> Wouldn't your beams start cracking at the bottom, where they are subject to traction?
You have a few mistakes here. I’m not trying to demean you, but I’m going to number them just for clarity, as it can get confusing when there are many misunderstandings.
1. You are intending to ask about tension (which the rebar helps with), not traction (the force your tires exert against a road).
2. Tension is not only experienced at the bottom of beams, the location with the most tension will depend on the geometry. For a vertical beam, I think tension will probably be pretty even through the whole beam in most “normal” designs and loading configurations. But it will really depend on the geometry and on the loads being applied.
3. I think when you say concrete beams you’re meaning columns (apologies if I’m wrong about this). Concrete columns are remarkably good at holding up without rebar, because they experience almost exclusively compression! And indeed, ancient Roman designs did not use rebar at all :). It’s certainly possible.
1.- My apologies for the terminology - I took one overview class on the subject in Spanish, and haven't looked at it in the last 60 years. 2.- Agreed - that's why rebar on horizontal beams (and slabs) sometimes goes on the top edge and shifts to the bottom edge. 3.- By beams I do mean horizontal beams. This also applies to horizontal slabs. However, vertical columns also need rebar, especially in earthquake-prone areas. If the ground moves horizontally in an earthquake, the (vertical) columns have to transmit the motion to the upper parts of the structure. This create huge tension stresses on one side of the columns so they need vertical rebar rods on their perimeter.
> 1. You are intending to ask about tension (which the rebar helps with), not traction (the force your tires exert against a road).
I don’t know if it is the case here, but it is a common mistake for some non-native English speakers. In some languages traction is a false friend.
And in English, traction also means pulling, but it got somewhat misapplied to the friction of tires, causing confusion in the language. For example, a tractor is something that pulls, and when a broken leg is put in traction, it's suspended to pull it apart and keep the muscles from pulling it together.
Tension, as you say, is indeed the term used in physics and engineering for the force on an object pulling it from either end.