Most construction, remodeling, and cleanout debris is fine to load. The limits come from state and federal waste rules and from the landfill that takes your load.
The usual exclusions apply. Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a roll-off container.
The Twin Oaks Landfill handles several items separately. Tires carry a per-tire fee, and appliances with Freon carry a per-unit fee. Computers, monitors, car batteries, and motor oil go to its household hazardous waste and oil recycling area instead of the landfill.
The City also runs a Used Oil and Tire Recycling Center for residents, which is a good option for items you pull from your load.
If you're unsure about an item, ask your account manager before it goes in.