ years
This is yet another Rectangular Tank Design Question!
I know these are inefficient but the client wants what the client wants from a space perspective.

Rectangular Water Storage Tank Design - I pretty much used most of the references that I found from this forum and multiple posts- One was is a British technical paper, One was an IIT-K paper, Kanti mahajan paper and Megesey book - Also used Roark's for plate bending and limiting deflections, stress.

My question pertains to anchorage ratio J.

Listed Below Relevant sections from each of the standard industry references.

I am looking at ASCE 7-16 (note ASCE 7-22 has same equations too) - Section 15.7-2
I am looking at API 650 - Section E6.2.1.1.1
I am looking at AWWA D100-21 - Section Section 13.5.4.1

All of the references listed above has same equations but they have been derived for Circular Cross section of Tanks- J being the Ratio of Overturning Moment Ms with Resisting Moment . Thinking of a circular cross section in mind The factor J decides the need for mechanical anchors. Points of interest on the ratio's being 0.784 and 1.54 which are from other threads and equations as I understand ( supposed to be approximately PI()/4 and PI()/2 ) - Not sure the derivation behind it.

Something similar to eccentricity being within kern type for no uplift, Uplift but still within for stability and outside of kern for requiring mechanical anchors? Analogy.

I am trying to figure out J for a rectangular Tank? What should be the values for it . Do I simply do standard rectangular slab check and see if eccentricity (M overturning/ Effective Weight) is less than Side dimension (L/6) ? What would be the point where it is considered stable and not requiring mechanical anchors? And point when it requires mechanical anchors ?

If Msx (Per AWWA D100 in X-Direction) - Design Overturning moment at the bottom of the shell - (Similar to Mrw (ringwall moment) is ASCE 7-16 And API 650) is the moment applied on slab about centroid from the applied Sax (seismic horizontal Load in X-Direction ) .

Then eccentricity e (similar to J) would be divided by resisting weight -

Calculating resisting weight from shell and roof around the whole Perimeter (2*(L+B)) = ((Weight of Shell+ Weight of roof load)/(2*(L+B)) * (1-0.4*Av)

API 650 and AWWA has reduction in this weight for the Vertical Seismic Force. ASCE 7-16 doesn't (That is a side question that don't want to delve into right now but any reference may be helpful as to why?)

For the weight of tank contents that can be used for resisting overturning (explained in ASCE 7-16 as This is the annulus of liquid limited by bending strength of the tank bottom or annular plate)

In my case i do not have a separate annular plate - So let's just consider without one - what should be the weight of this liquid ?

wL in AWWA calls this as 7.9*tb*Sqrt( Fy HG) <= 1.28 HDG - EQ (13-3) is this still applicable for Rectangular tank also Length max equation for L=0.216*tb*Sqrt(Fy/HG) which has a limits of 3.5% of diameter? Similar limits to the largest length dimension of rectangular tank ? What would be the limiting value replace "L" side dimension with D? Does anyone know the basis of this equation or limit and calculation ?

Is my general approach making sense for a rectangular tank ?

Any help in this direction would be much helpful .

IITK paper simply puts the ratio oh H/D(or L) needs to be less than (1/Ai (horizontal acceleration) - Not sure if it is that simple or needs other checks.

 

[JStephen]

I would calculate loads and load factors per ASCE 7, calculate overturning moment about one edge, and evaluate for stability.
For a non-code tank (ie, one not built to AWWA or API), I would evaluate the bottom, and the contents that can be lifted with the bottom, by any reasonable means (or even neglect that effect), and not worry a whole lot about the AWWA or API equations. For a small tank, it may be reasonable to assume the entire contents resist uplift.

I don't recall seeing a derivation for Eq. 13-3. I think you could make some assumptions about how the bottom behaved and come up with several different equations with different results, and would be hard put to say which was most reasonable. Sometimes, things like this have a good logical basis, sometimes, they come from committee votes by people with widely varying opinions. For a flexible bottom on a large tank, the higher you lift it, the more uplift resistance you get, so limiting the amount of uplift may be one of the goals.

 

[rohit307]

@JStephen - Thank you for your response.

I believe the Anchorage Ratio Check J is for the Shell buckling (or need for anchorage to prevent that) API also gives stresses on the plates based on where J lies - kind of reinforcing the requirement and corresponding stress checks to be confirmed if J is between 0.785 and 1.54 - If we look at the equations it does not consider the bottom plate weight or resistance from it. Thereby, my understanding is that this is more for the Buckling stress on the Ring Wall (Shell plate) . It is hence using only the weight from above (Shell + Roof) and the weight of the water that will move with it in close proximity to the Shell for it to buckle or fail. This was more for the Elephant foot Buckling failures ? As I read that other reference stated below.

The check you are mentioning and also shown in that attached IIT-K paper is a separate Global Slab / Foundation check as defined in API 650 (Section E.6.1.5 defined as Ms) and AWWA ( Section 13.5.3.2.2 defined as Mmf) as well . These values are used for foundation/Mat design and overall stability check. (Which i am doing anyways)

I also found the basis of the calc and the stress from another response posted by you on thread ( https://www.eng-tips.com/threads/api-650-tank-anchorage-ratio.520374/) . The document " Basis of Seismic Design Provisions For Welded Steel Oil Storage Tanks" From Wozniak and Mitchell. They essentially did a Equilibrium equation ( Assuming Virtual work) for a strip which would have 2 hinges to find that width to be considered for contents that move with the bottom of the shell plate buckling . I think I can still use this approach for the width of contents that needs to be considered. Trickier part is the limit.

Based on the document " Practice has been to limit uplift Length L, to 6 to 7 percent of the tank radius , the limitation of WL to 1.25 GHD limits L to about 6.8% to radius ( or other words 3.5% to Diameter) " - I guess it was more from practice and things found in industry . I am guessing the best alternative for me is to limit it to 3.5% of the length of the tank in the direction of the earthquake I am considering for the rectangular tank.

The additional continuation calcs for finding the plate shell stresses and eventually that Ratio that they came up with is going to be much trickier for a rectangular tank. They used Beta the angle subtended by the portion of the tank still in contact (Not uplifted) . Derived the ratio in terms of that angle and then varied that angle to come up with the ratio J for when it will topple over or be unstable and when it wouldn't see any uplift. That is my understanding of those Calcs.

I am trying to see if this can be replicated similarly for the rectangular ring wall and if i can also come up with stresses to be considered on the wall for it - Not sure if this is a futile effort or getting down too far into the rabbit hole for a project vs (Thesis / research) . ? Thoughts?

Your responses in this forum have been very helpful for a beginner (In tank industry) like myself and is much appreciated! Attached some of those relevant sections and basis that I am referencing.

For reference this is not a small tank by any means - We are looking at 55-ft Long, 9.5-ft wide and about 13-ft Tall . Hell lot of internal Bracing and Corner angles, Horizontal Stiffeners to make this work and keep the stresses and deflections in check per Roark. (We are in the range of 1/2" thick plates and SA516 Grade 70 Steel for the Plate and bottom shells)

 

[rohit307]

Update,

I went through the calcs of a rectangular Tank (Not trying to re-invent the wheel) but used Force per unit length from Uplift due to the Seismic force and the force per unit length due to download from the weights of things that can be considered just at the bottom of the shell ( Weight of shell+roof+ water in close proximity that will need to move for Shell to Uplift) .

For Ratio J perspective.
I figured it is self-anchored when no uplift occurs meaning maximum tensile at one end from Seismic moment <= wt (total download for unit length)
Thereby => Uplift from Msx for unit length at extreme point (right most point) / Download from wt <= 1 for Self-Anchored no uplift (Uplift force - Wt*L at highest tension point>=0).

For unstability similar to the Circular derivation where half of the ring is in uplift to create unstability,

Uplift from Msx at mid point - wt <=0

For uplift at mid point to be equal to wt the value of (Uplift Force - (wt*L/2) >=0 ) this results in the below equation.

Uplift from Msx per unit length at extreme point (Mid-point)/ Download from wt <= 2 ( For Section seeing uplift but not unstable)

The ratio turns out to be (In X-Direction)

3*Msx*(2B+L)
--------------- = Jrectangle and base on whether this is less than 1 (Self-anchored) to less than (2) Stable with Stress check reqd.
2L* (3B+L)* wt

where L is length along X
B is width along Y
wt is unit weight including consideration for reduction from Vertical acceleration (based on whichever code you want to follow) each code has differences

wt for ASCE 7 does not take impact from Vertical acceleration at all (wt in my equation above is total (wt + wa) from ASCE 7 Eqn15.7-2

wt for API 650 takes impact from Vertical acceleration for everything (including the weight of water needed to be displaced) - Equation E.6.2.1.1.1-1

wt for AWWA only takes impact from Vertical acceleration for steel weights and not for the liquid to be displaced - Eqn 13-32

Attached my approach if someone is interested or sees anything i missed please do respond and share.

Also a SIDE NOTE : There is debate that a rectangular tank cannot be an API 650 tank - I haven't seen explicit confirmation that it cannot be but would appreciate if someone can confirm that a " Rectangular Tank" cannot be API 650 citing some specific section or reference that justifies it, then it would be very helpful. it could be as simple as me miss something called out in the code itself

 

[Geoff13]

API 650 Clause 1.1.1 states : This standard establishes minimum requirements for material, design, fabrication, erection, and inspection for vertical, cylindrical, aboveground, closed- and open-top, welded storage tanks ...

Your tank is not cylindrical, and thus cannot be API 650.

 

[rohit307]

Thanks Portion of it was straightforward!