Dear all,

If you please help me to clarify the confusion regarding shakedown behavior as explained below
According to ASME B31.3, edition 2012:

SL ≤ Sh (302.3.5.a)

and according to Appendix P:
SL + SE ≤ 1.5 (Sc+Sh) (P1a)

Where B31.3 takes the allowable stress=2/3Sy, so we can represent right hand side in equations (302.3.5.a) and (P1a) as:

SL ≤ 2/3Sy (302.3.5.a)*
SL + SE ≤ 2Sy (P1a)*

As noted; equation (P1a)* is similar as mentioned in ASME Section VIII Division 2 related to protection against ratcheting using elastic stress analysis para(5.5.6).
Primary + Secondary ≤ 2Sy

The clarifications are:

1. The ASME Sec VIII Div-2, considered membrane stress due to pressure in the primary stress calculation; however ASME 31.3 considered only longitudinal stresses, equation (P17a), and not considered the hoop stress due to pressure.
Is that mean that ASME B31.3 less conservative (or not accurate) with comparison with ASME Sec VIII Div-2?

2. In case of the sustain stress reach its upper ceiling limit, 2/3Sy, Is this mean that expansion stress, according to ASME B31.3, allowed reach to the value 1 1/3 Sy ?

If yes, what about hoops stress? This mean that sum of sustain, expansion and hoop will exceed the 2Sy, is this accepted

3. Why stress range factor "f" is not considered at equation (P1a)?

thanks lot
best regards

Hi,

I'm afraid you are mixing the concepts and design criteria, and you make confusions.

For points (1) and (2):

ASME B31.3 does not address hoop stress in Code Stress compliance criteria. The reason is that it is assumed that hoop stress is mainly induced by pressure load. But internal pressure is the load used in pipe wall thickness determination (B31.3, Section 304). So, having the pipe wall thickness properly established prior to pipe stress analysis, it becomes useless to re-check the hoop pressure stress.

Of course, there are pressure stress concentration effects in pipe fittings (tees, elbows, reducers etc.), which definitely affect the actual hoop stress magnitude. However, B31.3 clarifies this issue at Sections 302.2.1, 302.2.2(a) and 303 - briefly, it is stated that:
a) "...pressure–temperature ratings contained in standards for piping components listed in Table 326.1 are acceptable for design pressures and temperatures in accordance with this Code", and that
b) "...Components manufactured in accordance with standards listed in Table 326.1 shall be considered suitable for use at pressure–temperature ratings in accordance with para. 302.2.1 or para. 302.2.2, as applicable. The rules in para. 304 are intended for pressure design of components not covered in Table 326.1, but may be used for a special or more-rigorous design of such components, or to satisfy requirements of para. 302.2.2. Designs shall be checked for adequacy of mechanical strength as described in para. 302.5.".

Conclusion: The typical piping fittings designed and manufactured as per the standards/specifications given by Table 326.1 have same strength at pressure load as the straight pipe having the designated pipe wall schedule.


Specifically for point (2):

Displacement strain (i.e. thermal expansion/contraction) stresses consist mainly in axial and bending stress components. Thermal expansion hoop stress is negligible. It's meaningless to evaluate "sum of sustain, expansion and hoop" as you wrote above.
Another issue: If Longitudinal Sustained Stress (SL) from pressure and weight reaches its allowable limit (Sh), then Thermal expansion/contraction stress range (SE) should not exceed f*[1.25*Sc+0.25*Sh], as given by eq. 302.3.5(1a). There is always a distinction between "cold" and "hot" allowable stress, and allowable stresses are determined as function of Tensile Strength, Ambient Yield Lmit and "Hot" Yield Limit. There is a rough approach to use Sy only for alowable limit reference.


Point (3)
Equation (P1a) refers to Allowable Stress for OPERATING CONDITIONS. Only Eq. (P1b) refers to EVALUATED RANGE OF CONDITIONS, e.g. to OPERATING STRESS RANGE, meaning that potential fatigue damage is considered.

Final Note. Appendix P has been deleted from B31.3 2014 Ed. Beginning from this summer, it should be ignored....


This is my opinion at this topic. I hope it helps...

Regards,

Hello Dorin,

Thanks lot for your valuable reply and help

I am only have a clarification on your above phrase "It's meaningless to evaluate "sum of sustain, expansion and hoop"".

The ASME Section VIII Division 2 related to protection against ratcheting using elastic stress analysis para(5.5.6)mentioned in briefly that:

" the primary plus secondary equivalent stress range, combination linearized general or local primary membrane stresses plus primary bending stress plus secondary stress, is limited to max of (2Sy,3Sm) or 3Sm (for SY/UTS>0.7)"

as mentioned the hoop stress is consider in check against the ratcheting and in same times ASME Section VIII, like as ASME B31.3, establish wall thickness at first based on pressure equation.

I know these are different codes but in same time i think that both of codes are depend and developed based on the same concept (The Twice Yield Method). The question here, why ASME B31.3 not considered hoop stress in his cyclic evaluation as ASME Section VIII??


Thanks lot
Best Regards

The Stress Categories and the corresponding Equivalent Stress Limits as defined and employed by ASME BPV Code VIII-2 (Part 5 - "Design by Analysis - see synthesis figure 5.1) are not provided and used by ASME B31 piping Codes.

Particularly speaking about Elastic Ratcheting (ASME BPV Code VIII-2, Section 5.5.6), the main Stress Categories involved by this design criterion are: a) Primary Local Membrane (PL); b) Primary Bending (Pb), and c) Secondary Membrane + Bending (Q).
The resultant Pl+Pb are generated by Mechanical Loads only (similar to Sustained and Occasional loads from B31 Codes), BUT are evaluated without considering the Stress Concentrations effects from discontinuities (e.g. orifices, thickness sudden variation, geometrical discontinuities, welds etc.). Actually, only the membrane stress (e.g. stress averaged value on wall thickness) increase due to discontinuities (such as orifice effect under uniform pressure load) and pure nominal bending stress (not altered by discontinuities) are addressed by PL+Pb sum.
Secondary Q stress includes GROSS structural discontinuities effect (geometrical discontinuities, orifices) and thermal stresses. This "Q" stress DOES NOT HAVE EQUIVALENCE in ASME B31.3 Code.

The resultant PL+Pb+Q stress for Elastic Ratcheting assessment (i.e. checking against SPS = 2 * SY or 3 * Sm) is calculated using the SECONDARY STRESS CONCENTRATIONS FACTORS, which typically may be determined by Elastic Finite Element Analysis (FEA) - see PRG FEA (i.e Paulin Research Group) software package and manuals.
By contrast, the Peak Stress determined as per ASME B31.3 Code using Stress Intensification Factors (SIFS) represents 50% of the resultant/full Equivalent Peak Stress Range = 2 x (PL+Pb+Q+F) as considered by ASME VIII-2. The ASME B31 Peak Stress includes, besides the Primary+Secondary stresses as defined by ASME VIII-2, the local stress concentration effects (i.e. welds, local thickness variation etc.).

Conclusion: The "Operating" stresses or stress-ranges as calculated by B31.3 Ed. 2012 Appendix P are actually peak stresses (or, accurately speaking, actual peak stress amplitudes with respect to "smooth" or "non-welded" pipe spool) determined by SIFs employment. If you double these peak stresses (or stress ranges), you'll obtain higher resultant stresses than PL+Pb+Q values, since the local stress concentration is also included. So, you cannot use Appendix P (as defined by B31.3 and applied by CII) for elastic ratcheting purpose.

However, there may be cases when pressure stress concentration should be considered - typically, non-standard fittings (e.g. not standardized by ASME B16.9 or B16.11 stds), such as fabricated reinforced tees (with reinforcing pad), stub-in branches etc.
The most recommended approach is to "isolate" such components within Caesar II models by upstream/downstream nodes, to identify the "internal" forces and moments developed in those nodes, and finally to analyze separately and accurately by FEA (3D shell elements) that component loaded by the forces & moments applied as boundary limits.
The analysis will be done as per ASME VIII-2 post 2007 and you'll have a full and reliable picture of the problem.

A simplified elastic ratcheting might be also performed using CII software, but replacing ALL typical SIFS (bending, axial, torsion) by the corresponding Secondary Stress Intensification Factors calculated separately for each fitting by FEA (PRG FEA - FE Pipe, Nozzle Pro etc.). You'll evaluate then the Operating stresses (P+W+T) and you'll find the "equivalent" PL+Pb+Q stresses. But you'll need to check the stresses manually.

Sorry for this extremely long reply, but things are complex and it appears you have not read enough so far. I don't intend to continue this topic discussion any more, but I hope I helped you somehow.
My final advice is that, if you are an active pipe stress engineer, you should use the latest B31.3 (2012 or 2014 from this summer) Code provisions, by employing CII v. 7.00 software with supplementary ASME ST LLC 07-02 and/or ASME STP-PT-073 documents, and, if your Company affords it, CII FEA Tools software - see Intergraph and PRG webinars about this issue, are extremely useful.

Cheers and good luck!

I think you would compare Section III NB requirements with B31 and understand the differences. A document with name "Background of SIFs and Stress Indices" is available on Internet and would guide you.

Again thanks lot Dorin and thanks Mariog
I am working now to follow your recommendations