Thermal stress in thick walled cylinder
Thermal stress in thick walled cylinder
(OP)
I am trying to approximate the stresses due to temperature and pressure in a thick walled cylinder. I attached the results of the calculation however, I suspect my formulas that I am using are incorrect.
I derived them by using the basic elastic theory equations. However as it can be seen, my axial stress is overly high so I am not sure if I am using the correct equations. Can anyone point me to the correct direction to get the proper equations or see what I am doing wrong in my calculation? I am trying to get API 530 to see what they use for stresses.
I derived them by using the basic elastic theory equations. However as it can be seen, my axial stress is overly high so I am not sure if I am using the correct equations. Can anyone point me to the correct direction to get the proper equations or see what I am doing wrong in my calculation? I am trying to get API 530 to see what they use for stresses.





RE: Thermal stress in thick walled cylinder
However without any clue as to the origin of those thermal equations and to what you intend to do, it is difficult to say more.
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RE: Thermal stress in thick walled cylinder
I am just trying to get the average stress that the tube experiences during service. It is a vertical tube inside of a furnace, so it is fixed to an outlet header at the bottom and to an inlet at the top. I used the thermal stress in cylinders and disk as given in attachment 1.
RE: Thermal stress in thick walled cylinder
There also is no thermal stress in the steady state if the temperature distribution is only due transient startup / shutdown conditions. If the temperatrue distribution is due to a steady heat transfer ( as from a flame in a furnace), then the thermal stress distribution shown may be correct if heated around the full circumference.
During a fast transient , the thermal stress in a thick walled cylinder can be found from the estimate provided in EN 12952-3 paragraph 13, and such a calculation can be used to compute fatigue damage.
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RE: Thermal stress in thick walled cylinder
Well the top of the tube is supported via a spring can connected to the trunions on the tube and the bottom of the tube is welded onto a header. The tube is also heated via a downfired burner from more or less all sides. But can I still use the equations for circumferential and radial stresses due to temp and pressure (excluding the axial due to temperature)? I'll have to look for that EN 12952-3 standard as I do not have that at the moment.
Also if the tube grows downwards, then it will in fact place extra load on the header, is there any way to estimate that? Or I use thermal strain = a*dT and then use stress = E*strain?
RE: Thermal stress in thick walled cylinder
What's forcing the tube downward?
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RE: Thermal stress in thick walled cylinder
(I am not saying that is what definitely happens, just trying to sort out my confusions)
RE: Thermal stress in thick walled cylinder
Not if it's fixed at the header end and free at the other. The weight does not change, so the header's stress is unchanged.
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RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
A picture would certainly help.
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RE: Thermal stress in thick walled cylinder
I have attached the drawing of the top section of the tube (bottom fixed to an outlet header)
RE: Thermal stress in thick walled cylinder
I haven't got the analytical solution at hand but have the results for a spreadsheet I've adapted for a general double wall cylinder (splitting the wall into two equal parts of the same material). These are shown in the attached Word document. You can check your forumla against the results shown here. If you use (incorrectly) plane stress, then the stresses are lower with a maximum stress on the inner face of 89 MPa instead of 127 MPa for generalised plane strain. You need to add on the stresses from the pressure loading to these thermal stresses.
Note that it'd be better to use a FE analysis on the whole vessel and to use these results to check your model at some point away from the effect of features.
RE: Thermal stress in thick walled cylinder
If the pipe is fixed top and bottom then axial compressive stresses will be present if the pipe isn't allowed to expand freely during heating.
If the pipe can expand freely without restraint from other components during the heating period then there will be no axial thermal stresses.
I've tried to follow your posts but its not clear to me whether the vertical pipe is restrained or not, although my gut feeling is that it is restrained.
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
It is a vertical tube (pipe), the top is the inlet and the bottom is the outlet.
At the top as shown in the drawing, there is a smaller pipe which enters it, this pipe is connected to a header at the other end. I don't know if to count this end as fixed.
The tube is supported via a spring support attached to the two trunions shown in the drawing as well.
At the bottom, the tube is connected to an outlet header so here is fixed.
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
I understand this, but my equations are incorrect right (for thermal at least)?
If they are not, I'd need to get the stresses at a common point to sum them up otherwise, I won't get the effective stress.
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
In general I'd just take D/t and see what ratio that gives me but I've seen that thick equations will be used if D/t >10 or in some cases 20. I decided to use the thick walled equations based on the pressure used (40 bars or 4 MPa). Is there a good rule of thumb to use?
[quote corus]Your calculation agrees with my results at the centre of the wall, but note that these are not maximum values, which occur at the inner and outer surfaces. The general expressions used for thermal stresses are attached in the Word document. The axial stress is just the sum of the radial and hoop stresses./quote]
Ah thank you then I will re-do my axial equation then as I have an extra term.
RE: Thermal stress in thick walled cylinder
"Nobody expects the Spanish Inquisition! "
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
The part of the tube experiencing the downward firing is 1/2 inch thick with an ID of 4.22 inches gives 0.118 which is more than 1/20 (0.05), so it is thick?
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder
So using thick wall equations would be correct. Are there any official standards that state 1/20th of the ID is to be used as thin/thick walled?
RE: Thermal stress in thick walled cylinder
I am led to believe that the thick walled cylinder formula's are good for both thick and thin walled tube, the thin walled tube formula just simplifies the calculation by assuming the hoop stress is constant throughout.
desertfox
RE: Thermal stress in thick walled cylinder
RE: Thermal stress in thick walled cylinder