How many carriages are necessary to support a 1″ thick beech or oak tread?

Q: How many carriages are necessary to support a 1″ thick beech or oak tread? I’d like to replace my carpeted stairs. I ripped up a few and found there are only 2 carriages supporting the edges of the treads.

Is it necessary to have a third carriage in the centerĀ for the new 1″ tread?

A: Treads are generally mortised into the stringers, but granted, not always. How long are the treads?

Follow-up Q: The treads are 36″ long. The stringers/carriages (I’m not sure which is the proper term) sit under the stairs at the edges of an enclosed stair. I was planning to glue the treads onto the stringers, screw them down, and plug over the screw holes.

I’m worried that even a fairly rigid tread will sag after a lot of use unless there is a centre stringer to support it. At the same time, it would be nice to avoid having to make another stringer to match the 2 that are already installed. I can picture there being slight differences that would be hard to correct. Do you think I should bother making a third stringer?

A: No, I don’t see the need. 1″ or 1 1/8 thick hardwood is really tough to bend. If it was 12 feet long plank you might get some bend in it. Not a 3 ft. slab.