I have a question regarding the way CAESAR calculates the allowable expansion stress. I am using B31.3 'liberal allowable', equation (1b) in the code book. The code states that Sh is the "basic allowable stress at maximum metal temperature expected during the displacement cycle under analysis." It appears though, that in certain cases CAESAR is using the maximum temperature that I enter for an element, regardless of which temperatures are involved with a particular load case.

For example, lets say that I have an element with three temperatures entered on the input spreadsheet for this particular element, T1=100, T2=400 and T3=1000, with corresponding Sh1=20,000, Sh2=20,000, and Sh3=5,000. The load cases in the file might be:

L1=SUSTAINED
L2=L1+T1
L3=L1+T2
L4=L1+T3
L5=L2-L1 (exp. code check 1)
L6=L3-L1 (exp. code check 2)
L7=L4-L1 (exp. code check 3)
L8=L3-L2 (exp. code check 4)
L9=L4-L2 (exp. code check 5)
L10=L4-L3 (exp. code check 6)

The numbers are not from a real problem, I just made them up for the example. It seems from the code that I should have 2 different allowable stress values for the 6 expansion stress ranges above, calculated using Sh=20,000 for L5, L6 and L8 and using Sh=5000 for L7, L9, and L10. When I run a file similar to the example above, CAESAR correctly calculates Sa for L5 and L6 based on Sh=20,000, but it is calculating Sa for L8 based on Sh=5,000 even though the maximum metal temperature on this particular element encountered during this displacement cycle is T2=400. I am thinking from the above statement from the code that L8 should be based on Sh at T=400, and I should be able to calculate a somewhat higher allowable stress range for this particular load case using Sh at T=400 in equation (1b). Is this correct?

The expansion stress range allowable is f*(1.25*Sc+.25*Sh), so the effect of Sh is small. When we factor in the Liberal Allowable term, this equation becomes f*(1.25*(Sc+Sh)-Sl). Since Sl can vary from 0 to (essentially) Sh, depending on the state of stress at that locality, I can see how you might think that CAESAR II is not doing this correctly at first glance.

I suspect, though, that if you are very careful in your checking of the output, you will find that it is all being done correctly. One problem I have with your made-up problem is that most materials have ratio of Sh/Sc that is fairly close to 1, so it becomes even more difficult to determine whether CAESAR II is using the correct value for Sh without careful arithmetic.

A material with a ratio of Sh/Sc of 0.25 as in your example would not likely be the material of choice for that application. Among other things, the normal support spacing spans from the suggested span tables in the Code would have to be revised downward severely to account for the loss of structural load resistance capacity in the hot load case.

But you are correct that the thermal stress range for a T=400 load case should be higher than the thermal stress range for T=1000. And you are correct that CAESAR II should NOT use the material properties at T=1000 for any part of the analysis of a T=400 hot load case (See 302.3.5(d) where Sh is defined as "Sh = basic allowable stress (6) at maximum metal temperature expected during the displacement cycle under analysis").

Hello, Thanks for the reply...I think you answered my question about the allowables, but I still think that CAESAR is calculating them using the wrong temperature on certain load cases. I did use Sl (from CAESAR output for the particular element) when calculating Sa, and the numbers match up exactly if I intentionally use the higher temperature.

For a simple test, I set up a simple file with two straight pipe elements and a 90 degree bend in the middle. I anchored the two ends. I set all of the densities and pressure to 0.0001 to take sustained stress out of the picture. I ran load cases similar to the example above, except I set T1=71, T2=71 and T3=900 (ambient=70). Material is A106B (just for the test, so Sh1=20k, Sh2=20k, Sh3=6.5k).

When I run this file, I get expansion allowables (liberal) of 50,000 for L1 and L2, which I would expect (20k * 2.5 - 0), but the allowable for L8 is 33k which I can tell is calculated using Sh = 900 (1.25 * [20k + 6.5k]. I would expect this Sa to have been 50k though, because L8 the piping only encounters T1 and T2, which are both 71 - I get zero expansion stress for this stress range, because the temperature is not changing, but CAESAR is still calculating Sa using Sh=900.

CAESAR II is using the lowest Sh in the system (for a given pipe element) when if determines the expansion allowable for a combined Tx-Tn load case. This is because the liberal contribution (Sh - Sl) from the Sustained case uses the lowest Sh, therefore the other 0.25 must be associated with the same Sh value.

I agree, Richard. Sh is being brought forward as a component of the Sustained load case. While this is not strictly applicable to the analysis of a thermal cycle between two intermediate temperatures, the following argument carries a lot of weight.

The paragraph in 302.3.5 immediately before equation (1d) reads:

"When the computed stress range varies, whether from thermal expansion or other conditions, Se is defined as the greatest computed stress range. The value of N in such cases can be calculated by Eq. (1d):"

While I believe this could have been worded more clearly (I would call it the "most severe stress range," not the "greatest computed stress range."), the intent is that all the expansion stresses are evaluated against the same allowable stress range. It's not strictly necessary to do this since you are entering the stress range for each load case into eq. (1d), but there's no harm in it. It's inconceivable that a piping system that passed the Code expansion stress check for the most severe (largest computed) stress range would fail a Code expansion stress check, even using the expansion stress range allowable for the overall temperature envelope.

The advantage (and there is one, of course) of reporting the expansion stresses as CAESAR II does is the following. You can quickly evaluate the equivalent number of cycles using Eq. (1d) by raising the Ratio % column to the 5th power for each reduced stress range and multiplying by the number of expected cycles, then summing the results. This does save the step of listing the stress range for each intermediate thermal range and dividing by the stress range for the most severe thermal range. More importantly, working with the percentages gives you a quick way to weed out cases with negligible effect accurately. For instance you can almost always ignore cases with stress ranges <25% (25^5 < .001) without much loss of accuracy in the final result.

The edit function is not working properly.

On the previous post, I meant to say that it's inconceivable that a system that passed the expansion check for the overall maximum thermal range would fail at an intermediate temperature range even using Se from the maximum thermal range.

"I meant to say that it's inconceivable that a system that passed the expansion check for the overall maximum thermal range would fail at an intermediate temperature range even using Se from the maximum thermal range."

I realize this is not a typical situation, but I think this is exactly what I have. The pipe in question is being displaced by thermal movements of other (much stiffer) pipes elsewhere in an interconnected system while this particular pipe remains cool. This is why L8 is my worst case for this particular piping element, and I am questioning whether I can calculate a lower allowable for this particular element for L8 (happens to be the 'greatest computed displacement stress range') based on the maximum temperature it encounters during the displacement cycle (maximum of T1 and T2).

For example, lets say I have two peices of equipment A and B. A is rigidly mounted to the floor, and B rests on a greased slide plate. A and B are connected by a 10" pipe and a 2" pipe. The lines may have a few bends, but the 10" line is stiff enough that it drives the movement of equipment B as well as the 2" line. The operating scenario dictates that 2" line has T1=400, T2=400 and T3=1000, and the 10" line has T1=70, T2=1000, and T3=1000, i.e. the 10" can never be at ambient while the 2" is at 1000) so L8 turns out to be the greatest stress range for the 2" line, but the temperature over the range never exceeds 400 on this line.

When I encounter this, the actual allowables are usually fairly close as CraigB mentioned above, but the sustained stress is usually very low, so I end up with 2-3ksi (or 5-10%) difference in Sa calculated at the max temperature for the stress range vs. the max temperature entered on the element. I have a couple of situations where Se on L8 is usually right around Sa and 2-3ksi is the difference between passing and failing.

I had this sort of situation in the back of my mind when I posted my earlier answer. I think there is a good argument that, under the language of the Code, you can consider your L8 case to be the "greatest computed stress range." (Maybe the Code guys are smarter than I give them credit for!) In any case, you may have to drop the high temperature case out of your analysis to get CAESAR II to use the proper Sh for L8, then run another analysis with the high temperature case included to show the analysis at max temperature.

You can treat these as load cases to be combined using Eq. (1d), but will have to either do it manually or load all the data into an Excel workbook (easier than you think, since you can write it all to Word first) and automate the calculation. If you choose to do that, I recommend that you consider your L8 conditions to be the case at which all other cyclical fatigue evaluation is performed. This means that one cycle at the max operating temperature will be the equivalent of more than one cycle at L8 temperature. You may or may not like the resulting value of "f" that you have to use based on your equivalent number of cycles.

Thanks for all of your help on this.

Also, you may know this already, but you can actually copy the output reports to Excel directly through the screen output (not going through MS Word). Right click copy does not work, but you can select the text and hit CTRL+C to copy and then paste directly into Excel. I've found that the screen reports run faster than the Word reports for large files, and when copying into Excel you don't get the headers and footers in the middle of the report.

... or if you're running Version 5.20, click the "Export to Excel" button on the toolbar.