The B31.1 and B31.3 piping codes recognize two types of stresses and classify them as primary and secondary type of stresses. That being the case, pipe stress analysis programs also classify their calculated stresses in the same manner. Primary stresses are load driven stresses as a result of bending moments caused by these loads and hoop and longitudinal stresses caused by internal pressure. The classic method of calculating primary stresses is force divided by area, bending moment divided by section modulus or some variation of the above to satisfy free-body equilibrium. Secondary stresses are displacement driven stresses usually resulting from thermal expansion or cold to hot displacement at equipment or vessel connections. Secondary stresses in computer programs are calculated by multiplying the calculated strain (displacement) by Young’s Modulus to arrive at a certain value of stress. The stress/strain curve is linear up to the yield point and strain multiplied by Young’s Modulus will equal stress so long as the calculation is on the linear part of the stress/strain curve. Beyond yield, the stress/strain curve exhibits a plastic regime where the value of stress doesn’t increase linearly with strain. The computer stress analysis software’s calculation of thermal expansion stress beyond the yield point is a fictitious stress because the basis of the calculation (stress/strain curve linearity) is no longer valid.

Both codes (B31.1 and B31.3) limit the thermal expansion stress to less than yield to guard against thermal ratcheting. Thermal ratcheting is the result of incremental plastic deformation upon each application of thermal loads beyond yield. The effect is cumulative and non-reversible. Thermal ratchet cycles are similar to fatigue cycles in classic endurance tests. Many cycles of thermal ratcheting are required before failure will occur. In the case of a computer pipe stress analysis program’s calculated thermal expansion stress of 60,000 psi, it is my opinion that this piping system can safely ratchet to this value of thermal expansion stress at least 1500 to 2000 times before failure.

I would like the forum’s opinions on the above “discussion” and is the logic of my opinion flawed ?

Pat LaPointe
Fredericton, New Brunswick,
Canada

There are a set of three very good books on this subject written by David Burgreen. Unfortunately, they are out of print. Good technical libraries may have copies you can borrow.

You should consider Figure 302.3.5 in B31.3 (and the analogous Table 102.3.2(C) in B31.1) as definitive on this issue. Under B31.3, when f=1.0, and assuming that Sh = Sc, your allowable stress range is 1.5 * (2/3 Yield), or Sy. But this is a stress range, so that at either end of the cycle (after the system has shaken down) the peak stress should be 1/2 Sy.

You talk about a calculated thermal expansion stress, but I assume you mean a thermal expansion stress range. The underlying assumption of the B31 codes is that alternating stress ranges cause local yielding (thermal ratcheting) until the magnitudes of the peak stresses in the hot condition and in the cold condition are essentially equal. This is certainly a valid assumption for highly stressed systems, and for systems that are not highly stressed, we really don't care if this happens or not.

Your discussion also assumes that the material allowable stress is based on yield. In reality, most carbon steels have allowable stresses based on tensile, rather than yield, strength. Even taking f=1.2, you would need an Sc of 33.3 in order to be allowed to design a system to a 60 ksi thermal stress range (33.3 x 1.5 x 1.2 = 60). There are a few materials that would qualify, but this is far beyond the capacity of even API 5L X80, which is a carbon steel grade that has a specified minimum yield of 80 ksi.

So, IF you have a material that can support a thermal stress range of 60 ksi with an f of 1.2, and IF you indeed load your piping to that extent, under B31.3 your predicted fatigue life of the system is about 3,000 cycles. You could use equation (1c) from paragraph 302.3.5 to calculate it to more significant digits, but nobody's going to count the actual number of cycles that precisely anyway. And unless you're as old as Luf or Breen, if you design a system with a fatigue life of 3000 cycles, it's probably going to fail in your working lifetime. Then you're going to have to waste a lot of time and energy defending yourself, brcause the owner is going to conveniently forget (a) that you ever explained to him that the system was going to have a design life of 3,000 cycles, or (B) that he approved it, or (C) that he even understands what fatigue life means.

I think you may have assumed that a 30 ksi yield steel can support a 60 ksi thermal stress range. Neither B31.1 nor B31.3 would agree with you. I am on their side.

I also think that, even though you are correct that a calculated secondary stress beyond yield is fictitious, you don't want to go there. Don't forget, even though the secondary stresses are displacement based, once the material yields the primary stresses are still being applied. And primary stresses are NOT self-limiting. An implicit assumption in the phenomenon of thermal ratcheting is that the yielding is sufficiently localized to limit gross damage as a result of the primary stress field. Once you get to the point that you are calculating thermal stress ranges of 2X yield, I don't think that assumption is valid any more.

As a tip about books. Many out of print books are sold as second hand. There are some shops, which specialize on second hand technical literature. I made a quick search on David Burgreen. Several references. Look first in this case:
amazon.com
abebooks.com

Hello,

Craig may have been referring to this tome in particular:

Design Methods for Power Plant Structures
by David Burgreen
Language: English
Publisher : C.P. Press, : Jamaica, N.Y. ©1975.

This is pehaps the most lucid explanation of Code terminology and concepts that I have ever read - a book often overlooked due to its simplicity but of the greatest value to true students of pressure technology. Dr. Burgreen has passed but he was a gentleman of many skills - chief among those was the fact that he was a very nice man.

Regards, John.

Here's how I see the allowable stress (SA) in B31.3...

SA = f(1.25Sc+1.25Sh-SL)

1.25Sc+1.25Sh handles low cycle fatigue. Change in stress cannot exceed the hot and cold limits. You'd be yielding at every half cycle. This could be 1.5Sc+1.5Sh to get to 2 times yield (assuming Sc=2/3 Syc & Sh=2/3 Syh). 1.25 is used to remain on the "safe side".

f handles high cycle fatigue. f drops as cycles increase. B31.3-2004 allows f=1.2 for some materials. If f=1.2, then f(1.25Sc+1.25Sh)=(1.5Sc+1.5Sh) - see above.

-SL is included to prevent ratcheting. I like Ron Haupt's example. Hang a very large weight below a vertical run of thin straight pipe anchored at the top. The weight takes axial stress to the yield limit but does not fail (SL<Sh). Now run a horizontal branch off that run and (thermally) cycle it. When going hot, the strain will yield on one side at the anchor; when going cold, the strain will yield the pipe on the other side at the anchor. That vertical pipe is now longer. Repeat this process and the ratchet will continue to "failure". So this "-SL" term approximates the state of operating stress in the system. This is what Appendix P does for you. It throws the SL on the other side of the equation (and uses the right sign) and sets a limit for the operating state of stress. This is useful since SL can change - SL is the longitudinal stress due to sustained loads and while the load is sustained, the stress can change due to changing support configurations (e.g. lift off). Questions arise about which SL to use in setting SA.