nipra03,
My thoughts are (based on B31.3 only, the other B31’s are probably similar):
ELBOWS
Normally ASME B16.9 standard elbows are used. These are B31.3 'listed components', i.e. approved by the code for use in piping systems, ref. table 326.1. If you modify these in any way, they become unlisted components. The code interpretation 18-06 even states that a seemingly inconspicuous modification as trimming the elbow from 90° to say 75° will cause the elbow to become unlisted.
Because the modified elbow is unlisted, you will have to prove the design according to section 307.4.2. If you do it by calculation, this means that you need to do “detailed stress analysis (e.g., finite element method) with results evaluated as described in Section VIII, Division 2, Part 5”.
So for elbows, in my view the answer to your question is NO, you can’t calculate replacement reinforcement for elbows using the rules for straight pipe. Such a calculation would also be complicated by the fact that, except for the welding ends, you don’t know the required wall thickness of the elbow, as the wall thickness is not specified in ASME B16.9, nor do you know the actual, fabricated wall thickness (unless you do a UT measurement).
So if you really need to have a branch on the elbow, the best way forward is probably to buy a branch weld fitting, like e.g. a Elbo Pipet from WFI. WFI claims to have proven all their fittings by proof tests, which is an option given for unlisted components according to B31.3 section 307.4.2.
Regarding the SIF: Modifying the elbow will also tend to change the SIF. However, since the branch is presumably smaller OD than the pipe and is added in-plane, the change may be small. The purpose of SIF is to predict fatigue failure and fatigue cracks on elbows will normally develop on the sides of the elbow, i.e. not in the elbow plane and hence not at the location of the branch. So I think you are justified in leaving the SIF as is when doing the stress analysis of the main line. An analogy is trunnions (dog-leg supports) welded to elbows. I believe that for trunnions it is common practice to leave the SIF for the elbow as is, and - if the trunnion has large forces - to do a separate local stress check for the trunnion-to-elbow connection.
BENDS
B31.3 in 304.2 give rules for calculating the required wall thickness of the extrados of the bend, which is presumably where you wish to place your branch. So – contrary to the B16.5 elbows – you actually know what the required wall thickness is and presumably you also know the actual wall thickness. This makes it possible for you to do a branch reinforcement calculation same as you would for straight pipe. Also bends normally have much larger bend radii than elbows, which means that their geometry doesn’t deviate as much from straight pipe and that it is therefore more justifiable to use straight pipe rules. To my knowledge this approach is not specifically endorsed or prohibited by the code. My estimate is that it is probably OK, in particular if the branch OD is much smaller than bend OD.
That was my considerations; hopefully others will also give their views.