# Shear Force and Bending Moment Diagrams

1. Jun 20, 2013

### rdm42

Hello all,

I'm having some difficulty understanding the relationship between the diagrams. I understand that the area under the shear force diagram curve is equal to the moment. But let's say you have a cantilever beam, 10 m long, anchored on the left. There is an evenly distributed load over the whole beam and a downward force at the end of the beam (at x=10m).

1. If a beam is anchored (in this case, on the left side) does the shear force diagram start above zero at whatever the magnitude of the shear force is? Is that just the reaction force? My professor mentioned I didn't need to find the reaction force but I didn't quite understand what he meant.

2. Since there is a force at the end of the beam (at 10 m), that means on the shear diagram it will be a straight line down to zero. So for the moment diagram, I calculate the area under the curve of the shear force diagram, and that is the maximum moment (in this example)?

3. Does the moment diagram go to zero because the shear force diagram goes to zero after x=10?

Also I hope this is the right place for this, I am new and am unsure if this is the correct forum.

2. Jun 21, 2013

### SteamKing

Staff Emeritus
1. In order to construct the shear diagram for a cantilever (or any beam, for that matter), a free body diagram is required in order to determine the reaction force and moment at the fixed end. I don't understand the comment of your prof.; you may have misheard or misunderstood what he said.

2. The shear diagram for the cantilever will have the reaction force plotted at the fixed end, and beyond this point, moving towards the fixed end, the loads applied to the beam will be used to construct the remainder of the shear diagram. If no concentrated load is applied at the free end, the shear force must equal zero at the free end.

3. A similar situation pertains to the bending moment acting on the cantilever. The moment diagram starts with the reaction moment, and the shear force diagram is used to construct the remainder of the moment diagram until the free en is reached. Unless a couple is applied at the free end of the beam, the moment there must equal zero.

shows several example problems with solutions showing the construction of the shear and moment diagrams.

3. Jun 23, 2013

### rdm42

Got it, thanks!

4. Jun 4, 2014

### doktrintr

Bending moment and shear force