I am building a 40 x 60 shop. My neighbor says he can get the saws to cut concrete at work. My question is how deep do we need to cut it it will be five and a half inches and also how big of squares should we cut it in?

If you're talking about control joints to control where the cracks happen: depth - 1/4 the thickness of the slab. spacing - 24x to 30x the thickness of the slab.

That is what I needed to know. Thanks.

Most of the floor I have done called for 1 third the thickness of the pad .for a small floor like this 2 cuts the 40 way 4 cuts the 60 way.

use a mask

I always thought a rule of thumb was 10x10 pieces

Mitch outside should be about 10x10 or no more than12x12. Inside there's not much of freeze thaw cycle.. So cuts can be farther apart.

Larry, I would break it in 10ft squares as that figures easily with your slab. I have always been told 1/4 the depth of the concrete is best depth of cut, but our saw is set at 1 1/4 inch so that is what we always do.
Talk to 10 engineers and you will get 10 opinions on how it needs cut though. Had one tell us to cut a slab into 20ft squares a while back and it was just a 4 inch thick slab. Had another tell us to take the thickness of the slab, multiply that by two and you have the feet the cuts should be apart. So 5 1/2 X 2 = 11 ft. On his line of thinking that 4 inch slab should have been cut on 8 ft centers.

You need to cut it 1/3 of the depth of the concrete and I would cut it in 10' squares. You need to make the green cut as soon as you can get on it without marking the surface.

Whenever I cut concrete, I would rather be smaller than larger sections. Less chance for random cracks. You didn't say if a pole building or just monolithic slab. Cracks on inside corners of poles are a pain.

What I'm getting is cut about 1 3/4 deep with about 10 x10 squares as soon as I can walk on it without marking it.