Are Hoop and Longitudinal Stresses Additive? 4

[Eric W]

I know from having done PV code calcs that wall thickness is, in almost all cases, governed by hoop (circumferential) stress in thin wall cylindrical shells. Can someone help me understand why longitudinal and circumferential stresses are treated as mutually exclusive and not additive?

I'm looking at a slightly different application where I need to determine time to rupture using the Larson Miller Parameter. For this calculation, I have to determine stress in a thin wall cylinder under internal pressure and experiencing an external longitudinal load. I can calculate the hoop stress and the longitudinal stress. However, I can't help but think the total stress would be a combination of hoop and longitudinal. I can't find any references to understand why they would or would not be considered additive or similar to an equivalent Von Mises type stress equation. Which I understand is a combination of normal and shear (not considered in thin wall cylinders) or biaxial stresses.

What can the smart people offer me in advice for this one?

Thanks in advance,

Eric - master of the blue wrench

If you can't fix it with a hammer, it's an electrical problem.

 

[Pavel_1976]

There are three stresses in perpendicular directions (hoop, radial and longitude). In case of use maximum shear stress theory we should to take in to account maximum difference between two of these. In case of all positive stresses are the minimum stress it is pressure in radial direction and we could take to account that it is =0. Then only the maximum form hoop and longitude will be considered as equivalent stress.
In case of really high bending moment the longitude stress may be bigger then hoop stress and we should consider it also. But any way it considered as exclusive.
I’m not sure that this approach is valid in case of significant torsion moment or in case of thick shell and high pressure (significant radial stress).

 

[Eric W]

Thanks for the comments, Pavel. Since the cylinder is considered thin-walled, radial stress (shear) is not considered and so I am left with hoop stress and longitudinal stress. ASME code considers these stresses independent of each other and seemingly mutually exclusive when determining the minimum wall thickness requirements for the shell. There are no bending or torsional loads on the shell and to be more clear, the shell is centrifugally cast and approximately 11 inches (280mm) ID.

Eric W

Benevolent Order of the Blue Wrench

If you can't fix it with a hammer, it's an electrical problem.

 

[EdStainless]

We can treat them separately since in internal pressure applications the ratio is 2:1, so hoop dominates everything.
Cast shells are another issue altogether since they have near zero ductility and fatigue resistance.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[Pavel_1976]

EdStainless, I have different point of view. We have to extract equivalent stress in our assessment. To be compared with allowable stress. We can’t take just maximum stress from any point. First of all we have to obtain the principal stresses i.e. when all stresses are without shear stress. In our application we can consider all stresses (hoop, latitude and radial) as principal stresses. That way I said that the torsion could makes our theory not entirely true. Then if we take in to account the maximum shear theory then we have to get equivalent stress as ABSMAX(S1-S2,S2-S3,S3-S1). Where Si is a principal stress.
Second assumption we can use that all Si>0. This is important for longitude stress where stress from pressure is always >0 but from bending moment is +/-. We take in to account that stress from pressure always bigger than from the bending moment. In that case we can assume that:
S1 = 0…Pressure
S2 = Longitude stress
S3 = Hoop stress
And all Si>0.
So in these conditions ABSMAX=S3-S1=S3

But in case if S2<0 then we have to take in to account S2 as
EQ_STRES=S3-S2 then
EQ_STRES>S3

 

[Morcuse]

Pavel, please refer to the first section of Moss' Pressure Vessel Design Manual for more information. I believe it will satisfy most of your concerns.

 

[Krausen]

This is a question on Stress Theory. Under ASME VIII-D1, you do not need to worry about this since the code is based on “Design By Rule” principles that are time-tested & generally conservative. Additive principal stresses do not become a thing until you get into ASME VIII-D2, Part 5 (Design By Analysis), or other codes based on pure analysis where you must under principal stresses, secondary stresses, etc.

 

[Pavel_1976]

Morcuse, thanks for your comment. I am not familiar with ASME VIII/D1. I see it is important to point here which division we speak about here.
From the book:
"ASME Code, Section VIII, Division 1 does not explicitly
consider the effects of combined stress. Neither does it give
detailed methods on how stresses are combined. ASME
Code, Section VIII, Division 2, on the other hand, provides
specific guidelines for stresses, how they are combined, and
allowable stresses for categories of combined stresses.
Division 2 is design by analysis whereas Division 1 is
design by rules. Although stress analysis as utilized by
Division 2 is beyond the scope of this text, the use of
stress categories, definitions of stress, and allowable stresses
is applicable.
Division 2 stress analysis considers all stresses in a triaxial
state combined in accordance with the maximum shear stress
theory. Division 1 and the procedures outlined in this book
consider a biaxial state of stress combined in accordance with
the maximum stress theory. Just as you would not design
a nuclear reactor to the niles of Division 1, you would
not design an air receiver by the techniques of Division 2.
Each has its place and applications. The following discussion
on categories of stress and allowables will utilize information
from Division 2, which can be applied in general to all
vessels."

 

[TGS4]

I need to jump into this conversation because are a number of things being said that are just not true.

1) ASME Section VIII, Division 2 is not, repeat NOT, a Design-By-Analysis Code. It is a Design-By-Rules Code that just so happens to also contain Design-By-Analysis rules (that are applicable to a large number of Codes and Standards).

2) Just like Division 1, Division 2, first and foremost uses the maximum normal stress criteria. It is only in 4.3.10 that Division 2 introduce the von Mises criteria. And yes, the DBA rules also use von Mises as the invariant to align between the multi-axial stress state. ASME PTB-1 has some good discussion on why von Mises is used.

3) To address the OP’s question about why you can’t just add hoop and longitudinal stresses: it’s because those stresses are mutually orthogonal. When you “add” stresses, you are obliged to respect the tensor nature of the stresses and only perform such mathematical manipulations as is appropriate for tensors. Adding mutually orthogonal tensor violates the fundamental physics of the problem. Simply put, to add the two together would just be wrong.

4) The bulk of Moss’ book was written prior to the 2007 rewrite of Division 2. Most references that he has to Division 2 is, unfortunately, out of date. But generally-speaking, his book is really really good, and I have the utmost respect for Dennis.

5) The OP mentions the Larson Miller parameter. That means you’re getting into the creep regime. Whatever you think you know about structural mechanics, you can throw out in creep - elasto-visco-plastic behaviour is completely different. Seriously - at this point don’t even try to understand it - just get an expert involved. Heck, I even have my own experts that I rely on for creep behaviour.

 

[GD2]

Eric W,
If your intention is to determine the rupture/service life, you don't have to bother about principal stresses. Allowable rupture stress values are given in Sec II Part D for 100,000 hrs. But then, you are stuck at 100,000 rupture life.

There is a different procedure to determine rupture stress based on your design life. Read API RP 530.

GDD
Canada