Construction has been completed on Knoll North, a 90,000-square-foot office building in Columbia. The five-story structure is the first of two planned for Knoll North Executive Office Park, a 36-acre complex being developed by the W. A. Kehoe Co. in Howard County at the intersection of Rte. 29 and Rte. 175.

The developer has tentative lease commitments from three firms for a total of 12,000 square feet, said Kehoe vice president Richard Pettingill. The $6.5 million structure at 1 Knoll North Dr. has between 17,000 and 20,000 square feet per floor.

The reinforced concrete office includes double-pane, bronze-tinted windows and was sited to make use of passive solar heating. The builder, Thomas P. Harkins Co., began construction in July.

Construction of the second building in the complex is scheduled to begin this summer, adding 60,000 square feet to the complex, Pettingill said. He added that development plans also call for installation of an exercise and jogging trail at the perimeter of the site.

Other developments in real estate in the Washington area:

* National Computer Graphics Association, a non-profit information management group, has leased 8,000 square feet at 8401 Arlington Blvd. in Fairfax. The association will relocate from offices at 2033 M St. NW.

* Bellemead Development Corp. has purchased 7 1/2 acres in Germantown, where it plans to develop a hotel and 1 million square feet of office space.

* Barnes, Morris and Pardoe, Inc., a commercial real estate firm, has relocated its Washington and Northern Virginia offices to 919 18th St. NW and 8300 Greensboro Drive in McLean.

* Mattress Discounters, a chain of bedding stores, has leased 4,500 square feet at 2332 Greenspring Ave. in Timonium, 5,264 feet at 8300 Pulaski Hwy. in Baltimore and 3,000 square feet at 7572 Ritchie Hwy. in Glen Burnie.

* Broventure Co., Inc., an investment firm, has purchased and will occupy 16 West Madison St. in Baltimore following renovation of the 10,000 square foot town house.

* Five leases have been signed for office space in the Maryland Trade Center at 7500 Greenway Dr. in Greenbelt: Bradford Communications Corp., a developer of electronic data bases, has leased 5,994 square feet; the Visiting Nurses Association has leased 865 square feet; Argo Systems, Inc., an electronics and engineering firm, has leased 3,569 square feet; Gill Marketing Co., Inc., a manufacturers representative, has leased 2,425 square feet; and Ryan Financial Services has leased 1,138 square feet.

* Frank S. Harris Associates Inc., a consulting firm, will occupy 2,000 square feet of leased space at 2301 M St. NW.

* Physical Dynamics, Inc., a defense consulting firm, has leased 11,800 square feet at 1777 North Kent St. in Rosslyn. A. J. Rowe Associates, Inc., a public utility consulting firm, has leased 3,000 square feet at the same address.

* General Systems Group, a data processing consulting firm, has leased 2,351 square feet at 6849 Old Dominion Dr. in McLean.

* Metropolitan Life Insurance Co. has leased about 3,000 square feet at 1110 Vermont Ave. NW and about 2,000 square feet at 1333 New Hampshire Ave. NW. Copy Data Systems has leased 1,400 square feet at the New Hampshire address.

* The American Association of Equipment Lessors has leased about 6,500 square feet at 1300 North 17th St. in Arlington.

* Volume Footware Retailers of America, Inc., has leased over 5,000 square feet at 1319 F St. NW.

* the Abacus Group, a mortgage lending concern, has leased 1,800 square feet at 1900 M St. NW.

* Moore Johnson, Inc., a management consulting firm, has leased about 4,000 square feet at 1110 Vermont Ave. NW. National Family Planning and Reproductive Health Association has leased over 3,000 square feet at the same address.