The Commissioner and local authorities of cities and towns in their respective jurisdictions, upon written application by the owner or operator of any empty, oversize and overweight, rubber-tired, self-propelled hauler or loader used in the construction and coal mining industries, may issue to such owner or operator a permit authorizing operation upon the highways of such equipment with gross empty weights in excess of those established in §§ 46.2-1122 through 46.2-1127 and sizes in excess of those established in §§ 46.2-1105 through 46.2-1108. The permits shall be issued only after an engineering analysis of a proposed routing has been conducted by the Virginia Department of Transportation or local authorities of counties, cities, and towns in their respective jurisdictions to assess the ability of the roadway and bridges to be traversed to sustain the vehicles’ size and weight. The fee for a permit issued under this section shall be based on the costs assessed against the applicant to cover engineering analysis, not to exceed three hours. No permit issued under this section shall be valid for the operation of the equipment for a distance of more than 75 miles.