Most construction and household debris is fine to load. The limits come from Arkansas landfill rules and from the landfill that takes your load.
Arkansas law keeps whole tires out of landfills unless they're shredded or split. Landfills can't knowingly take car batteries, and yard waste isn't supposed to be landfilled just to get rid of it. The Little Rock Landfill doesn't accept tires at all.
On top of those rules, keep hazardous waste, liquids, paint, solvents, fuel, and asbestos out of a standard dumpster.
Sherwood's public works page lists what its garbage carts won't take, and many of those items belong in a roll-off instead. Lumber, shingles, rocks, tile, marble, and granite are on that list. Paint must be fully dried before it goes in household trash. The City also stopped picking up refrigerators, freezers, and air conditioners, so tell us before you add one to a dumpster.
If you're unsure about an item, ask your account manager before you load it.