Ordinary construction and cleanout debris is what these containers carry. Tennessee does not publish a statewide list of banned materials, so the limits here come from the city's own rules and from what its transfer station takes.
Shelbyville's definition of hazardous waste is broad, and it is the list to read before loading. The city treats asbestos, batteries, oil, paint, pesticides, household cleaners, lawn and garden products, intact drums and cylinders, vehicle parts, dead animals, and any medical or biological waste as hazardous. Home maintenance and improvement materials and commercial or industrial waste are on the same list for the purposes of city collection, which is exactly why a rented container is the route for remodel debris.
Liquids, wet paint, solvents, and fuel stay out of any standard container. Unused water-based latex paint has a free drop-off at the city transfer station, which is a genuinely useful alternative.
Two facility refusals are worth knowing. Fence wire is not accepted at the transfer station at all. Leaves have to be bagged and taken to the transfer station rather than to the city burn pit, where only limbs and brush may be burned.
Treated and painted wood has its own dumpster at the burn pit, but that one is for city residents only, so a contractor cannot plan around it. Ask your account manager about anything unusual before it goes in.