Solving 3D Statics Homework with Free Body Diagram

  • Thread starter goonking
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    3d Statics
In summary, the conversation discusses solving a 2-D problem by setting a moment equation using one of the three rings as the reference, and using the two equations of statics to solve for the remaining forces. The individual also shares their own method of finding the remaining forces through a lot of substituting. The final result is Ay = Cy = 190.
  • #1
goonking
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Homework Statement


upload_2016-4-12_19-53-5.png


Homework Equations

The Attempt at a Solution

Free body diagram
upload_2016-4-12_20-3-27.png
Setting moment at the origin = 0

(Rb X B) + (Ra X A) + (Rc X C) = 0

solving the 3 determinants and setting the coefficients of i, j, and k to 0, I get:

8Bz - 10 Cy = 0

-12 Az + 10 Cx = 0

12 Ay - 8Bx = 0

I have too many unknowns.

summing forces :

∑Fx = Bx + Cx = 0

∑Fy = Ay + Cy - P = 0 => Ay + Cy = 380

∑Fz = Az + Bz = 0

I still have too many unknowns.Any suggestions?
 
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  • #2
goonking said:

Homework Statement


View attachment 99005

Homework Equations

The Attempt at a Solution

Free body diagram
View attachment 99006

Setting moment at the origin = 0

(Rb X B) + (Ra X A) + (Rc X C) = 0

solving the 3 determinants and setting the coefficients of i, j, and k to 0, I get:

8Bz - 10 Cy = 0

-12 Az + 10 Cx = 0

12 Ay - 8Bx = 0

I have too many unknowns.

summing forces :

∑Fx = Bx + Cx = 0

∑Fy = Ay + Cy - P = 0 => Ay + Cy = 380

∑Fz = Az + Bz = 0

I still have too many unknowns.Any suggestions?
Just like you would do when solving a 2-D problem, it is better to write a moment equation using one of the three rings as the reference, rather than picking another arbitrary point like the origin. Using one of the rings as the reference for the moment equation eliminates one of the forces, and you should be able to solve for the remaining forces using the two equations of statics which you are allowed to write.
 
  • #3
SteamKing said:
Just like you would do when solving a 2-D problem, it is better to write a moment equation using one of the three rings as the reference, rather than picking another arbitrary point like the origin. Using one of the rings as the reference for the moment equation eliminates one of the forces, and you should be able to solve for the remaining forces using the two equations of statics which you are allowed to write.
you mean for example, taking ∑Mc = 0 along the x-axis : (Bz)(8) + (Ay)(15.62) - (P)(10in) = 0

(Bz)(8) + (Ay)(15.62) = (380)(10) = 3800
 
Last edited:
  • #4
actually, I was wrong, I had all I needed already, it was just A LOT of substituting but in the end, I got Ay = Cy
plugging into Ay + Cy = 380

Ay = Cy = 190

A lot of subbing to find Ay = Cy12 Ay = -8 Cx = -8(12/10 Az) = 8(12/10) Bz = . . . and so on
 

FAQ: Solving 3D Statics Homework with Free Body Diagram

1. How do I create a free body diagram for a 3D statics problem?

To create a free body diagram, start by identifying all the forces acting on the object in 3D space. These include external forces such as weight, tension, and friction, as well as internal forces like normal forces and shear forces. Next, draw a simple, labeled sketch of the object and indicate the direction and magnitude of each force using arrows. Make sure to include all the forces acting on the object and label each force with a letter or symbol for easy reference.

2. What is the purpose of a free body diagram in 3D statics?

A free body diagram is a visual representation of all the forces acting on an object in 3D space. It helps to simplify a complex problem by breaking it down into individual forces that can be analyzed and solved using equations. It also helps to identify any missing or unknown forces, making it an essential tool in solving 3D statics homework problems.

3. How do I solve a 3D statics problem using a free body diagram?

To solve a 3D statics problem using a free body diagram, start by applying Newton's laws of motion to the object and writing out the equations of motion for each direction (x, y, z). Next, plug in the known values and use algebra to solve for any unknown forces or variables. Make sure to include proper unit conversions and use vector addition to find the resultant force if needed.

4. What are some common mistakes to avoid when using a free body diagram in 3D statics?

One common mistake is forgetting to include all the forces acting on the object in the free body diagram. It is important to carefully identify and include all external and internal forces to accurately solve the problem. Another mistake is not labeling the forces or including the correct direction and magnitude of each force. It is also important to pay attention to units and make sure they are consistent throughout the problem.

5. Can a free body diagram be used for non-static problems in 3D?

Yes, a free body diagram can also be used for non-static problems, such as problems involving motion or acceleration in 3D space. In these cases, the free body diagram will include additional forces, such as the object's velocity and acceleration. The same principles of identifying and solving forces still apply, but the equations of motion will be more complex.

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