COLUMBUS, Ohio (AP) _ Negotiators shifted the search for a national pattern contract for the rubber industry Sunday to talks with B.F. Goodrich Co. after pacts covering 36,000 workers in the Big Four tire companies expired at midnight.

Officials of the United Rubber Workers said workers at the Big Four companies - Goodrich, Goodyear, Firestone, and Uniroyal - would work day-to- day as negotiations continue.

Union spokesman Curt Brown said Saturday that talks with Goodyear Tire & Rubber Co. in Dayton were broken off when union negotiators were unable to reach a settlement. The search for an industry-pattern agreement switched then to talks with Goodrich representatives in Columbus, he said.

The union wants a three-year pact that would set an example for contracts covering all of its members at the Big Four companies, which has been the industry practice. But Firestone officials have said they would not abide by a pattern settlement.

Goodrich has about 7,200 URW members. Goodyear, the largest of the Big four, has 15,500.

''Discussions are going on and that is all we can say at this point,'' Goodrich spokesman Donovan D. Husat said Sunday.

Both sides agreed not to reveal details of the talks, which have been under way since March 5, although Goodyear was not picked as the original target company until early April.

Goodrich was the pattern-setter in 1982 and in 1979, Brown said.

The Akron Beacon Journal reported Sunday that one of the stumbling blocks was believed to be pensions.

The URW, whose members average $12.39 an hour, also has said it wants a general wage increase, continuation of a cost-of-living allowance that has yielded $1.16 per hour over the last three years and a voice in corporate board rooms.