The struggle to afford the average $71,200 house in Fairfax County is forcing many families into deep financial trouble and eroding the stability of family life, according to a county study of mental health released yesterday.

The study, based on 117 detailed interviews conducted during the past year, said that many Fairfax families -- including some who make far more than the $28,500 the typical family there earns -- have spent more money than they can afford on their homes.

As a result, the study found that financial worries and the stress of two-career marriages have left many families in "deep trouble."

"Many families in Fairfax County appear to have sold their family's present for a housing future," said Robert C. Weigl, a social psychologist who designed the study for the Mount Vernon Center for Community Mental Health. The study was conducted in the rapidly growing southern half of Fairfax, which has more low-income families and a more transient population than the rest of the county.

The human costs of becoming part of Fairfax County, which has the highest average spendable household income in the United States ($27,582), often are marital fights, divorce, child neglect and alcoholism, according to the study.

"Fairfax County is exceedingly wealthy and its citizens have a veneer of success about them but... these surface appearances are deceiving and only partially compensate for the tension produced by the competitive nature of the area," the study said.

The study's conclusions reflect the opinions of 117 "well-informed persons," including businessman, health workers, high school leaders, librarians and civic leaders, who were asked to identify the area's economic and social problems.

The study admits a built-in bias against some individuals such as the very young and vey old, who were not interviewed. It also admits that interviews asking about memtal health problems tend to elicit negative answers.

The conclusions about money problems and family strife, however, were echoed yesterday by members of the county Board of Supervisors, police and by recent complaints about youth boredom in the suburbs.

"In an area where there is so much emphasis on money, you are bound to have family tensions," said Supervisor Alan H. Magazine (D-Mason). "People can't reconcile their expectations with what they can actually do with their money."

Supervisor Marie B. Tavesky, a Republican representing the Springfield area, which the study calls a "teeming bedroom community" of 35,000, said that mortgage payments of $700 and $800 a month are frustrating many homeowners and causing a growing "malaise."

"People are strapped and they are so strapped because they are trying to maintain a style of living that maybe we should all get away from," Travesky said.

During a press conference yesterday, Weigl said the most surprising aspect of the study is the finding that families normally considered rich, with annual incomes higher than $50,000, are unhappy.

"They don't feel rich," Weigl said. The psychologist, who counsels affluent families in the Mount Vernon area, said that professional couples often expend "a huge amount of energy staving off financial ruin, (energy) that mihgt be used to work on a marriage or rear kids."

Weigl said many families in southern Fairfax are "seriously dysfunctional." He said their most common problems are child neglect, stress-induced alcoholism and marital troubles. The study, which deals with the opinions of those interviewed, did not provide statistical evidence of these problems.

But a January report by the Fairfax-Falls Church Community Service Board found that nearly one out of every 10 teen-agers in the conty had an alcohol-related problem. The Fairfas County Office of Research and Statistics reported that in 1977, the last year for which figures are available, the number of divorces (2,711) exceeded the number of marriages (2,470).

The Mount Vernon study said that despite economic and social problems, most people find Fairfax a physically attractive place to live. "People are civil. The schools are well staffed... Most of the housing is imaginative and compatible with nature and the natural setting," said a section of the study dealing with the Springfield area.

Despite the attractions of suburbia, the study found that many families fo not understand basic financial planning, that many people don't know or care about their neighbors and that children are often confused and bored.

"The economic system which had given birth to a sweeter life in the suburbs produced a recreational wasteland for adolescents and a lack of natural gathering spots for people of all ages," the study said. It also said many parents do not pay enough attention to their children.

The study found that many persons interviewed were worried about violence and vandalism by suburban children. In a Fairfax County courtroom on Tuesday, lawyer Louis Koutoulakos, who is defending the three youths accused of burning Fort Hunt High School in December, argued that the suburbs themselves are to blame for some of the vandalism there.

"These youngsters today have nothing to do but sit around and be bored while the community, which does not give them anything meaningful to do, goes to cocktail parties," Koutoulakos said.

The Mount Vernon study recommended the county provide more counseling services for families, created more organized youth activities and advised potential newcomers of the danger of spending too much on housing.