Fitting rods into a wooden truss (cut off edges) I believe to have a very simple problem but I'm somehow too stupid to solve it. I want to fit a wooden rod in between two plates. To do so, I need to cut off the top and the bottom end so that the ends of the rods lie flat on the surfaces of the top and bottom plates.
I have tried the following:

Use the shear operation. But it turns out it doesn't work like intended when the rod is already rotated (I'm confused however why this is?). Shearing also begs the problem that there is no option to adjust the face to exactly horizontal (or is there?)
Use edge slide without clamping (c). I thought this would work great combined with the snapping options, so that the top and bottom edges of one end would snap neatly to the top face of the bottom plane for example. It turns out to be quite buggy and it snaps to everything else than the top and bottom plane.

Now I'm wondering whether there is an easy option to solve this seemingly easy problem :/ Any ideas?
The Shear tool won't work the way you want because your object is oblique. The Shear tool moves the selected vertices on one of the 3 axis, it doesn't slide the vertices along the existing edges, therefore the object you want to shear needs to be parallel to one of these axis if you don't want it to be deformed, and it is not the case here. Examples with shear on the Y axis:


In your case the solution is to use the Knife tool (K to activate, Z to cut through, C to cut perpendicullary).
That said, we don't know if you want to merge your bar with the other ones, in that case you'd better use the Bridge tool to join 2 faces of the horizontal bars.