Hi Abadran,
The code standard defines 4 axial code stresses (due to various sign combinations in the stress formula) and a single Hoop code stress. These formulas are provided in the Quick Reference Guide under Code Stresses and International Code Stresses.

I'll focus here on how CAESAR II determines the code stresses and allowable.

After the software calculates the 4 axial stresses it pick the largest and the smallest (sign taken into account) among them and discards the remaining axial stresses. Lets label the 2 axial stresses the software picked as A1 and A2.
The following steps are then performed:

1. Compare A1 to the upper and lower parts of the envelope boundary and pick the boundary closest to A1 (call this envelope boundary B1). Here B1 is just the allowable axial stress.
Do same thing for A2 and call its boundary B2.
B1 and B2 are envelope points at the calculated hoop stress location.

Consider now the following scenarios:
2. If both A1 and A2 are both inside the envelope, then if A1 is closer to B1 compared with A2 to B2, the software then picks A1 and B1 over A2 and B2. If A2 is closer to B2 then the software picks A2 and B2.

3. If A1 is outside the envelope and A2 is inside then the software picks A1 and B1.

4. If A1 is inside the envelope and A2 is outside then the software picks A2 and B2.

5. Assume both A1 and A2 are outside the envelope. The software then compares the absolute values of the separation between A1 and B1 to the separation between A2 and B2. The software picks the largest separation.

6. Let say that the software picked A1 and B1. These values together with the calculated Hoop stress and its allowable hl(2:1) will be displayed in the report "Stresses [Multiple Code/Allow]".

7. The governing code stress and allowable in the report "Stresses" is obtained as follow. From step 6, the ratios |A1/B1| and |Hoop/hl(2:1)| are calculated. The code stress producing the largest ratio goes into the report "Stresses" together with its allowable.


What happens if the calculated Hoop stress is > hl(2:1)?
In this case, we simply get the max of the absolute values of the 4 axial stresses. This max value with the sign retained and the allowable al(2:1) are displayed in "Stresses [Multiple Code/Allow]". The calculated Hoop stress together with the allowable hl(2:1) are also displayed there.
For code stress and allowable in the report "Stresses" we display the Hoop stress and hl(2:1), respectively.

I hope this has answered your question.