Pressure vessel shell calculation 1

[FSB01]

I have a question regarding a shell calculation. Why is code using different formulas if it is outside or inside diameter?

If long. stress formula is Sl=P*Rm/2t, why is code using P*(Ri-0.4*t)/2*E*t.
Or if Circ Stress is Sc=P*Rm/t why it is used P*(Ri+0.6t)/E*t

Why is, for the longitudinal stress Rm=Ri-0.4*t and why is Rm=Ri+0.4*t for the circumferential stress?

And shouldn’t Ri always be used if it is internal pressure?

 

[MJCronin]

Please post this question in the "boiler and Pressure Vessel" forum

I think that you will find that, in the USA the equations in the ASME code are a product of a committee, not a product of fundamental mathemetics and/or research.

What country will this vessel be built in ?

-MJC

 

[FSB01]

I think that I have posted it on "boiler and Pressure Vessel" forum, haven’t I?

This is only theoretical question, as where are those expressions coming from?
I am working with ASME Section VIII for some time and I was not able to find an answer, yet.

 

[TomBarsh]

Offhand, I am not certain where the different formulas based on shell ID or OD are obtained, but certainly it is from basic engineering/mathematical principles as MJ has stated (with the extra tweaking done by committees).

Practically speaking, there will be differences in required thickness and these are applicable for different situations.

For example, it is convenient to analyze pipe by its outside diameter because this is a given. Analyzing a pipe for required thickness based on the OD formula will obtain one value. In fact, this value will apply for all pipe schedules of the same size (OD). This makes it convenient to determine the required thickness and select a pipe schedule.

But analyzing the same pipe based on inside diameter will obtain different required thickness for each pipe schedule because each one has a different ID. This is not so convenient.

Of course, in the end you can make an example where the nominal thickness of the shell is equal to the required thickness. For this case the required thickness based on OD will give an equivalent ID (OD - 2 * nom thk) equal to the actual ID.

ie: take a 24" OD x 0.25" thk shell. Determine the MAWP; the required thickness for this pressure is then 0.25". Then determine the required thickness for same pressure but based on 23.5" ID. They will be the same to a level of precision.

 

[prex]

I think that those formulae, with slightly differences among various national codes, are the result of refinements and tests over now much more than one century.
However there is a theoretical explanation, that however does not explain the small differences in different codes.
It resides in the maximun shear stress theory that's widely accepted as the basis for assessing the strength of plate structures like vessels.
In this theory the governing stress is the so called stress intensity, or the maximum difference of the three principal stresses at any point.
In a shell with internal pressure, when the circumferential stress governs, the average through thickness circumferential stress is indeed PR_i/t. To obtain the stress intensity this has to be added to the through thickness (compressive) stress, that equals P at inner face and zero at outer face, so that the average through thickness is P/2. The stress intensity becomes PR_i/t+P/2=P(R_i+0.5t)/t, quite close to code formula.

prex

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[FSB01]

I am not sure if that is the root for the formulas. I think that is the base for Division 2 calculations (maximum shear theory).

My approach is that (for circ. stress) Rm is neutral line diameter of the shell. In that case Rm=Ri+0.6t would mean that that line is 60% inside of the thickness.

Other thing could be that we are assuming that stresses are equal through the thickness, however this is only the approximation and “0.6” factor is there to account for the difference.

That is still not explaining why is for the long. Stress Rm=Ri-0.4t?

 

[TomBarsh]

Here is a numerical example comparing the two ASME formulae.

For 24" OD x 0.25" thick shell:

P = 420.1681 psi is the MAWP. Then find required thickness based on this pressure.

t = P * R /(S * E - 0.60 * P)
= 420.1681 * 11.75/ (20000 * 1 - 0.60 * 420.1681)
= 0.25

t = P * Ro / (S * E + 0.40 * P)
= 420.1681 * 12.0 / (20000 * 1 + 0.40 * 420.1681)
= 0.25

 

[FSB01]

Thank you Tom, it is clear that those formulas are coming to same result.

The reason for my question is that I will be interviewed soon and this is the type of the question that I anticipate.
My interest is in the relation of the code formulas to the stress theory.

 

[eliebl]

Thanks Tom. If I may elaborate further, the calculation based upon the outside diameter and will give a required thickness on the assumtion that OD - 2tr will give ID. If the calculation is performed based on ID the the result will give a required thickness of ID+2tr to equal OD. This tr will only be equal if the shell thickness considered is EXACTLY the tr.

I was caught off guard on a heavy wall forging 2-3" thick on an exchanger with a design pressure around 3000 PSI. The tr for the OD and ID equasions will have a LARGE difference in required thickness. This can have an influence on reinforcement calculations as there appears to be less material available for reinforcing.

EJL

 

[TGS4]

Heavy-walled vessels are a totally different issue. You will note that the thin-walled equations (P*D/t) are slightly modified to deal with this. HOWEVER, there are warnings in Div. 1 to deal with this. Realize that even the thin-wall equations are approximations. The ACTUAL formula is found in the 2007 edition of Div. 2. There are no approximations in that formula, and it is valid for all D/T ranges.

One word of warning that I always follow with respect to formulae - know the conditions for which the formula is valid (D/T, P, etc), and understand the error as you approach the edges of the validity envelope.

 

[boilerengineering]

The best explanation I was given on this matter is simple. If you only know the I.D., as in the case of determining the shell thickness of a drum, you would run the calculation using the inside radius. when determining the required thickness of say a header where the O.D. is already known, use the equation incorporating the outside diameter.

 

[carthago]

Starting for instance with the ASME formula
t = P * Ro / (S * E + 0.40 * P)

if you replace Ri by Ri= Ro-t in the above formula,
you work it out and you isolate t,
I mean : t = P * [Ri +t ] / (S * E + 0.40 * P)

You will fond the formula giving t versus Ri,
this should give you the same formulas as in ASME for
t versus (Ri)