Equivalent Force couple to single resultant

In summary, when reducing a system involving different forces and a couple in a 2D plane to an equivalent force-couple system, you can use the resultant system to find the line of action of the force with respect to the point of reduction. There can be more than one correct solution depending on the point of reference used.
  • #1
triindiglo
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0
I have reduced the problem involving different forces and a couple in a 2D plane to an equivalent force-couple system. The force F is -27.5lbi + 11.65lbj, and the couple is -66.8inlbk.
I need the single offset resultant that accounts for the couple.

The way I thought to solve it was to take the couple and set it equal to r (unknown xi +yj) crossed with the force. But this gives me two unknowns with one equation, and I don't know where to go from here.

Thanks!
 
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  • #2
You could pick a point where one of the components of the force will have zero moment, and equal the product of the lever arm and component with moment respect to said point to the magnitude of the couple, then repeat by reversing the components. You'll end up with an x and y which will give the location of the force vector line of action with respect to the point as it were your origin. If you divide both magnitude of force and couple, you'll get the lever arm from said point to the force line of action.
 
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  • #3
So there is more than one correct solution?
 
  • #4
triindiglo said:
So there is more than one correct solution?

What I meant is your resultant at a certain location will account for the couple. It'll be a resultant system (no couple) which is what you are looking for, no?.

Coplanar resultant-couple systems can always be reduced to a resultant acting on a certain location with respect to the point where you reduced the system. This is because the couple and the resultant will always be normal in this case.

This means the line of action of the resultant will be in the same place regardless of the point of reference (origin or where you did the moments for the resultant-couple system reduction) you used, so "more than one correct solution" means same place but with different points of reference.
 
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  • #5
I apparently read your first post before you edited it or something, so I was talking about something else. The edited one clarified it for me though.

Thanks
 
  • #6
triindiglo said:
I apparently read your first post before you edited it or something, so I was talking about something else. The edited one clarified it for me though.

Thanks

Great!, and Welcome to PF! :smile:
 

1. What is an equivalent force couple to a single resultant?

An equivalent force couple is a pair of equal and opposite forces that act on a body at different points, resulting in a moment or torque. This force couple has the same effect as a single resultant force acting on the same body.

2. How is an equivalent force couple different from a single force?

An equivalent force couple consists of two forces acting at different points, while a single force acts at a single point. Additionally, an equivalent force couple produces a moment or torque, while a single force only produces a linear motion.

3. Why is it important to understand equivalent force couples?

Understanding equivalent force couples is important in engineering and physics, as it allows for the simplification of complex systems into a single resultant force. This simplification makes it easier to analyze and calculate the overall effect of the forces on a body.

4. How do you calculate the equivalent force couple to a single resultant?

To calculate the equivalent force couple, you can use the principle of moments. This involves finding the sum of the moments of the individual forces about a chosen point. The magnitude of the equivalent force couple will be equal to the sum of the forces, and the direction will be perpendicular to the plane of the forces.

5. Can an equivalent force couple be balanced?

Yes, an equivalent force couple can be balanced if the two forces are equal in magnitude and opposite in direction. This means that the moments of the two forces will cancel out, resulting in a net moment of zero.

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