How can I calculate the strain in the xy plane (cylinder cross section)?

My first notion was to use the following Poisson's formula:

Δd = -dv(ΔL/L) where d is the diameter of a rod. I would then assume my cylinder is three rods (the cylinder is placed in solid rock). I can calculate the axial strain in each rod; but not the direction. I was thinking that I could add the strains to get the strain in the xy plane but I am having a problem visualizing the vector direction.

Am I completely wrong in my assumptions? Is there a better way to quantify this problem?

I have never posted in this forum. This is not a homework question despite my phrasing it that way. If it belongs in the homework forum please let me know.

Thanks, n