Shear and Moment Function Trouble

[1question]

Homework Statement

In the question (see attached images), it asks me to draw the shear and moment diagrams for the beam shown in the figure. To do this, we use the equilibrium equations. What I do not understand is why M is present in the equilibrium equation for bending. Isn't the pivot point at M? If not, where is it? All three of the moments that can cause bending are present in their equation...

Homework Equations

N/A

The Attempt at a Solution

I think that one of the moments should be omitted. However, I am likely wrong as both a textbook and my Prof have all 3 moments in there. I would greatly appreciate an explanation of the proper logic. Thanks.

 

[tiny-tim]

hi 1question!

i think M represents an applied moment, not an applied force

as a moment (a couple), it has no location

you can think of it as two equal and opposite forces of strength F
and a distance h apart, with Fh = M

clearly, the position of those two forces (in a particular plane), makes no difference

(eg if one is at the pivot point, the other must be h above or below it)

since it makes no difference where you put it, it can be shown anywhere on the diagram

in practice, you show it where the clamp (etc) is, since that's actually where the opposite forces are being applied!

 

[1question]

Oh. That makes a lot of sense. Thank you Tim!

 

[SteamKing]

M and V represent the shear force and the bending moment which develop as a result of the distributed load on the beam. They are included in the diagram because they contribute to the equilibrium of the free body of the beam segment where the cut is made. By writing the equations of equilibrium as shown in the Solution Box, you are able to determine V(x) and M(x), the shear force and bending moment functions, in terms of L, w, and position x.