Six years ago, Alexandria officials began to choose sites to rebuild several dozen public housing row houses that had to be torn down because they were in the path of the Braddock Road metro station.

Gladys West, now 69, was one of those forced to move. From the window of the house she moved to nearby, she watched and listened as the wercking cranes and bulldozers began to build the station on the land where she had lived for 14 years. But there has been no such building activity at the various locations scattered around Alexandria where the new public housing units are supposed to be built.

What happened to Alexandria's efforts to build new public housing in a case study in the kinds of social and governmental barriers that frequently block the path to new housing for the poorest of the poor in the Washington area.

Those barriers can take many forms. In Alexandria, residents who lived near many of the proposed sites in 1974 irately opposed the notion of having new public housing near them. Over the years, there were disputes with the federal Department of Housing and Urban Development over where the new homes should be built and how the city should complete its project.

Twice this year, when the Alexandria Redevelopment and Housing Authority advertised for developers, only one builder responded.

There is no question that the Washington area could use more public housing. If everyone now living in the estimated 15,000 public housing apartments and homes in the District, Fairfax County, Alexandria, Montgomery County and Prince George's County moved out today to make way for new tenants, there still wouldn't be enough units for the estimated 15,900 families on public housing waiting lists in those jurisdictions.

Nor is the situation likely to get better soon. The area office of HUD said that only about 280 public housing homes will be added here this year in the District, Fairfax County and Montgomery County.

Alexandria's plans to build new public housing took an important step forward this week. An official at the HUD area office said the government has approved a $2.9 million bid from the Dittmar Company in Arlington to construct the houses.

Vola Lawson, an official with the suburbs' housing authority, said construction could began in early September.

"We've been waiting for these units" Lawson said, "We need them." Costs are going up all the time." Plans call for 19 two-bedroom row houses, 26 three-bedrooms, and five four-bedrooms to be built at four sites.

The 40 families were displaced from their John Roberts Homes, near the railroad tracks were relocated over the last three years by the Alexandria Redevelopment and Housing Authority, a state-established body that acts as the city's urban renewal agent, and Metro. The families have been promised the opportunity to move into the new row houses when they finially are built.

But West said it has taken so long to build the new homes that she no longer is interested -- a feeling echoed by others who moved.

"I don't want to put up with moving again now." West said "I'm pretty well satisfied I have good neighbors and I'm on a bus line.

The famliies were moved -- some twice -- into other sections of the John Roberts Homes, into other public housing, and into subsidized privately owned apartments. About 45 percent of the adult tenants had jobs according to Alexandria records. Twentynine of the families are black and 11 are white.

In 1972, the housing authority and the Alexandria City Council signed an agreement saying that if any public houisng unit is demolished by public action, it must be replaced with another public housing unit "within a reasonable period of time."

At one point in 1974, as many as 20 sites were suggested as places to put new public housing. Finally, Alexandria officials chose five locations -- only to have HUD write back they disapproved of some of them, mainly for enviromental reasons.

The new public housing also was delayed because Alexandria officals expected their public housing plans to include not only replacement of the John Robets Homes, but also the construction of a new building for elderly residents, and the demolition of some deteriorated units at the Cameron Valley public housing complex.

Cameron Valley's 368 units had been built as temporary government housing during World War II. Ten new units were to built there as part of the project.

But HUD twice rejected the Cameron Valley demolition plans, stressing rehabilitation rather than demolition and new construction. It took many months to resolve that dispute.

Alexandria isn't the only jurisdiction that has had problems building public housing. Harry Williams, a former lawyer for a buildier who constructed public housing for the elderly in Bethesda, noted that though his firm was chosen to develop the building in the early 1970s, it wasn't dedicated until 1978.

Williams said the corporation he represented ran into zoning problems, a federal moratorium on subsidized housing, a county sewer moratorium, and increased construction costs. It seemed, he said, as if "a kind of Murphy's law" -- the rule that says that if anything can go wrong, it will -- afflicted the project.

"The delays resulted in tremendous cost increases" Williams said. "The [Montgomery County] Housing Opportunities Commission had to convince HUDD that costs had changed ... Public housing is a victim of the economic times. It's a real problem from the standpoint of inflation and tight money. The amount of federal funds available are able to subsidize fewer and fewer units."

Local officials say that many builders don't want to participate in government-subsidized programs because they envision mountains of paperwork and bureaucratic delays. The emphasis today on building subsidized housing in scattered locations, rather than in massive projects, discourages developer who don't want to get involved in samll projects.

Officials at the Washington area HUDD office said they are sympathetic to the problems of local governments and that they try to be flexible. Cost guidelines are brought up to date each summer, and vary from metropolitan area to metropolitan area.

If HUD had no cost ceilings, developers obviously would be interested in building more public housing, said April LeClair, deputy Director of housing for development at the area HUD office. But she added, "We're not so restrictive that we can't produce housing that we have money for. We can use all the money we've got."

D.C. housing director Robert L. Moore said the District uses some money that comes from HUD to subsidize public housing projects. Half a million dollars the current fiscal year, Moore said.

The District by far has the majority of the area's public housing -- nearly 12,000 units. About one out of every four public housing units in the area is for the elderly. Arlington County has no traditional, government-owned public housing.

Earl Morgan, a Prince George's County housing authority offical, said his Maryland suburb doesn't intend to develop new public housing. The county's elected officials long have complained that Prince George's has been the dumping ground for low-and moderate-income, privately owned housing.

HUD's cost guidlines, he said "hold us very tight."

Morgan said the county is concentrating on a federal rent subsidy program that uses existing, privately owned apartments. The program has become one of the most active housing programs locally and nationally.

"It maintains a scattered-site profile, with no undue concentration of low-income people," Morgan said.