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# API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

## API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

(OP)
I've been asked to look into the addendum 4 and help find and understand the changes from the previous version. I would like somebody to confirm my understanding of the Moment terms as defined in Section 3.11.2 Unanchored Tanks. This is what I think:

Mpi = Moment about th shell to bottom joint from design
internal pressure. I think that this is
(int'l press.)x(cross sect. area of TK)-(Weight of TK shell + roof)x(radius of TK).

Mw  = overturning moment due to horizontal plus vertical
(wind press.)x(Height x dia.)x(Height/2) for shell.

Mdl = moment about the shell-to-bottom joint from the
weight of the shell and roof supported by the shell.
I think it is: (weight of shell+roof)x(radius)

Mf  = moment about the shell-to-bottom joint from liquid
I think it is:
(weight of liq. per API definition)x(radius)

Are my assumptions correct? I appreciate any advice.

jcoots

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

This is how I understand it:

Mpi = (int'l press.)x(cross sect. area of TK)x radius

Mw  = (wind horizontal press.)x(Height x dia.)x(Height/2) +
(uplift wind pressure on roof)x(horizontal roof area)x radius

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

I agree with JStephen on Mpi and Mw, and jcoots on Mdl and Mf.

Stupid question though, when summing the moments, shouldn't we have the proper positive and negative signs in there?  For instance, if Mpi and Mw are negative moments (CW), then shouldn't Mdl be positive since it acts in the opposite direction (CCW)?  Or vice versa, depending on how you choose to define the positive direction of your moments.

Otherwise, your moments are going to be HUGE.

Thoughts?

KLee777

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

The moments would cancel on one side of the tank but add on the other side.  You have to take the worst case and sum tbem.  I am in agreement with KLee777 on the moment calculations.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

Note that there is a maximum vertical uplift pressure from wind.  See 3.2.1.e.2

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

IFRs,

If I sum the moments around the point shown in Fig 3-23, with the CCW direction being positive, then Mpi and Mw would be negative, and Mdl and Mf would be positive.  Makes sense from a physical standpoint, but when calculating the criteria of 3.11.2, I can't keep these signs, because then inequality doesn't make sense.

Example:

Mw = -7.7E+5 lb-ft (CW rotation about the point)
Mpi = -1.47E+5 lb-ft (CW)
Mdl = +8.93E+5 lb-ft (CCW)
Mf = assume zero for now (haven't calculated this yet since I can't find proper reference to E.2.1.1) (CCW)

Then,

0.6*Mw+Mpi = -608847 lb-ft
Mdl/1.5 = +595561 lb-ft

This "passes" the first criterion.  But, if I were to choose the CW direction as being positive instead, then Mdl is no longer larger than 0.6*Mw+Mpi and it fails the criterion.  Thus,

0.6*Mw+Mpi = +608847 lb-ft
Mdl/1.5 = -595561 lb-ft

1st criterion fails.  Tank needs anchors.

My assumption is that when calculating the crtieria, you treat the calculated moments as *magnitudes* only, with no sign.  So my tank really does need anchors after all, since 608847 > 595561, failing criteria #1.  Wind and internal pressure prevail over dead load.

Do you agree?

Also, I believe the reference you gave was supposed to be 3.2.1.f.2, at least that's where it resides in Addendum 4.

Thanks,
KLee777

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

I was just looking through this again this morning.

When calculating moments for overturning checks, all the moments are positive.

However, the Mw as calculated for the overturning check shouldn't be the same as the Mw used elsewhere for anchor bolt loadings- one is the moment about the center of the tank, one about the edge- but they are confused in the standard.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

#### Quote (JStephen):

However, the Mw as calculated for the overturning check shouldn't be the same as the Mw used elsewhere for anchor bolt loadings- one is the moment about the center of the tank, one about the edge- but they are confused in the standard.

Really?  Then why is Mw defined in Table 3-21b as "wind moment in ft-lbs (see 3.11)."

The Mw in 3.11 is defined about the edge, but its definition appears in the anchorage section (3.12) in Table 3-21b.  So you're saying that we shouldn't be using the Mw defined about the edge for the calcs in Table 3-21b?

Not sure I understand where another Mw value was calculated about the center of the tank...although I'm not as familiar with API 650 as I wish I was, so I'm still learning.

Which Mw is used in Appendix F in the equations in F.4.2?  The value calculated in 3.11?  (Wow, I am starting to confuse myself.)

Thanks for the answer on the moments, by the way.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

Wind moment is wind moment.  It is defined in Section 3.11.  While I agree that section F.4.2 dropped the lower case "w" I think that one would use the same definition of wind moment unless it was re-defined for a specific section, which it is not.  This would be a good question to submit to API for review.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

No, the wind moment varies depending on where you sum moments, due to the axial load included in it.  If you sum moments about the centerline of the tank, the moment arm for the uplift force is zero.

The equations giving equivalent force for a moment are based on F = (Mc/I +/- P/A) x A.  For a thin ring cross section, I=pi*R^3*t, A=2*pi*R*t, and F=2M/R +/- P.  This is the basis for the 4M/D terms in the equations for U.

Where you have wind moment due to a lateral load of M, and wind uplift of P, the equivalent bolt load should be 4M/D+P.  But if you take Mw as M+PR, then 4Mw/D becomes 4M/D + 4PR/D = 4M/D+2P.  The axial load part gets doubled in there.  It's a conservative error in this case.

I've sent an email to API on the matter, although I wouldn't expect any changes until the next edition, whenever that is.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

While it is true that the moments vary depending on where you sum them about, the where in this case is the shell-to-tank bottom joint, so they add.  If you sum the moments about the tank centerline, there are no moment arms except for horizontal wind.  I see what you are saying and I agree with your analysis.  Looking at it another way, for overturning stability or anchor calculations (or in fact for any calculations) why should there be a moment arm for the uplift wind load?  If it is pure and uniform uplift, it should have no effect on overturning of the tank.  You could have a million pounds of upwards force and the tank might need anchors but it would never blow over.  Now I'm wondering why the wind uplift is a concern for anything but tension in the anchors.  Oh well - confused myself again!

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

I agree that using the uniform uplift per the new addendum of API 650 in the overturning moment calculation is a conservative approach.  The old way of finding the effective vertical projected area and taking the moment arm about the shell to bottom seemed much more realistic to me.  I can't argue with using this uplift force in the overall uplift for anchor bolt design, but it would create a conflict if API did not use it in the overturning moment also (in my opinion).  This is because the way that they calculate overturning moment is based upon the entire shell overturning about a single theoretical point 180 degrees from the wind resultant force that creates a subsequent "uniform" uplift around the shell about this point.  I think everyone would agree that this is a conservative approach.  I can understand simplifying it like this for the shell overturning, but I can't say that I agree with incorporating the roof uplift using a 0.5D moment arm.  Also, taking the moment about the tank centerline wouldn't be practical because, again, we are only talking about shell overturning.  This reacts differently as, say, the overturning during an earthquake where the tank bottom and the product are incorporated into the calculation.

### RE: API 650 Addendum 4 Sec. 3.11.2 Moment Definitions

Guys,

At least one of the questions to clarify ambiguious information in this section has been asked.  Here is the response from API.

John,

The answers to all these questions is yes.  We will fix these problems in the next addendum.

Best regards,
Gordon
API
Gordon Robertson
1220 L Street NW
Washington, DC  20005
P-202-682-8190
robertsong@api.org

--------------------------------------------------------------------------------

From: John Walters [mailto:Jwalters@ptctanks.com]
Sent: Wednesday, August 16, 2006 11:49 AM
To: Gordon Robertson
Subject: API650, Tenth Edition, Addenda 4, Paragraph 3.11.1

Background Section;  The purpose of this inquiry is to obtain an interpretation of the standard.

Main Section;  In Addenda 4, paragraph 3.11.1 includes a definition of Mf and refers to wL as defined in E.2.1.1.  We do not find a definition for wL in E.2.1.1.

a.  Is wL the same as wL found in paragraph E.4.1 of Addenda 3?
b.  Should this be shown as wa as defined in E.2.1.6 of Addenda 4?
c.  In the formula for wa, is the factor Fby the same as Fby as found in paragraph E.4.1 of Addenda 3?
d.  Should the factor Fby be shown as Fy as defined in E.2.1.6 of Addenda 4?

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