I need to analyze a continuous beam of length L and three supports: A (at x=0), B (at x=L/2), and C (at x=L). An applied load P is applied at x=3L/4. Now, at A, the continuous beam is bolted to a bracket (drawn in orange). At C, the continuous beam is bolted to another bracket that is welded to another beam (drawn in green), at its midspan (see the image attached). The beam with the welded bracket is perpendicular to the continuous beam.
If I'm not mistaken, the bracket acts like a cantilever beam, and the applied load causes torsion on the perpendicular beam due to the bracket welded. I tried finding the reaction forces using the superposition method for statically indeterminate beams, described in many MoM books (I consulted Philpot's).
According to this method, when dealing with a beam supported by another beam, a compatibility equation must be used, after determining the deflections at the point of interest. The first step when solving this type of problems consists of eliminating the redundant reaction (let's say A, in my structure) and finding the other reactions (B and C) using static equilibrium equations, since eliminating the redundant reaction leaves a statically determinate beam (released beam). In my case, I find that following these steps don't really apply, because reaction force C is determined once a compatibility equation is used when finding deflections at point C. It is something like a paradox: reaction force A is found by finding reaction C, but reaction C is found by finding reaction A, and so on. How can I solve this issue? Is there another analytical method that tackles these cases? Am I just doing something incorrectly? Am I on the edge of discovery of a new MoM method? (just kidding).