The provisions of this traffic code regulating traffic on the streets of the city shall apply to the operation of vehicles on any private or dedicated or undedicated street or bridge, by whatever name known, which is within the city and which forms or is generally recognized as a part of the city street and highway system. The Safety-Service Director is hereby authorized to erect such traffic control devices and to enforce such regulations in accordance with the provisions of this traffic code on such private, dedicated or undedicated streets or bridges as are necessary for the safe and orderly movement of traffic.