Complex compound cut

I need some help working out the geomtry of a compound cut.

What I have is a 90 deg. inside corner formed by 125mm PFC's (steel channel). I want to do a bird's mouth cut into 75mm steel tube and have this fit into the inside corner ... one side of the bird's mouth will be under the bottom flange of the PFC, and the side will be up the vertical back of the PFC.

This is for a steel sub-frame that supports one end of a building. The sub-frame is in-turn supported by a series of 75mm steel struts, 4 of which are required to be cut into the inside corners as described above.

I have about 16 of these struts to cut, so would like to make-up a cylindrical cardboard template which I can use to trace onto the steel tube.

Any ideas on how to work this out?

Thanks, peter

I don't have a clear picture of what you're trying to accomplish,but I won't let that stop me. (Something like a hip roof?)

There's a drafting process called "descriptive geometry" to develop sheet metal patterns for such intersections. That would work, of course, only if you're familiar with it. And even then, it may take a few trial fits.

Here's how I measure odd-shaped small objects for later incorporation in a design, modified for your objective:
Set up a mockup of the three pieces; the two channels with the tube held back a bit. Take small strips of cardboard long enough to span the gap. Individually tape the strips to the tube and to each other. Mark an index point on the tube and one of the strips. Cut the strips free of the tube and unwrap to provide your pattern, and transfer the pattern to a single piece of cardboard, filling in the triangular gaps as needed; use the same thickness cardboard so you don't gain extra circumference.

Joe