[Summary: If two forces are such that the component of one of these forces forms a couple with the other, than which of the two cases (obtaining resultant via adding forces or obtaining moment and a resultant force via the method shown below) are correct? Read further for clear and detailed explanation]
Let two forces, F1 and F2, act on a rigid body and have a common point of application at Point A. Then their resultant force, R, can be calculated by the normal use of parallelogram as shown in the image below:
Now, since forces can be moved along their action lines in rigid bodies (statics), let the same forces be moved along their action lines as shown in the image below (Img.2):
Assume that the y-component of F2 is equal but opposite to F1. This means that the y-component of F2 and the force F1 act as a couple, and cause Moment in the rigid body, which is equal to F1 multiplied by the distance between them. In addition to this moment, we also have the x-component of F2 left over, which is the resultant force on the rigid body.
So, does this mean that, given the following conditions:
1) If any two forces Fa and Fb have intersecting action lines,
2) A line perpendicular to the action line of Fa at the point of intersection divides the plane (or rigid body) in two parts,
3) And Fb points towards a different plane (or different part of the rigid body) than Fa,
Then we have a resultant force (found by the parallelogram law) and moment at the same time?
But then what is the point of application, O, of the resultant force found in the second Image (Img. 5)?
But if this is so, then shouldn't the parallelogram be only defined in a way where the two forces are directed towards the same plane?
Or is this entire thing true? Can the forces actually be moved and resolved in a way they are here? Why or why not?
[Sorry if the post is messy and incomprehensible. I tried, as much as I can, to explain the question in the most organized fashion...]