Primary bending stress

[Paulettea]

Dear All

Can anybody help me understand the occasions that primary bending stresses occur?

I tried table 5.6 in ASME BPVC VIII-2 but it seemed a little paradoxical in some ways. Try the highlighted cases in the image.

 

[imransaeed1804]

See attached. This is from book by Denis R. Moss

 

[Paulettea]

Thank you imransaeed1804. I can understand that for flat shells or shells that are close to flat there must be some deformation in the shell so that they can be in equilibrium with pressure as an external force. This deformation is in such a way that causes some curvature and bending stresses will be the result.

What I do not understand is the contents of table 5.6. As I have shown the first highlighted case says gradient through thickness for any shell, remote from discontinuity is secondary. However, in the second highlighted case it is obvious that for cylindrical shell there is bending stress Pb.

 

[TGS4]

In the case of most bending stresses, the stresses exhibit characteristics of both primary-ness and secondary-ness, the Code Committee made the choices listed in Table 5.6 for a variety of reasons - usually based on experience. There's nothing fundamental that ought to be read into the List of Example Categorizations in Table 5.6. They are just the judgment call of one specific group of engineers.

 

[Paulettea]

TGS4, I tried very hard to find a case of primary bending stress due to pressure in a pressure vessel but I cannot find anything. I think for pressurized shells that are not flat the bending stresses are all secondary. However, if a flat shell is under pressure there will be primary bending stress since the bending stress has to be in equilibrium with the moment due to pressure. But even in stresses due to pressure on a flat shell there will be some secondary bending stress due to straining of the flat head in order to reach some curvature.

On the whole, in the beginning I thought that primary bending stress is very easy to understand. The more I try to understand the occasions where this stress occurs the more I feel difficulty dealing with this stress.

 

[TGS4]

Indeed. That entirety of stress categorization is difficult, and gets more difficult the more you understand. Hence 5.2.1.2.

 

[prex]

Paulettea, assuming of course you mean general primary bending stress, another case is: if, in calculating a flat head, you assume it to be totally or partly clamped to the shell, then you'll have a general primary bending stress in the shell too.
And I don't clearly understand you when you say

there will be some secondary bending stress due to straining of the flat head in order to reach some curvature

Do you agree that a purely hinged flat head will only have (general) primary bending stresses? IMHO there are two cases: if you calculate the primary bending stress as if the flat head was purely hinged (often primary stresses are calculated by formula), then all other bending stresses due to the restraint at the periphery will be secondary, but if you calculate the bending with a model of the actual boundary restraint, then you'll have to classify the bending at the periphery as primary general.
This shows that the stress classification is not carved in the stone, in other words is not purely objective, it is instead partly subjective, as it depends on how you build your classification model.
Also, as another example of difficult classification, the fraction of the bending stress in a flat head (even if purely hinged), that is caused by a non zero Poisson's ratio, should be classified as secondary, as it is deformation related. However this is not very important, as that fraction of stress is generally low.
These examples show indeed that the primary bending stress is not 'very easy to understand', but you'll be able to sort it out in the end

prex
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