Bridgestone, Japan's largest tire manufacturer, which has been making a determined push into the U.S. market, has agreed to buy a truck-tire plant in Nashville, Tenn., from Firestone Tire and Rubber Co.

The $52-million transaction will put Bridgestone in a position to be the original-equipment supplier of tires for the 120,000 light trucks a year that Japan's Nissan Motor Co. plans to build at a new plant in nearby Smyrna, Tenn.

Bridgestone is a giant of the worldwide tire industry, fourth in total sales behind Michelin of France, Goodyear and Firestone. Up to now, however, it has had only a minuscule 1 percent share of U.S. market and has imported all the tires it sells here.

Firestone, which has been selling off inefficient and underused plants in an effort to return to consistent profitability, negotiated with Bridgestone for more than a year over the Nashville facility. An agreement in principle was announced last month.

The Nashville plant, built in 1972, is said to be a modern, efficient facility. It produces radial truck tires, which is one of the fastest growing sectors of the tire market, but under Firestone has been operating at about half its 3,000-tire daily capacity because of the depressed market for U.S.-built light trucks.

Bridgestone has a reputation among tire industry analysts for high efficiency and productivity levels in its work force. Bridgestone and Michelin are reportedly the only two tire companies in the world that are growing in real terms, and Bridgestone has announced its intention to increase U.S. sales from $200 million a year to $1 billion.

By purchasing a plant instead of building its own, as Michelin did, Bridgestone evidently hopes to escape the high capital debt burden that has limited the profitability of Michelin's U.S. operations.

Still unclear is the fate of the United Rubber Workers Union contract covering the 900 employes at the Nashville plant. Union officials said that since the plant is still owned by Firestone, it will be included in the nationwide master contract negotiations scheduled for later this month, but Bridgestone has not said what it intends to do about union representation.

In a related development, General Tire and Rubber Co. said it will close its manufacturing plant in Akron, Ohio, later this year.