Most household and construction debris can go in your container. Ohio's landfill rules set the main limits.
Ohio's landfill rules bar hazardous waste, asbestos without the proper permits, PCB waste, medical waste, liquids in bulk, low-level radioactive waste, and whole or shredded scrap tires. Loads made up of separated yard waste are also turned away, though tree trunks and stumps are allowed.
Batteries have their own rule. Ohio law keeps lead-acid batteries out of landfills, and stores that sell car batteries must take the old one back when you buy a new one.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Tires need to be declared, since Ohio's scrap tire rules apply to loads with more than 10 tires. Clean cardboard, glass, and cans can go to the county's 24-hour recycling drop-off on State Route 36 instead.
Ask your account manager about anything you aren't sure of before it goes in.