Div-2 Part.5 Protection against plastic collapse

[Paulettea]

Dear All,

I am using ASME BPVC Sec. VIII-2 for my design by analysis. I faced difficulty while I tried to interpret the criteria provided by the code for protection against plastic collapse. The formulas are as follows:

P[sub]m[/sub]<=S (5.2)
P[sub]L[/sub]<=S[sub]PL[/sub] (5.3)
P[sub]L[/sub]+P[sub]b[/sub]<=S[sub]PL[/sub] (5.4)

What I cannot understand is that why both equations 5.3 and 5.4 shall be satisfied? I mean if equation 5.4 is satisfied then it seems that equation 5.3 is satisfied automatically.
The second question is that what happens if the secondary plus primary stresses exceed S[sub]PS[/sub]? Is that a kind of failure or is it not important at all?

Warm Regards

 

[PVDEngg]

Hello Paulettea,

I will try to answer your first question using para. 5.2.2.2 of VIII.2 i.e. STRESS CATEGORIZATION. Looking at Equations 5.3 & 5.4 simultaneously they might look like mathematical equations, but they are not. Please refer stress categories listed in para. 5.2.2.2 (a), (b) and (c). P[sub]L[/sub] is the equivalent stress, derived from ---, of the local primary stresses and P[sub]L[/sub]+P[sub]b[/sub] is the equivalent stress, derived from --- of the linearized general or local primary membrane stresses plus primary bending stresses. Meaning membrane in later category (P[sub]L[/sub]+P[sub]b[/sub]) can be general or local. It's all the way separate stress category depending upon stress location under evaluation (i.e. region where stress classification line is). Reading paragraphs 5.2.2.2 (a),(b)and(c) in conjunction with Table 5.6 (which provides guideline @ relation between location and type of stress) and Figure 5.1 may help in better fashion.

The second question is that what happens if the secondary plus primary stresses exceed S[sub]PS[/sub]? Is that a kind of failure or is it not important at all? - it is failure, since S[sub]PS[/sub] addresses primary as well as secondary stresses (refer para. 5.5.6.1 (c))and not only secondary stresses which can redistribute themselves not causing failure and that's why code wants it within allowable.

Hope this helps.

 

[TGS4]

Regarding your second question, the failure mode, as described in the Code, is ratcheting. The location is susceptible to ratchet, may not shake down to elastic action, which would invalidate some of the assumptions of the fatigue analysis.

With all of your DBA questions, I would highly recommend taking a course. A Google search of ASME Section VIII, Division 2, Part 5 training should highlight some suitable options.

 

[Paulettea]

Thank you for your replies.
PVDEngg, So if I get you right PL + Pb is not the sum of two equivalent stresses rather, PL+Pb is the equivalent stress derived from the sum of two stress tensors.

TGS4, I have doubt regarding ratcheting criterion in 5.5.6.1.
(d) The allowable limit on the primary plus secondary stress range, S P S, is computed as the larger of the quantities shown below.
(1) Three times the average of the S values for the material from Annex 3-A at the highest and lowest temperatures during the operational cycle.
(2) Two times the average of the Sy values for the material from Annex 3-D at the highest and lowest temperatures during the operational cycle, except that the value from (1) shall be used when the ratio of the minimum specified yield strength to ultimate tensile strength exceeds 0.70 or the value of S is governed by time-dependent properties as indicated in Annex 3-A.
The allowable stress (Div.2) is given by:
S=min{Sy/1.5, Su/2.4}
Multiplying by 3 gives:
3S=min{2Sy, 0.833Su}
Now, here it can be seen that 2Sy is either more than 3S or equal to that. Therefore, the larger of these two values is going to be 2Sy.
Only in special cases where S can be higher than Sy/1.5 (Note G2 of table 5A SecII-D) in which S may be as high as 0.9Sy. It means that the SPS can be as high as 3*0.9*Sy=2.7Sy.
To my eyes if linear elasticity is showing stresses (primary plus secondary) higher than 2Sy ratcheting is inevitable. Even if there is residual compressive stresses with magnitude equal to Sy, there will be plastic strain and no elastic shakedown will occur.

 

[TGS4]

Paulettea - ratcheting is much more complicated than that. If you are truly interested in the topic, I would suggest researching the work by Bree.

The only current concern about the VIII-2 ratcheting limits is that S[sub]ps[/sub] can occasionally be greater than S[sub]u[/sub], which is generally not reasonable/appropriate.