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Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

(OP)
Hi all,

I am working on a calculation spreadsheet based on Plate and Shell Theory. I want to evaluate the allowable stresses according to ASME VIII, Division 2.

I have a problem with code interpretation, namely with Local Primary Membrane Stress (PL):


ASME Boiler & Pressure Vessel Code, Section VIII, Division 2 – Part 5

5.2.2.2 Stress Categorization

“b) Local Primary Membrane Equivalent Stress (PL)

1) The local primary membrane equivalent stress is the equivalent stress, derived from the average value across the thickness of a section, of the local primary stresses produced by the design pressure and specified mechanical loads but excluding all secondary and peak stresses. A region of stress in a component is considered as local if the distance over which the equivalent stress exceeds 1.1*S does not extend in the meridional direction more than sqrt(R*t).”

Definition of stresses (where S is the allowable stress):
General Primary Membrane Stress: Pm<=S
Local Primary Membrane Stress: PL<=1.5*S


If I understand correctly the membrane stress is considered Local if the axial (meridional) criterion of sqrt(R*t) is fulfilled – counting from stress level of 1.1*S. Then the stress needs to be below 1.5*S.
If the axial (meridional) criterion is not fulfilled then the stress is treated as General and the stress needs to be below 1*S.

But what about the stress area between S and 1.1*S ?


Schematic No.1:

http://img29.imageshack.us/img29/753/zl2a.png

The stress sigma (red circle) in schematic No. 1 , is not in the Local stress criterion region (is below 1.1*S) but is also above 1*S and that means the General stress criterion in not fulfilled. Also the axial (meridional) criterion is not fulfilled in this particular example (L’ > Lmax).


Schematic No.2:

http://img690.imageshack.us/img690/4905/4cy8.png

The stress sigma (red circle) in schematic No. 2 , is not in the Local stress criterion region (is below 1.1*S) but is also above 1*S and that means the General stress criterion in not fulfilled. There is no relative stress point exceeding the 1.1*S value to do the axial (meridional) criterion check: “…the distance over which the equivalent stress exceeds 1.1*S does not extend in the meridional direction more than sqrt(R*t)”.
Based on that it looks like only the General stress criterion applies and that means the pipe is overstressed.


If the stress state from schematic no. 1 is acceptable, i.e. the maximum stress is treated as Local and is below 1.5*S and the meridional criterion is fulfilled as well, but the stress state from schematic no. 2 is not acceptable, i.e. the maximum stress does not exceed 1.1*S so it cannot be treated as Local but is above 1*S so is higher than the allowable General stress, we end up with a situation that for a certain load value the maximum membrane stress in the vessel is above 1*S - the vessel is overstressed, however if we increase the load further the maximum membrane stress is above 1.1*S but below 1.5*S (assuming that meridional criterion is fulfilled) - the Local stress criterion applies and the vessel is not overstressed anymore. I do not know how to deal with this criterion "discontinuity". How come that in order to be within code requirements one needs to increase the load (pressure)? http://img27.imageshack.us/img27/7359/e0gr.jpg

I would appreciate your help with this issue. I would like to know how to treat the stresses between S and 1.1*S region? How to interpret the code guidance?

Best regards

RE: Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

In case no.1 you have a region where L<Lmax and all that region, including the parts with σ<1.1S, shall be checked against 1.5S (only the highest stress being relevant of course).
In case no.2 L=0 (stress below 1.1S everywhere), so the criterion for local stress is satisfied and the stress will be checked against 1.5S (satisfied a priori of course).

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

(OP)
Thank you for the reply Prex.


You wrote: "In case no.1 you have a region where L<Lmax and all that region, including the parts with σ<1.1S, shall be checked against 1.5S (only the highest stress being relevant of course)."

The problem with stress region between 1.0*S and 1.1*S is that the width is larger than the allowable value (L'>Lmax). The code says “…the distance over which the equivalent stress exceeds 1.1*S does not extend in the meridional direction more than sqrt(R*t)”. There is no information about the acceptable width for the stress region between 1.0*S and 1.1*S.

Second part of your post: "In case no.2 L=0 (stress below 1.1S everywhere), so the criterion for local stress is satisfied and the stress will be checked against 1.5S (satisfied a priori of course)."

There is a big problem with this statement. In case no.2 (stress below 1.1*S everywhere) we cannot measure the allowable width of this stress region (code says we do the measurement from 1.1*S stress level). It would mean that we can have a stress placed on the whole part (L>>Lmax), and we could treat it as Local (1.5*S is the allowable stress) if the stress is below 1.1*S. This would go against the General Primary Membrane Stress criterion where 1.0*S is the allowable stress. http://img842.imageshack.us/img842/3685/2emq.jpg

RE: Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

I only have ASME Section III handy right now, but the definition it gives (NB-3213.10) is below.

"Cases arise in which a membrane stress produced by pressure or other mechanical loading and associated with a discontinuity would, if not limited, produce excessive distortion in the transfer of load to other portions of the structure. Conservatism requires that such a stress be classified as a local primary membrane stress even though it has some characteristics of a secondary stress. A stressed region may be considered local if the distance over which the membrane stress intensity exceeds 1.1Sm does not extend in the meridional direction more than 1.0sqrt(Rt), where R is the minimum midsurface radius of curvature and t is the minimum thickness in the region considered..."

You can't treat the whole part as local because it needs to be "associated with a discontinuity". I think there are similar words in Section VIII, Div 2.

RE: Local Primary Membrane Equivalent Stress - 1.1*S and sqrt(R*t)

In case no.1 you are going beyond the code, and this is not necessary. If the code does not specify the extension of the portion with σ<1.1L, why worrying about it?
In case no.2, even if the useful citation by TERIO was not considered, this is where engineering judgement comes in. The code clearly stipulates that the over stressed region must be local, and this concept has a strong implicit definition in Saint Venant's principle.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

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