While they would use whatever form of transportation was available, most heavy industrial goods were shipped by rail. The Office of Defense Transportation was formed via executive order on December 18th, 1941 to manage the transport of all defense materials and personnel within the US via rail, road, or ship (including coastal, Great Lakes and inland waterways transport.) Joseph Eastman, who was previously a member of the Interstate Commerce Commission, was chosen to lead the ODT and reported directly to FDR.

There was certainly concern as to whether the rail industry was up to the task. The rail industry had suffered during the great depression and was smaller than it was in 1929. Also wartime traffic was different than the normal west to east peacetime traffic seen during preceding years.

The ODT monitored congestion at ports in order to not repeat the chaos seen in 1917. Freight was tied to ship schedules, cars were mandated to run at near full load, empty cars could be used on other lines rather than returned to their owner, and creating through routes for urgent materials. The east coast oil shortage of 1942 caused by the sinking of a number of coastal tankers was the biggest challenge faced by the rail industry, but they managed to pull enough tanker cars out of mothballs and weather the storm until a pipeline could be built from Texas to PA. On the west coast, the Southern Pacific was managing over fifty trains a day into and out of Los Angeles.

The shipbuilding industry on the west coast had consumed every plant possible of providing components and materials to the point that the Navy began building the sections of hulls for destroyer escorts and LSTs in Denver, CO and shipping them via rail to Mare Island and Puget Sound naval shipyards for assembly and the installation of equipment and machinery. Sections would be limited to 17'x10'x50' in order to pass through the tunnels over the Rocky Mountains.

I don't have a lot of information specific to Cincinnati, but some of the larger manufacturing companies in the area were Allis Chalmers, Wright Aeronautical, R.K. Leblond Company, and Cincinnati Milling Machine Company. Much of their products needed to be shipped elsewhere for heavy industry or assembly, but even material going oversea would be more efficiently shipped via rail to the east coast rather than via the Ohio and Mississippi Rivers.

Edit: If you are specifically interested in Cincinnati, this 1991 article from Queen City Heritage has a pretty fascinating description of how Cincinnati supported the war, and how local industry adapted. It also talks about Cincinnati's Union Terminal and rail yard as well as the shipment of raw materials via the Ohio.