# Equivalent force couple systems at a point on a rigid body

• reed2100
In summary, the conversation revolved around a physics problem involving a rod attached to a wall bracket with a force applied on one end. The question asked for the equivalent force-couple system at a specific point, which led to a discussion about the fundamentals and understanding of force couples. It was determined that the equivalent force couple would consist of a force and a torque acting at the specific point.
reed2100

## 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.

#### Attachments

• HW #1 - Force and Moment.pdf
1.5 MB · Views: 2,329
reed2100 said:
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..

## 1. What is an equivalent force couple system at a point on a rigid body?

An equivalent force couple system at a point on a rigid body is a combination of forces and couple moments that have the same effect on the rigid body as the original forces and moments acting on the body. This means that the resulting motion and deformation of the body will be the same, regardless of whether the original forces and moments are replaced by this equivalent system.

## 2. How do you determine the equivalent force couple system at a point on a rigid body?

The equivalent force couple system at a point on a rigid body can be determined by using the principle of transmissibility, which states that a force acting at a point can be transferred to any other point along its line of action without changing the resulting motion and deformation of the body. This means that the equivalent force can be moved to a desired point on the body, and the equivalent couple moment can be calculated based on the original moment and the distance between the original and desired points.

## 3. What is the difference between a force and a couple moment in an equivalent force couple system?

A force is a push or pull that acts on the rigid body, while a couple moment is a rotational force that causes the body to rotate around a point. In an equivalent force couple system, the force and couple moment are combined in a way that produces the same effect on the body as the original forces and moments, but they each have a different physical effect on the body.

## 4. How is the direction of the equivalent force and couple moment determined in an equivalent force couple system?

The direction of the equivalent force is determined by the original force, as it must have the same magnitude and direction as the original force in order to produce the same effect on the body. The direction of the equivalent couple moment is determined by the right-hand rule, where the fingers of the right hand curl in the direction of the original couple moment, and the thumb points in the direction of the equivalent couple moment.

## 5. What are some practical applications of equivalent force couple systems in engineering?

Equivalent force couple systems are commonly used in the analysis and design of structures, such as buildings, bridges, and machines. They allow engineers to simplify complex forces and moments acting on a rigid body, and determine the resulting motion and deformation of the body. This helps in making decisions about the strength and stability of structures, and can also be used to optimize the design for efficiency and cost-effectiveness.

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