Flush type connection: meridional stress is 1/10 times circumferential design stress 2

[inammanj123]

I am working on Tanks having flush type nozzle connection. I have doubts the way i am interpreting the requirement as per clause API650 5.7.81b, which says: "The vertical or meridional membrane stress in the cylindrical shell at the top of the opening for the flush-type connection shall not exceed one-tenth of the circumferential design stress in the lowest shell course containing the opening"

My solution:
API620 gives us the formula for meridional force/unit lenght,T1(5.10.2.5). Now using T1 and actual thickness of first shell course, i calculated the meridional stress using thickness formula of 5.10.3.2, and compared this vertical stress with my design stress, Sd.

In my case the shell thickness is 6mm and and using the above stated method my required thickness comes around 32mm. So this means i have to use this much thickness of insert plate, but this thickness is too high.

i also tried basic stress formula : pr/2t and also used ANSYS. With ANSYS even 16mm thickness is ok

Please I need urgent help that what is the right formula or method for this clause


Thanks
Inam

 

[JStephen]

I would suspect some sort of error in calculating the vertical force. The vertical force wouldn't be significant unless the tank is pressurized or subject to strong wind/seismic loading. (And I don't have the code in front of me to see if those are included in the section quoted.)

 

[inammanj123]

vertical force is less, but we have to satisfy API 650 condition, according to which it should be 1/10 of Sd!!

 

[JStephen]

Just playing with some numbers here- but for example, for a 50' diameter x 32' shell height tank-
Assume 2.5 psi internal pressure, which is fairly high for this size tank,
Allowing 71,000 lbs dead weight, net uplift is 635,000 lbs, or 337 lbs/inch.
Assuming G=1, hoop force is 4,910 lb/in.
So in that case, vertical force is 6.9% of horizontal.

 

[mariog123]

JStephen, I think the problem is rather in the API paragraphs.

In fact both API 650 and API 620 have the same requirement imposing a limit of vertical or meridional membrane stress in the cylindrical shell "at the top of the opening for the flush-type connection". It is true also that API 650 is inconsistent on the subject, because you can see such requirement in 5.7.8.1 b (5.7.8 Flush-Type Shell Connections), but you cannot see the same requirement in 5.7.7 Flush-Type Cleanout Fittings.

Fact is API 650 and API 620 ask for a limit related to "vertical or meridional membrane stress in the cylindrical shell" which should include a pressure term.
In API 620 this is clear because in 5.10.2.5 point c we can find formulas (10) and (11) for T1 and T2, where T1 includes a term equal with T2/2 (corresponding to the well-known fact that in cylindrical shells under pressure load (only), the longitudinal stress is half of circumferential stress). API 650 does not give any clarification how to calculate the longitudinal (vertical, meridional) stress.

However, the terminology and formulas are clear in any book of Strength of materials and that means that, in your example, we can say that the "vertical or meridional membrane stress" is 50%+ 6.9% of circumferential.

I consider your approach is correct, i.e. the correct requirement in both API 650 and API 620 should be that the effect of W+F (with the notations W and F as in API 620, 5.10.1 Nomenclature) shall not exceed 1/10 of the circumferential design stress Sd.
But it is not what API 650/620 require, they ask for a limit of "vertical or meridional membrane stress in the cylindrical shell".

Equally they would reformulate (for example) API 620/ 5.27.1.4 as "The longitudinal or meridional membrane stress in the cylindrical sidewall at the top of the opening for the flush-type connection shall not exceed 6/10 of the circumferential design stress in the lowest sidewall course that contains the opening."

 

[mariog123]

And a question....

I consider it is not clear what API intended to say in that paragraph.

I think they intended to say that such connections shouldn't be installed in cylindrical tanks where the longitudinal or meridional membrane stress in the sidewall, at the top of future opening, exceed "X" of the circumferential design stress.

However, as it is written the paragraph, I would consider that the requirement refers to the "as built" flush-type connection, case in which the reinforcement thickness of opening may be introduced in the calculation of "longitudinal or meridional membrane stress in the cylindrical sidewall at the top of the opening for the flush-type connection".

Your opinion, please?

 

[JStephen]

Mariog, I think I see the problem in your post, but don't know if that's the problem in the original post. In those T1/T2 equations, you should have a term of -W/A. In the case of a vertical tank, you'll have a pressure at the bottom, which is mostly hydrostatic, but -W/A will be very close to the same number as a negative, leaving a net very low vertical force. When you say, "corresponding to the well-known fact that in cylindrical shells under pressure load (only)", that is a completely different situation than how API-650 tanks are used.

API-620 includes design pressures up to 15 psi, and it is more likely to run into that issue with increased pressure. But the original post was for an API-650 tank, which is limited to 2.5 psi, and very few API-650 tanks are even designed for that.

 

[mariog123]

Dear JStephen,

I think your objections make sense, so I propose you to reformulate the problem.

We have a low-pressure tank "Cylindrical-sidewall, Flat-bottom Tank" under API 620 jurisdiction.
5.10.2.5 point c, instructs us that for cylindrical sidewalls of a vertical tank, R1 = infinity; R2 = Rc, the radius of the cylinder; and Equations of T1 and T2 become the following:
T1= (Rc/2)*[p+(W+F)/At]
T2 = PRc

I would add that T2 is the basis of dimensioning the thickness of course.

In case I want to have a Flush-type Shell Connection in my tank, this is possible under 5.27.1.1 provisions, i.e.
"A low-pressure tank of this configuration may have flush-type connections at the lower edge of the shell.
These connections can be made flush with the flat bottom under the conditions described 5.27.1.2 through 5.27.1.4.
5.27.1.2 The design pressure for the gas vapor space of the tank shall not exceed 2 lbf/in² gauge.
5.27.1.3 The sidewall uplift from the internal design and test pressures, wind, and earthquake loads shall be
counteracted, as noted in 5.11.2, in such a manner that no uplift will occur at the cylindrical sidewall, flat-bottom junction.
5.27.1.4 The longitudinal or meridional membrane stress in the cylindrical sidewall at the top of the opening for the
flush-type connection shall not exceed 1/10 of the circumferential design stress in the lowest sidewall course that
contains the opening."

In case I comply with 5.27.1.2 and 5.27.1.3, would I interpret the requirement of 5.27.1.4 other than evaluating the longitudinal stress based on T1 value, which includes also the effect of pressure p?
In case I calculate the thickness based on T1 and Sd, it is likely that I obtain a result around 50%Sd for the longitudinal stress, when calculate stress value based on T2 value, isn't it?
How to comply with 5.27.1.4 other than over-dimensioning the thickness?

 

[mariog123]

Dear JStephen,

Maybe it is worth to say that "P" in T1, T2 expressions of API 620 is the total pressure, in lbf/in.2 gauge, acting at a given level of the tank under a particular condition of loading.
One condition of loading is P= Pl + Pg, where Pl = gauge pressure resulting from the design liquid head at the level under consideration, Pg is the gas "internal" pressure above Design Liquid Level.

In your example hoop force is 4,910 lb/in and the corresponding longitudinal force is 2,455 lb/in that (API 620 says) must enter into the vertical force calculation.

 

[JStephen]

mariog,
In my example, if you use the API-620 equations, W will be the weight of the tank shell, roof, AND LIQUID above the level in question.
In that case, W = -3,920,708 lbs (liquid weight) - 71,000 lbs (tank dead weight) = -3,991,708
And At = 282,743 square inches.
At the bottom of the tank, P = 16.3667 psi (hydrostatic + 2.5 psi)
Taking F as zero, you then get T1 = 337 lbs/in, T2=4910 lb/in.
This is actually figured at the base of the shell, and numbers will vary above that point.

 

[mariog123]

Dear JStephen,

First, thank you so much for your patience in reading my words and explaining the matter.

I understand now, however I have few remarks on how API 620 considers T1 expression.

1. As API 620 says, P=Pl+Pg and add/substract a term related with metal, liquid and "F".
Considering weight of liquid (lets note it as W_liquid) and dividing it by At, we get exactly the hydrostatic pressure which is Pl.
So for our case:
T1= (Rc/2)*[p-(W+F)/At]=(Rc/2)*[Pl+Pg-W_liquid/At-W_metal/At-F/At]=(Rc/2)*[Pl+Pg-Pl-W_metal/At-F/At]= (Rc/2)*[Pg-W_metal/At-F/At]
and we may note that Pl (hydrostatic term) disappeared!

I try to convince you following your numerical case where I can calculate directly:
T1=(25*12 in)/2*[2.5 psi- 71,000 lbs/282,743 square inches]=337.33 lbs/in, which is exactly your result following API 620.
Again, as you can see the result is insensitive to the liquid height/ hydrostatic pressure.

So what is the effect of hydrostatic pressure? Of course it enters in T2 calculation (and gives the thickness), but does not enter into T1 result?
Under normal circumstances, for cylindrical tanks, T1 has no relevance. However in our case (flush-type connections) there is a condition of longitudinal (vertical, meridional) membrane stress in the cylindrical shell and I calculate it based on T1 which is insensitive to hydrostatic pressure!
Really? What is the physical basis of such result?

2, The main question: if I evaluate (for my curiosity!) by FEA the longitudinal membrane stress in the cylindrical shell of a tank, would I expect that the result is not depending on the hydrostatic pressure? With tank full, half-full or near empty would I get the same result for longitudinal stress in a particular position on the first course?

3. Understanding the API 620 intention, I have no hesitation to follow strictly API 620 "as is" and to evaluate longitudinal membrane stress in the cylindrical shell of a tank based on T1 expression.
In this case the condition 5.27.1.4 "The longitudinal or meridional membrane stress in the cylindrical sidewall at the top of the opening for the flush-type connection shall not exceed 1/10 of the circumferential design stress in the lowest sidewall course that contains the opening" makes sense and gives reasonable results.
However API 650 has no expressions of T1 and T2, but impose the same condition in 5.7.8 Flush-Type Shell Connections. Here I can be in trouble when I try to convince someone about the algorithm to calculate the longitudinal stress in shell, because I'm not convinced it is correct...

4. Is there In API 650 a particular reason for which the requirement has been included in 5.7.8.1 b (5.7.8 Flush-Type Shell Connections), but you cannot see the same requirement in 5.7.7 Flush-Type Cleanout Fittings? Why? what exactly makes the difference between the cases?

5. I would like to know your opinion/interpretation how the requirement has to be considered. Would I evaluate longitudinal or meridional membrane stress in the sidewall, at the top of future opening, or the requirement refers to the "as built" flush-type connection?

My best regards and thank you again.

 

[inammanj123]

dear all,

thank you for in depth reply. to summarize things i came to the conclusion that weight of the fluid and metal above the nozzle will have a negative value, this will give a small value of T1 and vertical stress. hence my original 6mm course is coming out to be sufficient, which is also inline with anys!!!!

The real problem was whether to use (p+W/A) OR (p-W/A)? so that means will be using the one with minus sign, taking into consideration,the direction of forces.

Thanks mariog123 and JStephen for clearing my concept.

best regards,
Inam

 

[mariog123]

Dear Inam,

Frankly speaking, JStephen clarified what API 620 wants to say.
I was rather blind because, on my side, W including liquid weight does not make any sense!

The reason is simple... P gives a longitudinal stress.
In a cylindrical shell, there is a tension stress due by P, regardless how API-650 or 620 tanks are used.

In API 620 the corresponding term is a positive (tensile) vertical force as +(Rc/2)*P.

There is also a compressive longitudinal stress term in shell, obtained dividing the gravity load transferred to shell (W+F) by the cross sectional area of shell.
The corresponding vertical load is obtained dividing the (W+F) load to the perimeter of the tank cross-sectional area:
-(W+F)/(2*π*Rc) with π=3.14159...
If someone wants to exercise math skills, the same expression can be written as:
-[(W+F)/(π*Rc^2)]*Rc/2=-[(W+F)/At]*Rc/2, obviously the physical meaning remains the same as previously.
It is exactly what API 620 considers, but it remains to detail the meaning of gravity load (W+F).

W+F represents gravity loads that we are able to transfere to shell: shell weight, roof weight (or a fraction of roof weight, case by case), structural devices or supports, external ties, braces, stairs, platforms or others like this.
Including liquid here does not make sense for me because I cannot describe any corresponding physical fact related to this calculation approach.
I'll be happy to succeed transferring product weight load as compression is shell, releasing the tank bottom from its duty....

 

[mariog123]

Dear JStephen,

Finally, I succeed to understand what is the problem and reconcile all the stuff.

API 620 considers a free-body approach which was rather confusing for me.
You made a good description in an old post that clarified by understanding:
"The free body diagram in this case is the upper part of the tank, floating in midair. It has a pressure force acting up on the bottom of the fluid. It has weight of contents and tank itself acting down. "

You are right, this is what APi 620 considers.
I would prefer another approach (which is equivalent), based on cause- effect i.e. a correlation between load and longitudinal stress effect:
- liquid hydrostatic pressure---> zero longitudinal stress (!!!);
- gas pressure---> Pg*Rc/2t longitudinal stress;
- W1+F load transferred to shell (anything but not the liquid content!)---> -(W1+F)/(2*π*Rc*t)= -[(W1+F)/At]*Rc/(2t)

And, surprising for me (but never too late for the truth... which is I need to educate myself more!), the longitudinal effect of pressure is not P*Rc/2 but Pg*Rc/2.
Indeed, looking into the document attached (a Roark's extract), the longitudinal stress due to liquid hydrostatic pressure is zero, the effect of gas pressure is Pg*Rc/2t (due to the "cap effect") and the effect of weight transferred to shell is -(W1+F)/(2*π*Rc*t)= -[(W1+F)/At]*Rc/(2t) with W1 not including the weight of liquid!
Now anything makes sense:
T1=Pg*Rc/2-(W1+F)/(2*π*Rc)=Pg*Rc/2-[(W1+F)/At]*Rc/2=[Pg-(W1+F)/At]*Rc/2 and the result is identical with the final result of API 620 for cylindrical shells.

My best regards.