# Draw a Free Body Diagram to find reactions.

"Find reactions at A and B. Draw a FBD and the positions for all forces, check for equilibrium."

For this I have got to the conclusion of A + B = 8kN (assuming the plank is in equilibrium). As the 8kN force is closer to B, the force here will be greater. 2 forces will be shown at A and B, both pointing upwards at the points. Does the fact the B is on a roller joint affect the direction of the force at B? And what is the approach to finding out reactions A & B.

Also, how do you check for equilibrium?

Thanks for any help in advance.

Attached Images

 InfoJunkie4Life Posts: 1,110, Reputation: 339 Ultra Member #2 Feb 17, 2010, 01:59 PM
The weight is 60% towards B and 40% towards A so 60% of the weight will be on B (4.8kN) while 40% will be on A (3.2kN). The rollers really don't affect anything unless you're including the flex of the plank in the mix, or height of points, or pressure on the ground. Both will be pointing up, and unless something moves, there should be equilibrium.
 leeroynew Posts: 41, Reputation: 10 Junior Member #3 Feb 18, 2010, 12:03 AM
This is what I got, I just didn't think the answer could be as simple as this lol.

Thanks for the help.
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #4 Feb 18, 2010, 07:22 AM
I you want to use the principles of moments, you'll have to do it this way:

As the system is in equilibrium, all clockwise moment are equal to anticlockwise moments.

Taking A as pivot, you have two forces on the system, the 8kN mass and the B support.

Moment due to mass = Fd = (8 kN)(3 m) = 24 kNm
Moment due to support B = Fd = (B kN)(5 m) = 5B kNm

Since they are equal,
24 kNm = 5B kNm
24 = 5B
B = 24/5 = 4.8 kN

Then, since the mass is spread on the two supports, A support (8 kN - 4.8 kN) = 3.2 kN.

## Check out some similar questions!

Draw a wiring diagram for maximum demand meter showing how it is connected to the supply