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Default How deep into the wood should a screw go?

Argh I'm new to woodworking, I don't know the terminology, so bear with
me please.

I'm making a freestanding shelves unit. I'm using shelf boards that are
sold per piece, and then I'm using two rather thick and long pieces of
timber (I think it was 5cm x 8cm x 2.4m) so that I would make it stand
upright and then fit the shelves on it. To do that I'll be using those
L-shaped pieces of metal. Two for the two pieces of timber to make it
stand and not fall on its face, each one of them (the metal L-shaped
things) will be ~30cm, facing away from the wall - the shelves will be
standing against the wall but not attached to it. Then I'll use smaller
pieces of those L-shaped metals to attach the shelves to the long
pieces of timber.

My question really is about the two long pieces of timber, when I
attach the L-shaped metals to them on which the shelves will rest (and
will be screwed, but I know I'll just use 12mm screws for those because
the shelves will be 20mm and will rest on the metal anyway), how deep
into the long pieces of timber should the screws go to make sure the
shelves don't fall off, and how long should I choose the screws to be?
Should they go a 1/3 of the way in, or 2/3s?

I should say that I'll be using the shelves for books, so I expect that
they'll have to bear some weight.

Many regards and thanks.

Better questions bet better answers. That is a much better question.

20 or 22mm. Go as far as you can without coming out the other side.

Wood screws have a tapered profile and their bite come from the thread (or
depth there of). Since the very tip of the screw (the first 4mm (1/4'")or
so) is narrow the threads can't be to deep and it can't get much bite. What
I am saying is that the 1st 1/4" of screw doesn't give you any significant
holding power.

If your screw is 2 inches (5cm) long that's not really significant, if your
screw is 10mm, that's nearly half your screw.

As others have said, it's tough to comew up with a simple rule.