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# Flat head thickness calculation - cylindrical pressure vessel.

## Flat head thickness calculation - cylindrical pressure vessel.

(OP)
According to ASME there is a calculation for flat head thickness (t) with the equation shown below. Is this applicable regardless of the ratio of head thickness to cylinder thickness ? I have a pressure vessel where the shell thickness of the cylinder is 100mm and the head thickness is 10mm, length of cylinder is 508mm, inner radius 254mm, The calculated allowed pressure value seems very low - in the region of 0.24 MPa (using C=0.33, yield strength 207 MPa) - does that seem a reasonable allowable pressure for such a design ?

thanks,

### RE: Flat head thickness calculation - cylindrical pressure vessel.

Chrissy123,

For the values provided and using Fy as SE the pressure is correct for 10 mm. Obviously for design you need to use S and likely E = 1.0 (but you need to confirm and understand what it means) so the allowable pressure in design would be even lower than what you have calculated.

However, your question requires more discussion. Look at UG-34 (assuming Section VIII, Division 1). If you do not have a copy your company needs to buy one. C isn't a constant factor of 0.33; look at the definitions to see what C is and what is included. Specifically look at C for welded covers and the increase in S by a factor of 1.5 so if you did use the yield stress your calculation is based on a number above yield. Research why the 1.5 factor is there; draw a free body diagram of the system and a rough deflected shape and know the definition of S.

Why does a low calculated pressure for a 10 mm thick flat head surprise you when the shell is 100 mm thick?

Patrick

### RE: Flat head thickness calculation - cylindrical pressure vessel.

(OP)
Hi Patrick thanks - Yes I know that C has other factors that need to be considered when calculating it. I also know that E isn't always 1 and further consideration needs to be given to that - so yes I will be refining the calculations based upon further work/investigations etc. I'm also tying in with flat plate theory too and investigating the bending forces etc and drawing free body diagrams as you say. Thanks for the reply though - I just wanted to ensure I was starting on the right track and I will continue to refine further ...

thanks,

### RE: Flat head thickness calculation - cylindrical pressure vessel.

It has been my rare experience that flat heads designed to the ASME rules are always about 4 to 5 times the thickness of the adjoining cylinder. If you look carefully at the flat head welding requirements,you can understand why no one selects these.

A useful exercise is to compare a pressure vessel flat head to an ASME elliptical and torospherical head.

You have not mentioned your material or Design pressure ....

But, for your diameter I would guess that a torospherical head would be cheapest ....

MJCronin
Sr. Process Engineer

### RE: Flat head thickness calculation - cylindrical pressure vessel.

(OP)
Thank you yes. I will be running comparisons also against other head types.

### RE: Flat head thickness calculation - cylindrical pressure vessel.

Roarks formula's for stress and strain provides very accurate calculation methods for calculating the stresses in flat heads.
The stress results are very close to what you will get with FEM.

The code rules require that the Membrane plus Bending stress at the centre of a flat head be less than 1.5xS.
You cold could take the results from your formula above and plug the geometry into the Roark formula to learn how conservative ASME VIII div 1 is.

I may be wrong, but I don't think that the formula that you are using is derived from any fundamental stress theory. It think it is just a clumsy formula that someone discovered that does the trick in designing safe flat heads. The C value is an adjustment factor to cater for different ways of restraining the outside of the head.

### RE: Flat head thickness calculation - cylindrical pressure vessel.

To DriveMe Nuts your partial statement ".. It think it is just a clumsy formula that someone discovered that does the trick in designing safe flat heads..." I don't know if you ever took classes in strength of material because if you take a close look at the formula that you are deriding, it has a lot of similarities to a beam formula loaded uniformly with it ends solidly contrained. It is not a perfect match but it is somewhat close. So I would advise that you work out the bending stress formula in which you would substitutes the moment of inertia of a rectangular cross section, diameter for length, rework the uniform load into an equivalent pressure and you will see the similarities.

### RE: Flat head thickness calculation - cylindrical pressure vessel.

Perhaps you should read my post again.

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