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My instructor gave the below example for identifying zero force members in truss. The members marked with the green zeros are the zero-force members, according to his solutions.

Truss system

I cannot understand why/if the answer is correct however. To my understanding:

  • member 8 should also be a zero-force member, since member 6 counters F1 already, and 3 and 14 are collinear.
  • If so, then member 9 should also be a zero-force member since 15 and 11 are collinear.
  • However, member 13 should not be a zero foce member, since it is direction countering the support reaction in support B.

Would greatly appreciate some validation / explanation of whether and why I was correct/wrong.

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2 Answers 2

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member 8 should also be a zero-force member, since member 6 counters F1 already, and 3 and 14 are collinear.

I don't see the reasoning here. The vertical contribution of 3, 6, and 14 together must counteract F1. Then, their horizontal contribution must counteract 8, and you haven't shown that this contribution is zero.

If so, then member 9 should also be a zero-force member since 15 and 11 are collinear.

Since this depends on the earlier disputed reasoning, it is also disputed.

However, member 13 should not be a zero foce member, since it is direction countering the support reaction in support B.

But 11 also counters that reaction. In addition, 13 must be a zero-force member because 12 and 16 are zero-force members and because the shared node isn't accelerating.

Perhaps you could explain why collinearity plays an important part in your reasoning. I'm looking for the sum of components in any direction; if there's only one component, it must be zero because the structure is static. This is related to collinearity but doesn't rely solely on the presence of collinearity.

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The simplest way to validate the solution is to draw and inspect the truss without the assumed zero-force members. The solution is correct only if it remains stable.

Your solution:

enter image description here

Note, member 13 can't carry force due to instability in joint "D":

enter image description here

Your teacher's solution:

enter image description here

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