That's my whole point. It doesn't matter whether point B rolls down or point A tranlates up. It's only the relative deflection between the beam ends that matters for defining the elastic curve.
If you solve the problem by our respective methods, you will find that my cantilever tip deflection at point A exacly matches your guided end vertical translation point B. And, more importantly, the slopes and relative deflections will be identical at all points along the beam.
OK I will do it when I have time. Got to do some office work also. To me it looks more of a coincidence like 2x2 = 2+2 but not in general form. The defelction of cantilever tip will not match with guided rotation.
I checked and answers of your beam are correct.
How did you figure out this beam ... conjugate beam concept. was never a big fan of it. Any way tip of cantilever still point down contrary to guided roller but perhaps that is ignorable difference here.
The solution doesn't use the conjugate beam concept, at least not as I understand it. The method simply uses superposition of two basic load cases combined with the recognition that my simplified model and your original one are statically equivalent.
If you load the cantilever with an upward force at point A and a downward force at midspan (to match your model exactly), you will find that the cantilevered tip points upwards, just as you would expect it to. There should be no difference, negligable or otherwise.
That's basically what I showed in the middle diagram of the sketch that I attached to my previous post. I only flipped the loads around in my third sketch to make it look more familiar. Perhaps that muddled my explanation rather than clarifying it.
I think I did the same mistake as BAretired. End B can slide but still support moment, interesting, have never come across one of these supports before at school or out of school.
I was not familiar with the OP's representation of a "FREE BUT GUIDED" support. I have seen it represented as a moment with no vertical support.
A simple beam of length 2L with load W placed L/2 from each end is symmetrical and each half has precisely the same elastic curve as the beam in this thread.
