The University of Utah will name its new football support building after the late grocery-chain tycoon Dee Glen Smith.

The Smith family has donated $1 million, or approximately one-half the cost of the building's construction. Walter P. Gnemi, U. vice president for administrative services, said the balance of the building's cost will be covered by other private gifts and gate receipts at athletic events.Scheduled to open by August, the building is located next to two football practice fields on Guardsman Way at 500 South. The building will house new weight and exercise rooms, lockers and coaching staff offices.

The U. Board of Trustees, the institution's governing board, approved the naming of the building at its monthly meeting Monday.

Smith, who started with a corner grocery store in Brigham City and became chief executive officer of the giant Smith's Management Corp., died of a brain tumor June 30, 1984.