Ipetu, I noticed that some signs were omitted and that, as written, they don't add up. The diagram though makes it clear that the moments are caused by a horizontal load at the beam level. Neither the load nor the reactions are shown, and we don't know which convention they are using, have they drawn the moment on the tension side or the compression side, so we don't know which is clockwise and which is anticlockwise.
That was why I suggested designing for plus or minus. I suggested 68kipft. to make them the same, however you could do the outer beams for + or - 68kipft at the one end and 54kipft at the other, and the middle beam for + or - 40kipft at both ends.
Michael.
Timing has a lot to do with the outcome of a rain dance.