National Savings and Trust Co., of Washington, announced yesterday that Douglas Smith will step down as the bank's chairman on Sept. 1, and will be succeeded by NS&T's current president, Joseph Riley.

Smith, who has been with the bank since 1931 and served as its chairman for the past 14 years, leaves his post to serve as honorary board chairman. Smith will reach the retirement age of 65 next month.

When he became president of the bank in October 1960, deposits were less than $87 million. At the present time, NS&T had deposits of more than $395 million.

Riley has been president of NS&T since March 1976 and was named chief executive officer two years later.

Smith, who has been active in dozens of civic groups and has served on the boards of 15 companies, has often been characterized as one of the city's few remaining personal bankers. He often dealt directly with bank customers from an office on the main floor of NS&T's main office at 15th Street and New York Avenue NW.

Smith was also involved in banking organizations. In 1962, he served as president of the District of Columbia Bankers Association and also had been a member of several committees of the American Bankers Association.

In addition to those changes at the top of the bank's management, Michael Ryan was named NS&T's executive vice president and chief administrative officer.

Ryan has been a senior vice president of the bank, joining its staff in March 1979. Stephen Couch, an NS&T trust investment officer, was also appointed manager of the Trust Investment Division.