Dear Mr. Diehl, Dear Mr. Ay,

I am currently working on some offshore projects where ASME B31.4/Ch.IX and B31.8/Ch.VIII requirements govern pipelines' design and analysis.

Because my previous experience with B31.4 and B31.8 was previously related to onshore piping/pipeline only, I've made some simple tests to comprehend how the Codes' stresses are assessed and qualified. I've noted on this Forum several previous posts that reveal unclear aspects and doubts regarding this matter.

So, I've tested a sample system through Caesar II / B31.4(IX) & B31.8(VIII) computer stress analysis. I've assumed 0 mm Corrosion Allowance and 0% Negative Mill Tolerance percentage, so that for ASME B31.8 / Ch. VIII Code, the Stress Intensity value to be manually checked against Caesar II results.

According to my understanding, it might be a problem in relation with Code Combined Stress assessment and interpretation (both for B31.4/Ch.IX and B31.8/Ch.VIII Codes).

As per B31.4/Ch.IX, Sect. A402.3.5, and B31.8/Ch. VIII, Sect. A842.2.2, the following Code Stresses are to be considered:

- Pressure Hoop Stress, Sh;


- Longitudinal Stress, SL:
(SL)+ = Sa + Sb (stretched extreme fibre of pipe section)
(SL)- = Sa - Sb (compressed extreme fibre of pipe section)

Sa = Axial Stress; generally, for internally pressured above-ground piping/pipeline, Sa is positive, because axial force load contribution is generally less significant than internal pressure load contribution

Sb = Bending Stress, always considered positive (in absolute value)

For Code Stress qualification purpose, the HIGHEST ABSOLUTE VALUE of SL is considered to be checked against the corresponding allowable limit:

SL = max { abs[(SL)+], abs[(SL)-] }

so that, for internally pressured above-ground piping/pipeline, generally we have
SL = abs[(SL)+] = Sa + Sb


- Torsion Stress, St;


- Combined Stress, Scomb (no symbol provided by Codes, notation choosed for reference only):

Scomb = 2 * sqrt{ [(SL-Sh)/2]^2 + St^2 } (Tresca Combined Stress)
or
Scomb = sqrt( Sh^2 - SL*Sh + SL^2 + 3*St^2 ) (Von Mises Combines Stress)


Now, both B31.4/Ch.IX and B31.8/Ch.VIII Codes specify that "maximum longitudinal stress" SL should be used in the both alternative Scomb formulas, meaning that

SL = max { abs[(SL)+], abs[(SL)-] }

value is to be used for Scomb calculation purpose. In other words, the same SL value as previously considered for Code compliance checking, is to be also considered for Scomb assessment.


However, in order to obtain THE MAXIMUM VALUE of the COMBINED STRESS, it is required to consider the MINIMUM ALGEBRAIC VALUE of the LONGITUDINAL STRESS SL.

Since for internal pressure load, Pressure Hoop Stress is always positive (Sh > 0), the maximum value of the [(SL-Sh)/2]^2 = [(Sh-SL)/2]^2 term is obtained for that fibre where SL takes its minimum algebraic value. For internally pressured above-ground piping/pipeline, this happens for the compressed fibre, where we have (SL)min = (SL)- = Sa - Sb, that is lower in absolute value than the maximum SL value previously established as SL = abs[(SL)+] = Sa + Sb for checking against its Code allowable limit.

The same assessment is valid for Von Mises sqrt( Sh^2 - SL*Sh + SL^2 + 3*St^2 ) stress, which takes its maximum value when SL term takes its minimum algebraic value around pipe circular cross section.

The above reasoning is also "made" by Caesar II, which actually and correctly assesses the Code Combined Stress (according to Tresca or Von Mises formula, as required by Caesar II configuration file) by considering THE MINIMUM ALGEBRAIC VALUE of LONGITUDINAL STRESS SL around pipe circular cross section.

Here is a simple example validated by Caesar II results:

Low Carbon Steel - Yield Strength Sy = 241.31 MPa
Design Code - ASME B31.8/Ch.VIII
System Location/Category - Platform Piping

Stress Values for the same element/node of CaesarII model:

Axial Stress: Sa = 21.24 MPa
Bending Stress: Sb = 69.62 MPa
Torsion Stress: St = -9.49 MPa
Hoop Stress: Sh = 58.94 MPa

Max Stress Intensity Scomb = 108.99 MPa
(i.e. Tresca Combined Stress)

Code Stress: 108.99 MPa
Allowable Stress: 217.18 MPa
Stress Ratio: 50.18%


For the above stress state:

Longitudinal Code Stress, according to B31.4(IX) & B31.8(VIII) definitions and interpretations, is:
SL = Sa + Sb = 90.86 MPa < 0.80 * Sy = 193.05 MPa - 47.07% Stress Ratio

Hoop Stress Ratio:
Sh = 58.94 MPa < 0.50 * Sy = 120.66 MPa - 48.85% Stress Ratio

Tresca Combined Stress:
(SL)min = (SL)- = Sa - Sb = 21.24 - 69.62 = -48.38 MPa
Scomb = 2 * sqrt{ [(-48.38-58.94)/2]^2 + (-9.49)^2 } = 108.99 MPa
Scomb = 108.99 MPa < 0.90 * Sy = 217.18 MPa - 50.18% Stress Ratio

Consequently, Code Stress has been considered as Combined Stress, which has the highest Stress Ratio.


Now, if Combined Stress was calculated considering in Code formula the "maximum longitudinal stress" SL corresponding to stretched fibre, SL = (SL)+ = Sa + Sb = 90.86 MPa, as B31.8/Ch.VIII states at Sect. A842.2.2(c) (page 105 for 2010 Edition), then Tresca Combined Stress would be obtained as

Scomb = 2 * sqrt{ [(90.86 - 58.94)/2]^2 + (-9.49)^2 } = 37.14 MPa (only!)

The above value is lower than Sh and SL, that is not correct. It is incorrect the Combined Stress to be lower than any of its individual normal component stresses!



I've submitted this subject in your attention because the projects that I'm working on require a certain stress report template, where ALL the Code Stresses should be qualified against the corresponding limits, and not only the Code Stress given by Caesar II output reports.

I'm aware that since Caesar II qualifies the system as safe and provides, for each model element/node, the Code Stress as being lower than corresponding Code Allowable limit, ALL the required Code strength criteria are fulfilled entirely.
However, as I've mentioned above, it is required the project stress reports to include ALL the Code Stresses qualification against their allowable limits.

So, practically, we've post-processed Caesar II results, by calculating/selecting the maximum values of the following reference stresses:

- Hoop Stress as obtained directly from Caesar II output results, so that it is checked directly against its allowable limit;

- Longitudinal Stress as calculated according to Code definition/interpretation, being the maximum longitudinal stress SL = max { abs(Sa+Sb), abs(Sa-Sb) }, which is finally checked against its allowable limit;

- Combined Stress as given by Caesar II output results as Max Stress Intensity (when Tresca Combined Stress is required), or Octahedral Stress (if Von Mises Combined Stress is required), so that it is checked directly against its allowable limit.


Combined Stress qualification raised some problems for our engineers.
When B31.8/Ch.VIII Code is used, this stress is assessed by using the minimum wall thickness obtained by subtracting corrosion allowance and mill tolerance. So, manual checking of Combined Stress values based on axial and bending stresses (that are calculated using nominal wall thickness) does not yield to the expected results coincidence.
In addition, when Code Combined Stress is calculated using the Maximum Longitudinal Stress SL according to Code definitions/interpretaions, significant lower Combined Stress values are obtained, as described above.


To conclude, I kindly ask you to confirm my understanding/interpretation of the subject under discussion.

I have also a suggestion. Maybe it would be useful to introduce in the future edition of Caesar II / Technical Reference Manual / Code Compliance chapter, a warning/comment/instruction regarding B31.4/Ch.IX & B31.8/Ch.VIII Combined Stress assessment based upon minimum algebraic value of (SL)min, and not based upon Code Maximum Longitudinal Value SL. It would be useful for the less experienced stress engineers.


Thank you and best regards,

Dear Dorin,

In the past (it's true that related to Restrained lines only!) B31.4 was more explicit in addressing this issue.

In previous editions of B31.4/ 419.6.4 Stress Values, they included an warning: "Note that the net longitudinal stress becomes compressive [...] and that according to the commonly used maximum shear theory of failure, this compressive stress adds directly to the hoop stress".

Maybe this sentence isn't so accurate as math language, but at least gives an warning about what is happening in your example: the maximum longitudinal stress is 90.86 MPa however in Tresca stress is combined with Sh giving the term 90.86-58.94=31.92 MPa (and eventually a S-comb of 37.14 MPa),
whereas the longitudinal compressive stress is -48.38 MPa (in absolute value about half of maximum longitudinal stress) and in Tresca stress is combined with Sh giving -48.38-58.94=-107.32 MPa which is the dominant term in Scomb= 108.99 MPa

Now this explanation is not longer part of the last B31.4. and IMO you are right saying both standards should provide more explanations about the subject.

Maybe they intended to say in B31.4 A402.3.5 (3):
SL = maximum the longitudinal stress, psi (positive tensile or negative compressive) (MPa)
= Sa + Sb or Sa − Sb, whichever results in the larger Combined Stress value.
(but this is just my speculative rewording!)

My best regards,
Marius

For both of these offshore Codes, CAESAR II does consider both positive and negative bending stresses. The worst situation (highest resultant stress) is used in determining the final Code stress values.

Dear Dorin,

You are right saying Codes are wrong referring to "maximum longitudinal stress" as a general rule to calculate the combined stress. Your example proves this.

However, there are cases when this rule is still valid. In math language, max(SL-Sh)^2 for SL1< SL< SL2 and Sh fixed
is given by SL=SL2=max(SL) when Sh< SL1< SL2 or when (SL1< Sh< SL2 and Sh-SL1< SL2-Sh); for the rest of cases max(SL-Sh)^2 is given by SL=SL1=min(SL). For mathematics such statement is reasonable, for practice...maybe not.

More linked to "SL" expressions, the cases when the maximum Tresca stress is given by maximum longitudinal stress have a strong positive tensile axial stress, a moderate bending stress and a hoop stress in accordance with inequalities, so they may be unusual for practice but not impossible.

As a conclusion, it is possible to have a math rule for SL giving maximum Tresca stress but it is not a unique rule; a rational and practical solution is to follow Caesar rule:
calculate both of them and see which one gets the highest combined stress,

My best regards.