B31.3 Cryogenic Modulus

[Mjconnol]

How to interpret the B31.3 code

For Cryogenic service should the Emin value of Youngs Modulus be used for the calculation of forces and the resulting stresses

OR

Should the calc be performed using Ea as installed with the stresses magnified by the ratio of Em/Ea (not Ea/Em as in hot service)

Any thoughts would be appreciated.

 

[metengr]

For cryogenic service, I would expect some type of flexibility analysis for the piping system. As part of this analysis you need to calculate extreme displacement conditions, per paragraph 319.5.1 (a) of B31.3. The equation in this paragraph states the use of Ea, which is the reference modulus at 21 deg C, and Em, which is the modulus at the minimum or maximum design service temperature. In your case Em would be the lowest service temperature and the value would be obtained from Appendix C.

 

[Mjconnol]

metengr

Thanks for the reply

I need to expand further on the issue and I should have been more specific. !!!!!

What I am having difficulty understanding is the proper interpretation of section 319.2.2(d)

Here's the scenario as I see it assuming there is material variation or a temperature differential somewhere in the system.

A) Hot condition Em < Ea

Solve the flexibility equation for the forces (F) using A * F = EI * D with E = Em for the individual members

Compute resulting stresses using code formula 319.4.4 and magnify the result of the calculated point stress by the ratio Ea/Em.

This intuitively makes sense. as the stresses are increased in value and further as the differences between members values of Em approach Ea the computed stresses approach the default value of the calc if Ea was performed using Ea for all members initially with no stress adjustment.

The Reaction forces (as the calc was based on Em) are already computed in accordance with section 319.5.1(a). If the calc was based on Ea and then multiplied by Em/Ea it effectively results in a calc using Em to begin with.

The cryogenic condition is where I am having difficulty

B) Cryogenic cycle Em > Ea

Following the same logic as above if the flexibility calc is performed using Em the forces are greater than if computed with Ea. Following the code rule to adjust the computed stress by the ratio Ea/Em would reduce the point stresses not "increase" them. Is this the correct interpretation?????

Note that if the calc was performed using Ea the Reaction forces 319.5.1(a) would be magnified by the ratio Em/Ea which falls in line with the calc being performed using Em to begin with.

The interpretation of the stress is what I am having difficulty with.

 

[metengr]

Ok. I would suggest you post your second part of the question in the forum below;
forum378

 

[bvi]

You are correct in your assessment. Note the Em is defined (see Appendix J) as maximum or minimum temperature. For the cryogenic condition, Em will be the elastic modulus at the cryogenic temperature and Ea will be the refererence modulus of elasticity at 70F.

Yes, if you follow the procedure in 319.2.2, you will decrease the stress range when multiplying the calculated stress using the actual modulus at temperature by the ratio, but that is expected. Note that if you simply used the standard rules, not 319.2.2, you would have calculated this lower stress anyway using the reference modulus of elasticity.

Also, correct, the reaction forces should be maginfied by the ratio (for cryogenic conditions) if the reference modulus was used in the flexibilty calculation.

 

[Mjconnol]

bvi

Thanks for the reply.

Is there a reason (that I am missing) as to why the "least [Ea}" value of the modulus is used for the stress calc in cryogenic service?

 

[bvi]

It has nothing to do with what is maximum or minimum. It is simply what is technically correct in a fatigue assessment, the fatigue correlation is essentially based on strain range versus cycles to failures in room temperature tests (although we do the evaluation in terms of stress) and the stress calc, if done using a different elastic modulus than room temperature, must be adjusted to get a consistent strain basis. It is the same in Section VIII, Div 2 fatigue analysis.