# How to find strain in an inclined member of a struss

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?

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.

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.

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.