Understanding Free Body Diagrams for Cantilevered Structures

In summary, the conversation discusses drawing a free body diagram for a structure supporting a pulley. There is a disagreement on whether there should be a moment exerted at the pulley and the correct direction and magnitude of the forces at the pulley end. The forces and moments at the fixed end are correctly shown, but there is confusion about the direction and magnitude of the forces at the pulley end. The concept of arbitrary reaction forces and moments is also discussed.
  • #1
pyroknife
613
3
For the attached picture I need to draw a free body diagram for the structure supporting the pulley.

At the fixed end (left), there would be a vertical and horizontal reaction force as well as a moment.

I am not sure what the forces and moments would be for the part connected to the pulley. What would it look like for this situation?
 

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  • #2
You're shown some of the forces. What others are missing?
 
  • #3
tms said:
You're shown some of the forces. What others are missing?

I did not show any forces in the picture.

There should be a force where the pulley is attached, but I don't know what direction that should be in.
Edit-I think there should be a reaction force where the pulley is connected in 'both' the x and y direction.
 
  • #4
There should also be a reaction moment where it's connected.
 
  • #5
pyroknife said:
I did not show any forces in the picture.
What about the string that runs over the pulley?
 
  • #6
tms said:
What about the string that runs over the pulley?

The 2 forces shown are given. They act on the pulley. The problem is to draw a free body diagram for the structure.
 
  • #7
Does the pulley exert any forces on the structure?

You've said the wall exerts a reaction force on the beam? What is it reacting to?
 
  • #8
The wall holds the cantilever beam. It exerts a horizontal and vertical (maybe) force on the structure. It also exerts a moment because it's cantilevered.

The pulley is being held by the structure, so yes, it exerts a force which should be both in the horizontal and vertical direction. My question is if this is right and if there is a moment exerted as well.
 
  • #9
There is no moment at the pulley, because the pulley bearings prevent this. But there is a vertical force and a horizontal force exerted by the pulley axis (spindle) on the structure.
 
  • #10
pyroknife said:
The wall holds the cantilever beam. It exerts a horizontal and vertical (maybe) force on the structure. It also exerts a moment because it's cantilevered.

The pulley is being held by the structure, so yes, it exerts a force which should be both in the horizontal and vertical direction. My question is if this is right and if there is a moment exerted as well.
Yes, there is a moment.

Are the bracket holding the pulley, and the pulley itself massive enough so the their masses have to be considered?
 
  • #11
Thank you.

It seems Chestermiller and SammyS may have conflicting opinions on whether there should be a moment exerted where the pulley is attached.

"Are the bracket holding the pulley, and the pulley itself massive enough so the their masses have to be considered?" I believe the structure is what's the pulley. I have as much info as you guys, so I'm not entirely sure. Typically for shear and moment diagram (which this is) problems, we ignore mass. This is what I assumed since they don't give you mass.

I think I agree with Chestermiller that there isn't a moment exerted at where the pullley is.
 
  • #12
Attached is what I think the free body diagram should look like.

Where the 4 arrows indicate the arbitrary reaction forces and the counter clock wise arrow represents the moment.
 

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  • #13
pyroknife said:
Thank you.

It seems Chestermiller and SammyS may have conflicting opinions on whether there should be a moment exerted where the pulley is attached.

"Are the bracket holding the pulley, and the pulley itself massive enough so the their masses have to be considered?" I believe the structure is what's the pulley. I have as much info as you guys, so I'm not entirely sure. Typically for shear and moment diagram (which this is) problems, we ignore mass. This is what I assumed since they don't give you mass.

I think I agree with Chestermiller that there isn't a moment exerted at where the pullley is.
There's a moment exerted at the junction of the structure and the wall. (I thought that's what the question was asking.)
 
  • #14
SammyS said:
There's a moment exerted at the junction of the structure and the wall. (I thought that's what the question was asking.)

Oh no, I mean where the pulley and structure were connected. It was a dumb question.
 
  • #15
pyroknife said:
Oh no, I mean where the pulley and structure were connected. It was a dumb question.
I agree that the two forces in the figure produce a zero moment about the pulley axis.
 
  • #16
pyroknife said:
Attached is what I think the free body diagram should look like.

Where the 4 arrows indicate the arbitrary reaction forces and the counter clock wise arrow represents the moment.
You have correctly shown the force and moment reactions at the fixed end, but at the pulley end, although you have correctly identified the 2 forces acting there, you have incorrectly shown the direction of those forces, and you have not indicated their magnitudes. Their direction and magnitudes must be properly shown on the FBD of the frame. The direction and magnitudes of the forces on the frame at the pulley can be determined by first drawing a FBD of the pulley, and then applying Newton's 3rd law.

When you talk about 'arbitrary' reaction forces and moment at the wall, I am not sure what you mean. You can arbitrarily choose their direction, I suppose, and their true directions will be determined when the equlibrium equations are applied. But their is no arbitation on their magnitudes (unknown until the equilibrium equations are applied), and no arbitration whatsoever in the magnitude and directions of the forces at the pulley end.
 
  • #17
If the reactions are drawn in the wrong direction, then their value will come out negative. The magnitude should still be the same. And don't say that a beam exerts a moment because its cantilever, it exerts a moment because the fixed support prevents it from wanting to rotate. What if the beam was supported by a roller or pin? Neither one of those supports have a moment reaction
 
  • #18
caldweab said:
If the reactions are drawn in the wrong direction, then their value will come out negative. The magnitude should still be the same. And don't say that a beam exerts a moment because its cantilever, it exerts a moment because the fixed support prevents it from wanting to rotate. What if the beam was supported by a roller or pin? Neither one of those supports have a moment reaction

A beam with a roller or pin is not cantilevered. The definition of a cantilever beam is one that is "built in" (to a wall).
 

1. What is a free body diagram?

A free body diagram is a visual representation used in physics to show all the external forces acting on a body. It helps to analyze the motion of an object and determine the net force acting on it.

2. When should I use a free body diagram?

A free body diagram should be used whenever you need to analyze the forces acting on an object. This can be in situations such as calculating the acceleration of an object or determining the tension in a rope.

3. How do I draw a free body diagram?

To draw a free body diagram, start by identifying the object you want to analyze and draw it as a simple dot or box. Then, draw and label all the forces acting on the object, such as weight, normal force, friction, and applied forces. Finally, use arrows to show the direction of each force.

4. What are the key components of a free body diagram?

The key components of a free body diagram include the object being analyzed, all the external forces acting on the object, and arrows representing the direction and magnitude of each force. It is also important to label each force with its corresponding variable or value.

5. Can a free body diagram be used for objects in motion?

Yes, a free body diagram can be used for objects in motion. In this case, the diagram will also include the velocity and acceleration vectors to show the direction and magnitude of motion. This can be helpful in calculating the net force and predicting the future motion of the object.

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