J.W. Bateson Enterprises Inc., the company that built the Dirksen Senate Office Building, the U.S. Naval Academy sports and swimming complex and the second phase of the Library of Congress James Madison Building, has acquired 80 percent of the Alexandria construction firm of Eugene Simpson & Brother Inc.

Simpson & Brother projects include the United Way of America headquarters, building No. 2 of the Torpedo Factory, and TransPotomac Plaza on the Old Town waterfront and the Mark Center Plaza II office building, all in Alexandria. The company had 1981 revenues of over $30 million.

Donald F. Simpson will continue as president and chief executive officer of Eugene Simpson & Brother Inc. The company was formed in 1933 by Simpson's father, Clarence C. Simpson, and his uncle, Eugene Simpson. Clarence Simpson has retired from Simpson & Brother to become president and chief executive officer of Simpson Development Co. Inc., which will manage Simpson properties not covered by the merger.

J.W. Bateson Enterprises Inc. is a wholly-owned subsidiary of Centex Corp. of Dallas, Tex., which has interests in cement products, oil and gas production and sales, homebuilding and general construction. The company owns Centex Homes of Washington Inc., developers of homes in Fairfax, Arlington, Montgomery and Prince George's counties.

Centex Corp., which begins its fiscal year on April 1, had first quarter earnings of $7.54 million on revenues of $225.5 million. It is listed on the New York Stock Exchange.