Simplification of force and couple system

In summary, the conversation discusses the concept of taking moments at a specific point in a figure, specifically point B in figure 4-35(c). The conversation explains that the diagrams are showing a static situation and that the curly arrows indicate the presence of a couple, while the straight arrows show the direction of the force vectors. The conversation also clarifies that the couple can be positioned anywhere along the length of the rod and that the choice of pivot point is for analytical purposes. Finally, the conversation mentions that the net moment will always be Fd when two forces are applied at a distance d apart.
  • #1
goldfish9776
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Homework Statement


In the figure 4-35 c , the bar is rotating at point b , but the book gave the taking moment at point b .. This is confusing... When we are taking moment at point b , the bar at particular point wouldn't move, am I right?

Homework Equations

The Attempt at a Solution

 

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  • #2
goldfish9776 said:

Homework Statement


In the figure 4-35 c , the bar is rotating at point b , but the book gave the taking moment at point b .. This is confusing... When we are taking moment at point b , the bar at particular point wouldn't move, am I right?

Homework Equations

The Attempt at a Solution

You're confused because you've jumped over a couple of steps.

Start with figure 4-35(a). Someone is holding a bar which has a vertical load applied at the opposite end. The point of the sequence of figures 4-35(a)-(c) is to show how the moment created by F at the opposite end of the bar can be replaced by the same force F located to the end being held plus a couple whose magnitude is equal to the force F multiplied by the distance d.
 
  • #3
SteamKing said:
You're confused because you've jumped over a couple of steps.

Start with figure 4-35(a). Someone is holding a bar which has a vertical load applied at the opposite end. The point of the sequence of figures 4-35(a)-(c) is to show how the moment created by F at the opposite end of the bar can be replaced by the same force F located to the end being held plus a couple whose magnitude is equal to the force F multiplied by the distance d.
the diagram 4-35c is confusing , it shows the point B is moving ... It should show point A is moving , right ? Since B is the pivot ...
What does -FB means ? recative force of Force B ? Or we apply the same force at point B in opposite direction ?
 
  • #4
goldfish9776 said:
the diagram 4-35c is confusing , it shows the point B is moving ... It should show point A is moving , right ? Since B is the pivot ...
What does -FB means ? recative force of Force B ? Or we apply the same force at point B in opposite direction ?
You're still confused. Nothing is moving. The straight arrows merely indicate the direction of the force vectors. The curly arrows are there to indicate that a couple is present and the direction (CW or CCW) of the moment.

The force -F which is shown at B indicates the reaction to the force F applied at the free end of the rod. It is the applied force F and its corresponding reaction -F which are responsible for creating the couple M, shown in figure 4-35(c). The thing to keep in mind here is all three diagrams represent a static situation.

A suggestion: don't just look at the diagrams and expect to fully comprehend what is being described. There is a discussion in the text just above these figures which would answer most of your question here if you would read it while looking at the diagrams.
 
  • #5
SteamKing said:
You're still confused. Nothing is moving. The straight arrows merely indicate the direction of the force vectors. The curly arrows are there to indicate that a couple is present and the direction (CW or CCW) of the moment.

The force -F which is shown at B indicates the reaction to the force F applied at the free end of the rod. It is the applied force F and its corresponding reaction -F which are responsible for creating the couple M, shown in figure 4-35(c). The thing to keep in mind here is all three diagrams represent a static situation.

A suggestion: don't just look at the diagrams and expect to fully comprehend what is being described. There is a discussion in the text just above these figures which would answer most of your question here if you would read it while looking at the diagrams.
Ok, the f at point a cancel off -f at point b , causing the moment to occur at point b ...but the text gives taking moment about point b , doesn't it means the pivot is situated at point b ?
 
  • #6
goldfish9776 said:
Ok, the f at point a cancel off -f at point b , causing the moment to occur at point b ...but the text gives taking moment about point b , doesn't it means the pivot is situated at point b ?
Yes. The point is, the couple can be positioned anywhere along the length of the rod.
 
  • #7
goldfish9776 said:
Ok, the f at point a cancel off -f at point b , causing the moment to occur at point b ...but the text gives taking moment about point b , doesn't it means the pivot is situated at point b ?
It depends what you mean by a pivot. If you are thinking of it as the stick undergoing an actual rotation as a result of these applied forces, with the pivot being the point that remains stationary, you have no idea where the pivot will be. It depends on the mass distribution along the stick.
If you simply mean the point that you choose to take moments about for analytical purposes, then as SteamKing posted, it doesn't matter which point you pick.
What the text is saying is that if you apply two forces F and -F along lines of action a distance d apart then no matter where you put your axis the net moment will be Fd. That is the nature of a couple - it does not act around any particular axis.
 
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What is a force system?

A force system is a collection of forces acting on a body or object. These forces can be either concurrent (lines of action intersect at a common point) or non-concurrent (lines of action do not intersect).

What is a couple system?

A couple system is a pair of forces that are equal in magnitude, parallel in direction, and opposite in sense. These forces act on different points of a body and cause rotational motion.

How do you simplify a force system?

To simplify a force system, you can use vector addition to combine the forces into a single resultant force. This resultant force will have the same effect on the body as the original force system.

How do you simplify a couple system?

To simplify a couple system, you can use the principle of moments to find the net moment of the system. This net moment can then be replaced with a single equivalent force at a specific point, known as the center of moments.

What are the benefits of simplifying force and couple systems?

Simplifying force and couple systems can help to analyze and understand the effects of forces on a body more easily. It can also help to simplify calculations and make it easier to determine the overall behavior of a system.

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