How Do You Calculate the Couple in a Force-Couple System at Point O?

[Bradracer18]

Homework Statement

I've attached an image. The question states:

Replace the three forces shown, with an equivalent force-couple system at point O(origin).

I've got a little ways, but I am stuck at the couple. I don't know how to use the distance in the couple. Need to know what distance to use, and from where.

Homework Equations

R = Fx + Fy

C = Mo = ra/o x Fa + rb/o x Fb + rc/o x Fc(is this correct, or do I use x and y?)---this is the part where I'm stuck.

magnitude C = sqrt(Cx^2 + Cy^2)

The Attempt at a Solution

Fx = 200cos60 + 300cos45 + 250cos30 = 528.6 i

Fy = 200sin60 + 300sin45 - 250sin30 = 260.3 j

R = 528.6 i + 260.3 j

C = Mo = ?

Am I correct up to this point too?

View attachment sample exam1.bmp

 

[radou]

Homework Statement

I've attached an image. The question states:

Replace the three forces shown, with an equivalent force-couple system at point O(origin).

I've got a little ways, but I am stuck at the couple. I don't know how to use the distance in the couple. Need to know what distance to use, and from where.

Formally, you should first find the resultant of the three forces. To find the couple, you first have to find the moment caused by the resultant force at point O, and then replace that moment with an equivalent couple.

 

[Bradracer18]

Ok, I did find the resultant(R).

And, to find the couple, don't I just find the moment(at the origin)?

Here goes...but this is where I get confused.

528.6(9) + 260.3(30)...i have no clue, I know this isn't right.

Any way you could show me like part of how to do it? So I get the concept?

 

[PhanthomJay]

Ok, I did find the resultant(R).

And, to find the couple, don't I just find the moment(at the origin)?

Here goes...but this is where I get confused.

528.6(9) + 260.3(30)...i have no clue, I know this isn't right.

Any way you could show me like part of how to do it? So I get the concept?

you've got the correct components of the resultant force at the origin. But now you must sum moments of each horizontal component of each force about the origin, and sum moments of each vertical component of each force about the origin, and add them together to get the couple about the origin. Watch your plus and minus signs (clockwise vs. counterclockwise).