Arlington County Board chairman-elect Walter L. Frankland Jr. has unexpectedy stepped down as his county's Metro Board of Directors representative.

Frankland, a 53-year-old Washington lobbyist for silver interests and a frequent critic of the financing of Metro's 101-mile, $7.2 billion system, based the decision on the fact that it would be "too time consuming" to judgle both positions.

Earlier this week, Frankland denied suggestions that current board chairman Dorothy T. Grotos, who opposed his former plan to remain as Arlington's Metro delegate, had influenced his decision to step down.

Grotos, who last year became arlington County's first Republican-endorsed board chairman in nearly a decade, said yesterday, "I've always thought that these jobs should rotate. Metro has become an ingrown club, and that's a weakness. Some people have been on the [Metro] board since it started."

Without Frankland's decision to resign the Metro post, Grotos would have been left without a prominent leadership role on the Arlington County Board. Fellow Republican Stephen Detwiler will be president of the Metropolitan Washington Council of Government (COG) and the new board vice chairman, the remaining major assignments.

Still, Grotos said she was "surprised" by Frankland's move and denied published reports of controversy over the Metro post.

"It was a pretty peaceful situation," Grotos said. "We didn't agree, but there was no further discussion. I was surprised because he feels strongly about Metro. But it was nothing like what happened last year."

In January 1979, there was speculation that Frankland would emerge from the Republican-dominated board as both the board chairman and Arlington's Metro representative. Grotos bitterly objected at the time. A compromise was reached in which Grotos was elected to the chairmanship.

Frankland, vacationing in Jackson, Tenn., was unavailable for comment yesterday. Sources indicated, however, that Frankland plans to continue to speak out on Metro operations.

Grotos said "common sense" would dictate her role on the Metro Board of Directors.

'I would like to see it [Metro] run more like a business than the largest public works project in the world," she said.