Pipe with temperature diff at the wall 1

Yes, there is a formula. It can be found in the Timoshenko textbooks, or in the german boiler code TRD 301 annex 1.

One other issue is the cooling may bring the pipe wall temperature below the ductile brittle transition temperature- you may wish to check that issue also.

At the inner wall ,the tangential ( circumferential)thermal stress is:

stress= E*B*(To-Ti)/(1-v)/2
E=Youngs mod
B=coef thermal expansion
(To-Ti)= wall temp diff
V= poison's ratio

assumes thermal stress conc factor for pipe = 1.0

What you should compare the pressure + thermal stress with is the yield minimum stress of pipe material: as long as the resulting stress intensity (Tresca stress) is lower than two times the yield stress, the pipe will sustain an infinite number of cycles.
More dangerous is the brittle transition recalled by davefitz: API 5L is a welded pipe and is certainly not the best choice for those operating conditions.

prex

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Hi davefitz,

thank you for your reply. This formula is very interesting. It has no length dimensions, so it independent from any size data. It only has to be applied on cylindrical bodies. It involves the basic material properties. And the only external condition is the ÄÔ, which can be relatively easily measured.

Unfortunately, I don’t have Timoshenko’s book, which, from a quick search I have done in the web, seem to be a “Bible”. I will try to read it, if I can find it in any bookstore (I live in Greece).

And now I will come to the subject. As you said the stress (in the Timoshenko folmula) is tangential in direction (circumferential). Is it the same direction with the stress caused by internal pressure (neglecting the axial stress caused by the end cap effect)? I suppose it is.
I have done some quick calculations and the result are:

assuming for steel, E=200 GPa, B=4.45e-06 (deg C)-1, v=0.32

1. for ÄÔ=50 deg C , thermal stress=32 MPa (=4700 psi) which is 14% of the yield strength

2. for Äp=65 bar (=940 psi), D=50mm and t=5mm, hoop stress=32.5 MPa that is about the same with the previous thermal stress

Of course the distribution of the stress in the radial direction is different between these two examples. In the pressure example it is almost constant, while in the temp. example it goes maximum, minimum, maximum.

Now the question: Regarding only the theoretical models (and neglecting any end effect), combining these two conditions (imposing Äp and ÄÔ together as in the previous examples) will result in having a total stress equal to the sum (which for the inner wall be 64.5=32+32.5 MPa). And if instead of ÄT=50 deg C, we impose -50 deg C, can we say that (for the inner side) the total stress will be about 0? Do you confirm?

Thanks again.
Costas

It is not clear that you'll actually get a 100 oF delta T across the pipe wall at the conditions stated.

typically you'll see pipe wall delta's of less than 5 deg or so. it will be close to the fluid temperature with most of the drop occuring at the outside wall.

with icing the delta T will even be less.

I'd be more concerned with the issue of ductile-brittle transitions raised in the other responses