Solving Couple and Force Problem - How to Move F from O to C

[Marioqwe]

I do not understand the solution of this example.

It says that in order to eliminate the last couple, we can apply the force F at another point C. But how do they move the force from O to C just like that?

 

[PhanthomJay]

There is no force applied at O, just the couple is applied at O. A couple is a free vector that can be moved anywhere and still produce the same torque about any point. As long as you have a force-couple system, you can represent the couple and force as a single force applied at a single point, as long as the sum of forces do not change. Here, you have a 400 N force and a couple...the equivalent force must be 400 N applied at a certain poinr to give the same torque as was produced by the couple and force in their original position.