Solve Statics Question: Vertical Reactions at A,D,F

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In summary, the diagram shows 3 wooden beams supported at A, D, and F with only vertical forces. The solution uses 3 basic equations and algebra to determine the vertical reactions at each point, with the final solution being D=1/13P, F=9/13P, A=3/13P. There is a question about why D=2/3C=2E instead of D=2/3C=2(P+E), with the suggestion that force P may only be applied to beam BEF and not DCE. However, it is clarified that P is applied to the system of beams at the intersection of BEF and DCE.
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JoshuaR
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Homework Statement



d7ebb587e9b4ddd7d3e68141e14356e4.jpg


This is the diagram of the question. There are 3 wooden beams nailed together and supported at A,D, and F. Assuming only vertical forces, what are the vertical reactions at A, D, and F?
The solution uses this diagram to make three basic equations:
smallunit.jpg

(1) for BEF, F=2/3(P+E)=2B
(2) for ECD, D=2/3C=2E
(3) for ABC, A=2/3B=2C

For (2), why is it D=2/3C=2E and not D=2/3C=2(P+E)?
Why doesn't P come into the equation? Isn't it acting at point E? I understand the solution completely except for this one point. Thank you.

Using algebra I can get the solution of D=1/13P, F=9/13P, A=3/13P
But only if D=2E rather than D=2(P+E)
 
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  • #2
Someone suggests that force P may be only applied to beam BEF, not on beam DCE. Would that make it work?
 
  • #3
JoshuaR said:
Someone suggests that force P may be only applied to beam BEF, not on beam DCE. Would that make it work?
That is not quite correct, force P is applied as shown, to the system of beams, at the intersection of the 2 beams BEF and DCE. Draw a Free Body Diagram of beam DCE. Isolate it such that you cut the beam with your Free Body Diagram immediately to the right of joint E, such that P, the applied force, does not enter into the diagram, and therefore the given solution appears correct.
 

1. What is the purpose of solving statics questions about vertical reactions at points A, D, and F?

The purpose of solving statics questions about vertical reactions at points A, D, and F is to determine the amount and direction of forces acting on these specific points in a structure or system. This information is crucial for designing and analyzing stable and balanced structures.

2. What factors affect the vertical reactions at points A, D, and F?

The vertical reactions at points A, D, and F are affected by various factors such as the weight of the structure, the external loads applied, and the constraints or supports present at these points. The distribution of these factors also plays a significant role in determining the vertical reactions.

3. How do you calculate the vertical reactions at points A, D, and F?

The vertical reactions at points A, D, and F can be calculated using the principles of statics, specifically the equations of equilibrium. These equations state that the sum of all forces in the vertical direction must equal zero at each point. By setting up and solving these equations, the vertical reactions can be determined.

4. Are there any assumptions made when solving statics questions about vertical reactions?

Yes, there are some assumptions made when solving statics questions about vertical reactions. These include assuming that the structure is in a state of static equilibrium and that the material used is rigid and does not deform under the applied forces. These assumptions may not always hold true, but they provide a good approximation for solving these types of problems.

5. Can the vertical reactions at points A, D, and F be negative?

Yes, the vertical reactions at points A, D, and F can be negative. This indicates that the force is acting in the opposite direction of the assumed positive direction. It does not necessarily mean that the force is physically negative, but rather that it is acting in the opposite direction of what was initially assumed.

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