According to Goldsboro City Ordinance 2010-51, the following applies to burning within the city limits
No person shall ignite, cause to be ignited, permit to be ignited, allow or maintain, kindle or maintain within the corporate limits of the city any nonpermissible open burning fire. Since the city does provide public pick up of trash, leaves and other yard debris, the burning of such material is prohibited.
Open fires for cooking and heating shall be allowed when such fire is not composed of leaves or yard waste, and the location of such fire, and the items necessary for its containment, comply with the North Carolina Fire Code, and provided that the emission of smoke and fumes do not irritate, annoy or constitute a nuisance to others. Open fires for cooking and heating shall comply with the following:
(A)   Such fires shall be contained in a campfire pit, confined to a container no larger than a 55-gallon drum or other device approved by the Fire Code Official for such use. Fuels for such fires must be naturally cut wood and untreated lumber.
(B)   Warming fires in approved containers shall be located not less than 15 feet from any structure.
(C)   An appropriate means of controlling the fire (i.e. extinguishers) shall be available while the fire is burning.
(D)   Burning of construction materials like insulation, asphaltic materials, tires, copper wire or treated lumber is prohibited. Warming fires shall not be used to dispose of paper, trash and excess construction materials or other synthetic salvageable materials.
For more information about the City Ordinances, Visit https://codelibrary.amlegal.com/codes/goldsboro/latest/overview