Everyday construction and cleanout debris is what these containers are for. The city's crews will not collect construction, remodeling, or repair debris at all, which the code treats as industrial refuse and leaves to the property owner or contractor.
The real limits come from the county landfill, and they are specific. Bartow County refuses hazardous waste outright, and it will not take whole tires, lead-acid batteries, biomedical waste, or animal carcasses. Asbestos is accepted only when it arrives wet and double-bagged to the county's thickness standard, and only when it came from inside the county.
Mixing is the expensive mistake here. Construction and demolition debris is accepted only in its own designated area of the landfill, and only if the load does not contain other kinds of solid waste. It cannot go into the lined household landfill at all. Yard trimmings have a third destination again, the county's inert landfill. One bag of household trash in a load of lumber and drywall can send the whole thing to the wrong place.
Hazardous waste, liquids, wet paint, solvents, and fuel stay out of any standard container. Loads also have to be covered in transit under county rules, so nothing should be mounded above the rails.
If an item has you guessing, ask your account manager before it goes over the side.