Solving Truss Force Issue: CD & DE Equal to 0?

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Members CD and DE are considered to have forces equal to zero due to the symmetry of the structure and loading conditions. This symmetry leads to an equilibrium state at joint D, where the forces in CD and DE must balance out. The downward force is counteracted by the vertical components of other members, maintaining structural stability. The clarification on the values of G and Ay being 6 instead of 8 is noted but does not affect the symmetry argument. Understanding these principles is crucial for analyzing truss structures effectively.
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In the attached problem, I don't understand why members CD and DE are equal to 0. I was under the impression that the combined vertical components of BC and CD should equal 6+downward components of BC and EF, as to counteract the force straight down, but this is not the case.

My questions:

Why are the forces in members CD and DE equal to zero?

If they are equal to 0, what stops the downward force from moving the structure?

Thank you

Note: G and Ay are 6 and 6, not 8 and 6 as shown. I used the right values for my calculations, but for some reason wrote 8 down
 

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It's not clear from your post: Who is saying that members CD and DE are equal to 0? Are you talking about the forces in these members?
 
Sorry yes - that's what I meant.
 
You still haven't answered the main question: who is saying that the forces in members CD and DE are equal to 0?
 
The answers in the back of the textbook
 
IF THE STRUCTURE AND LOADING ARE BOTH SYMMETRICAL THEN THE EQUILIBRIUM OF JOINT d REQUIRES SYMMETRY OF FORCES IN cd AND de. tHAT IS THE CLUE...
 
Hey, you don't have to shout.
 
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