Any Civil Engineer/Mechanical engineer on here please help me with this little question😅

I'm studying for an exam on structural analysis. In the slope deflection method of indeterminate beam analysis (or any method for that matter), if the moment of inertia of the cross section of two beams is different, is it true that the support in between them must sink? I've never heard that before till today from a course mate and just want to confirm that its true. Its kind of hard to Google a question like that. I asked Quora and haven't gotten any answer yet, thought I might as well give this place a shot since someone was able to help me out with a question I had while studying Vibration Analysis.