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I'm working through an FEA problem and I'm stuck.

Question: How can I determine the strain in member 3 from displacements known at node 3?

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It's at 45 degrees, I know I should be using some $cos\phi$ and $sin\phi$, and given the displacements I suspect there to be a negative strain (indicating compression), however, I'm not entirely sure how to find the strain in the inclined member using both displacements.

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Resolve the nodal displacements into the element coordinate system.

Most likely, one of the element coordinate directions lies along the element. Since you didn't tell us whether the element is a rod or a beam, we don't know if the other two directions are important or irrelevant for finding the strains.

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Strain = (deformed length - L3) / L3

You can find the deformed length from the deformed position of node 3 and Pythagoras' theorem.

You can find the deformed position of node 3 by adding the displacement vector to the coordinates of node 3.

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