B. F. Goodrich Co. and Uniroyal Inc. announced yesterday they will merge their tire-making operations to form the second-largest producer of automobile and light-truck tires in North America.

The combined tire-production operations of the two companies would have $2 billion in sales, based on last year's figures, and 21,000 employes, ranking second in the industry to Goodyear Tire & Rubber Co., and ahead of the current No. 2 firm, Firestone Tire & Rubber Co. The joint venture is subject to completion of detailed agreements and approval by either the Federal Trade Commission or the Justice Department's antitrust division.

The joint venture, based in Akron, Ohio, would be called Uniroyal-Goodrich Tire Co. and would operate nine tire plants in this country, Canada and Mexico.

None of the companies' remaining businesses would be involved in the joint venture. Both Goodrich and Uniroyal manufacture chemical and plastics products, and Goodrich also produces wheels and other equipment for the aerospace industry.

Goodrich's stock closed at $35.62 a share, up 38 cents on the New York Stock Exchange. Uniroyal is a privately held company, following a leveraged buyout last year with the investment firm Clayton & Dubilier Inc., in which the acquisition was essentially financed through borrowed funds. The joint venture will reduce the debt on Uniroyal's books; the firm is also planning the sale of its chemical operations in the spring.

Although both companies are veterans of the U.S. tire industry -- Goodrich ranks third and Uniroyal fifth in sales -- they have concentrated in different areas. Uniroyal is a major supplier of tires for General Motors Corp.'s new cars, and also supplies Ford Motor Co. and Volkswagen of America. It ranks second to Goodyear in this part of the market.

Goodrich abandoned competition in that field in 1981, but produces new replacement tires for passenger cars, as does Uniroyal. Together, the two companies would have 15 to 20 percent of the replacement tire market, analysts said, counting their own products and brand names they make for others.

Uniroyal's strength as a supplier of tires for new passenger cars, the so-called "original equipment" market, and Goodrich's replacement tire operations, "make for a perfect fit," said Uniroyal Chairman Joseph P. Flannery.

Because the two companies' tire operations complement each other, analysts said they expected no antitrust opposition.

"I don't know it will really change very much," said W. Dudley Heer, an industry analyst with Duff & Phelps. "It doesn't change the fact that Goodyear dominates the business."

Goodyear's share of original equipment sales to the automobile industry was 32 percent last year, up slightly from the year before, while Uniroyal's and Firestone's shares showed small declines, according to Modern Tire Dealer magazine. Goodyear reported a $327.9 million profit on sales of $7.1 billion for the first nine months of 1985. Goodrich had a $349 million loss on sales of $2.4 billion, while Uniroyal had a $44 million profit on $1.56 billion in sales in the same period.

In original equipment market, the auto companies are demanding buyers, while in the replacement market, fierce import competition keeps profit margins tight, analysts noted.

"Nobody's going to complain about the merger ," predicted Donald F. De Scenza, senior analyst with Nomura Securities Inc. "Profits are so low and the market is so difficult. You could argue a combination like this will make the industry more competitive because it will keep two companies in the business that might otherwise leave it in the next recession."

The joint venture will be equally owned by its two parent companies, and will have plants, equipment and other assets totaling at least $500 million, according to Flannery. Its debt will total about one-half its capital, a debt-capital ratio that Flannery called stable.

The debt will include the pension obligations of both companies' tire operations, spokesmen said. Uniroyal reported an unfunded pension liability of $400 million last year, before it became a private company, while Goodrich's unfunded pension liability now is "substantially" more than its last reported figure of $16 million, at the end of 1984.

The bulk of each companies' unfunded pension liabilities represent commitments to tire workers, and both companies presumably would like to have those commitments off their financial statements, said De Scenza. In fact, those commitments will become part of the new venture's liabilities, spokesmen said.

The venture is intended to stand alone, without additional capital from either partner, a Uniroyal spokesman said. Assuming a continuation of current operations, the venture should be able to generate enough cash to pay debts, meet pension obligations and provide $100 million a year for capital expenditures, the spokesman said.