Questions and discussion for this lecture live here. Fire away by hitting Reply below 
Sean, if we put in zero for x in the function M(x), we find the value + 550 kNm, but the graph actually starts at -550 kNm. You math is sound regarding solving for Mcut, but I believe we should have noted that Mcut = - M(x) assuming M(x) is relative to our deformation sign convention. I think what happened is that we left the value in the static sign convention after puzzling out why my answer differed from yours.
If I integrate with V(x), I get the correct values after assuming the constant “C” is the initial moment, -550 kNm, and that is what I would expect. Tension is definitely primarily at the top of the beam in this problem, so, again, I am pretty certain M(x) should have been multiplied by a negative due to the -ve sign convention.
Am I missing something, or is my reasoning about right?
Hi @DAVID_G_RUTHERFORD,
Apologies for the delayed reply here…this one slipped under the radar!
You’re not missing anything, but here is a simple way to think about interpreting the result of the M(x) equation;
The way we interpret the sign of the moment given by the M(x) equation is relative to or in relation to the assumed direction of the moment at the cut.
So, when we made our cut at a distance ‘x’ from the left side of the beam, to reveal M(x), we drew it clockwise, which in this case, corresponds to tension on the top side of the beam
Now, when we evaluate the equation, M(x=0) we get a +550.5kNm. The positive here is read as, “the moment generates tension on the same side of the beam that we assumed M(x) did”…i.e. tension-top, which is what we see on the BMD at A.
Similarly, we note that the bending moment at say x=3.5 will generate tension on the bottom side of the beam. If we evaluate M_cut(x=3.5), we get -37.4kNm. Again, the negative here is interpreted as “this moment is opposite in sense of rotation to what was initially assumed for M_cut”…i.e. tension on the underside.
Hope that helps,
Seán
@Sean , No worries. I don’t know how you keep up with it all as is. Much respect.
Oh, okay, so I guess the difference came about by how the problem was set up. I assumed a different direction.
Thanks for the clarification!