I'm afraid I have to eat some crow on this response. I gave you a response that wasn’t as detailed as it should have been. You specifically asked about a reinforcing fillet weld for a branch fitting. I gave you a response, but without sufficient explanation. So, let me try again.

First, weld-o-let, sock-o-let, etc. are trade names for an integrally reinforced branch fitting. You have to look up the requirements for a branch fitting. Per B31.3: 2004 (that’s what I have handy) Figure 328.5.4D item 1 depicts a branch similar to the one you are asking about. The branch could be constructed from pipe, a coupling, or an integrally reinforced branch fitting. The strength is derived from the CJP groove weld. The fillet is to reduce the stress intensification at the toe of the weld between the run pipe and the branch.  Reading provisions 328.5.4(b) and (c), the size of the theoretical throat of reinforcing fillet is denoted as Tc. Referring the provision, it is noted that Tc is the lesser of 0.7Tb or ¼ inch. Tb is the thickness of the branch.

Going back to my original response, I also included the fillet size for a slip-on flange or socket fitting.

The following is the discussion for the slip-on (figure 328.5.2B) and socket welds (figure 328.5.2C).

1.4T is the size of the fillet weld based on the thickness of the pipe.

So, for the purpose of conversation, assume the thickness of the pipe is 1-inch. That would require the fillet weld leg dimension to be 1.4 times the pipe wall or 1.4-inches.

Now, the strength of the fillet weld is limited by the shortest failure path through the weld or along the shortest leg if the fillet weld is an unequal leg fillet. We are only considering the equal leg fillet in this example.

To calculate the shortest path through the fillet weld, assuming the weld is an equal leg right triangle, it is observed that the shortest failure path is defined as the theoretical throat.

To calculate the theoretical throat, one multiplies the leg dimension by 0.7. If you multiply 1.4-inches by 0.7, boom! You get (almost) 1-inch. So, the theoretical throat is equal to the thickness of the branch. Assuming matching filler metal is used, the strength through the theoretical throat is equal to the strength through the pipe wall.

These calculations are approximations. The code uses 1.4 rather than 1.414 and it uses 0.7 instead of 0.707, so there are some "rounding errors". The code also doesn't take into consideration some of the failure mechanisms observed in real world applications, but the calculations are conservative and relatively easy. It makes sizing the fillet welds for branches, socket fittings, and flanges pretty simple and straight forward.

I hope this helped.

Al