Understanding Free Body Diagrams for Cantilevered Structures

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SUMMARY

This discussion focuses on drawing free body diagrams (FBD) for cantilevered structures, specifically addressing the forces and moments acting at the connection points of a pulley. Participants agree that at the fixed end, there are vertical and horizontal reaction forces along with a moment due to the cantilever nature of the beam. The pulley exerts both horizontal and vertical forces on the structure, but there is a consensus that it does not exert a moment due to the bearings. The importance of accurately depicting the direction and magnitude of these forces in the FBD is emphasized, as incorrect representations can lead to negative values in calculations.

PREREQUISITES
  • Understanding of free body diagrams (FBD)
  • Knowledge of Newton's 3rd law of motion
  • Familiarity with cantilever beam mechanics
  • Basic principles of equilibrium in structural analysis
NEXT STEPS
  • Study the principles of drawing accurate free body diagrams for various structures
  • Learn about the application of Newton's 3rd law in structural mechanics
  • Research cantilever beam design and analysis techniques
  • Explore the effects of different support types on moments and forces in structures
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Structural engineers, mechanical engineers, students studying mechanics of materials, and anyone involved in analyzing cantilevered structures and their load distributions.

pyroknife
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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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You're shown some of the forces. What others are missing?
 
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.
 
There should also be a reaction moment where it's connected.
 
pyroknife said:
I did not show any forces in the picture.
What about the string that runs over the pulley?
 
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.
 
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?
 
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.
 
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).
 

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