Approximate Frame Analysis with Gravity Load

[@dougschmucker8212]

Not sure why comments from folks are not showing, here. John Riley posted: "Hi Doug, This video is awesome. I'm struggling a little to understand at 10:30 the shortcut where the carryover moment at the bottom is half the moment at the top of the propped cantilever? Trying to find an example of a fixed-fixed beam with applied moment to see where that assumption comes from." That carry-over moment of one-half when the "far" end is fixed and the "near" where we apply a moment (which has a roller support) comes out of the moment-distribution method. The carry-over can be derived with, say, the relaxation method. Relax the redundant support (the roller), apply the moment, let the beam deflect (calculate that amount: D0 = ML^2/2EI) and then put back into place with the roller support's reaction ... D = RL^3/3EI. That reaction will be R = 3M/2L. Then solve for the other reactions. M_far = M/2 where that M is the applied moment at the near end. That M_near would be 13.5 k-ft in this case.