Over 35 years in construction here...so not blowing smoke out my ass like some.
* 4" thick concrete should be adequate (assuming a strong base mat'l) unless your tractors are pretty big. Then you might consider 5".
* 3,000 PSI concrete is pretty standard in most areas. Going to 3,500 PSI would be beneficial and not cost much.
* expansion joints should be cut at a distance twice the thickness in feet. i.e. If you pour a 4" slab then 8' centers...a 5" slab then 10' centers. But more importantly, they should be cut asap. The same day if it's hot and dry, first thing the following morning if not. If cut too late, the concrete has already started cracking where it wants to. Remember "expansion joint" is a misnomer. Concrete is never larger than its original liquid state. A more accurate description is "contraction joints." Concrete
will crack. The key is to get it to crack where
you want it to crack and that's at the joints. You're setting up a weak plane by cutting the joint. Oh...and the joint should be cut a minimum depth of 20% the slab thickness...I prefer 25% (i.e. a 1" deep cut in a 4" slab)...residential contractors will want to lightly score it...about a 1/4" deep...a complete waste of time.
* unless you have moisture issues in your substrate (i.e. a low lying area) then I'd advise against vapor barrier. Pouring over vapor barrier means that the bleed water leaving the concrete as it cures cannot exit the bottom and all must exit the top. This can greatly reduce the strength of the concrete and increase the shrinkage cracking because the slump of the top 1/2 of the slab is significantly increased as the bleed water migrates thru it. It can also lead to exaggerated slab curling caused by uneven curing top to bottom. If you don't use a vapor barrier and it's been dry for a few days before you pour, then wet down the gravel substrate so the moisture isn't sucked out of the concrete too quickly. Lightly moisten the gravel, don't soak it. More below in the importance of slow, even curing of the slab.
* rebar is far superior to wire mesh. #4 rebar (1/2" dia.) at 12" to 18" on center each way (OCEW) would be good. The rebar should be placed on concrete chairs or set on small concrete bricks. If you used mesh then heavy mats that are also placed on chairs or bricks is the only way to go. Rolled mesh is worthless. Either way, don't allow the contractor to pull the mesh or rebar with "concrete hooks" during the pour instead of placing it on bricks or chairs. "Pulled" reinforcing will
always resettle to the bottom of the concrete and will be of no benefit there. Reinforcing must be in the center 1/3 of the slab to be of any use and the only way to ensure this is by using chairs or bricks. Using fine "chicken wire" mesh like was suggested earlier is laughable. Don't let the contractor use clay bricks...only concrete bricks.
* in addition to rebar or mesh (or in lieu of), you might consider adding "fibermesh" to the concrete mix, though this isn't necessary. Info here:
http://fibermesh.com/product/microsynthetic.html I'm not a fan of using
only fibermesh, I am a fan of adding it to conventional reinforcing. But there are a
lot of slabs out there with only fibermesh that have held up well...
* don't overwork (over trowel) exterior concrete, the more the surface is worked, the weaker it becomes. Screed it off, hit it with a float, minimal trowling to bring a bit of paste to the top, broom it, And walk away. (Though I'm not sure a broom finish is appropriate for a horse barn...that's something that others may be able to address)
* proper curing is essential. Concrete needs to dry out slowly and evenly. A membrane curing compound should be sprayed on, or the slab covered with wet burlap sacks...that are kept wet for a few days. Or simply set a sprinkler up on the slab and keep it wet for a few days...to a week.
* but maybe the most important thing required to produce a strong slab with no cracks is to not pour the concrete too wet. Most residential contractors pour concrete with way too much water in it because it's a LOT easier to work and move and screed off. They'll pour it with an 8" to 10" slump if you let them..."self leveling concrete" as we jokingly refer to it. All this excess water eventually leaves the concrete as it cures...that results in a loss of volume, and excessive shrinkage cracking. The excess water also results in a weaker mix than if it had the proper water/cement ratio. Commercial contractors pour about a 4" slump. A 6" slump is the most I would ever consider allowing. What's a 6" slump? I'm sure YouTube has some explanatory videos...everything's on YouTube these days!
Hope this helps.