Equivalent force couple systems at a point on a rigid body

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Homework Statement


Attached is a pdf of the assignment problems, I'm looking at problem 1 under the "Try" section. It shows a rod attached to a wall bracket on the left, with a force applied on the right side.

I'm also including a link to the solution, it's under "Problem 3.83" - http://www.academia.edu/9504768/SOLUTION_MANUAL

The force P has a magnitude of 250 N and is applied at the end C of a 500 mm rod AC attached to a bracket. Assuming α = 30° and β = 60°, determine:
a. The equivalent force-couple system acting at point B
b. An equivalent system formed by two parallel forces applied at A and B

(note) - I converted mm to meters first, fyi



Homework Equations


Moment = Force x distance from reference to point of application
Moment = cross product of Force vector and reference-to-PoA vector


The Attempt at a Solution



First I calculated the moment about point B : Mb = F*d = 250 N * .3 m = 75 Nm in -k direction (right hand rule).

Now the question asks me to...substitute?...a force couple at point B in place of force P? If I'm correct, an equivalent force couple is equivalent to another system of force(s) if it has the same effect on the body. So this force couple -at- point B would have to produce the same moment -about- point B. I don't understand that : How can I produce a moment about a point if I apply 2 parallel and equal forces AT that point? If I applied them to point B, wouldn't they just produce arbitrary moments about an infinite number of points down the rod EXCLUDING point B?

I can imagine what a force couple looks like, I've seen diagrams and think I understand the basics of it - but with what I understand I would think I'd have to apply a force some distance from point B, and apply a parallel force of equal magnitude but opposite direction an equal distance on the other side of point B. Kind of like 2 kids pushing around one of those spinning playground things. I can imagine part b) of this question more easily I think.

Does it look like I'm having a misunderstanding of the fundamentals of these concepts, or is the wording strange? Thank you for any/all advice, I appreciate it.
 

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  • #2
CWatters
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If I'm correct, an equivalent force couple is equivalent to another system of force(s) if it has the same effect on the body.
The equivalent force couple would comprise a force and a couple/torque. eg two separate things acting at B.

See..

 

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