Cantilever Beam Diagrams ...

So, here are a couple Cantilever Beam Diagrams ... courtesy of AITC (Am. Inst. of Timber Construction) ... on their way to the 6th ed. Timber Construction Manual (2011).

A real life example of this type of framing is pictured in an earlier post (sorry the photo isn't so good): http://woodengineering.blogspot.com/2011/06/beam-framing.html

Theoretically, the hinge can be placed to balance out the negative and positive moments in the `main' beam, and or make the moments smaller in the main beam (both beams, for that matter).  And, in fact, the `smaller' end beam(s) may be smaller both in length and section.

Notice that the hinge connections are (necessarily) at the locations of zero moment.

In fact, strictly for kicks and giggles, we could put a hinge at every location of zero moment.

In the words of the Director of Tech Services, AITC, ... "[But] the system would be unstable and impossible to install.  Otherwise nothing would change."

:) :) :)  I love it !!!

And, not only that! ... we would have twice, or three times the hardware, for the same amount of beam!

It's fun!