Demand for the groceries that the Arlington Food Assistance Center distributes six days a week has grown 235 percent over the past five years, and only recently dropped slightly from its peak, when 1,770 families filled a box of food for their meals.

So AFAC, Arlington’s food bank for the past 25 years, thought it was doing a pretty good job of letting county residents know where to go if they needed emergency food help.

But a new study conducted for AFAC by Virginia Tech researchers shows that almost 1,000 more Arlington families need help putting food on the table, but don’t know about or haven’t used the food bank.

Slightly more than four in 10 Arlington families with incomes under $60,000 experience “food insecurity,” the study says. That means that in 31,500 households, someone has limited or uncertain access to food, skipping a partial or full meal because of cost. But nearly half of those low-income families had not heard of AFAC, and when a county social services worker gives them a referral good for collecting groceries there, about 1,000 don’t use them.

The information stunned Charles Meng, AFAC’s executive director, and his staff.

“We’ve been focused so much on the fund-raising side of things that we haven’t given as much thought to the transient nature of our community,” Meng said Monday. “We had never focused on the fact that there’s even more people in the community who need us.”

People who qualified for help but didn’t use it said the weekday and Saturday morning distribution times or locations were inconvenient. In response, Meng said the food bank will add a second evening distribution to the current Thursday night hours, and will consider adding additional distribution points.

AFAC will also pass out postcards in churches and schools to let people know how to use the food bank.

“Nobody want to come to a place like AFAC to get their food,” Meng said. “They come because they need food. When they don’t need us, they don’t come.”

The survey, which cost about $40,000 and was paid for by a donation from the Geary-O’Hara Family Foundation, will help the nonprofit agency develop a strategic plan for how to serve growing demand, Meng told an affordable housing forum last week. AFAC will also be studying how to provide more of what Meng said was the second-highest cost items in grocery bills: fruits and vegetables.

The new study shows that AFAC’s current clients fall into three broad groups: the unemployed or underemployed, who have a part-time, no-benefit, minimum-wage job; the elderly living on fixed incomes that no longer cover their living expenses; and people with physical or mental disabilities, whose incomes are not enough to pay for three meals per day.

The survey reports that 86 percent of AFAC’s client households make less than $25,000 per year, most are women, and most rely on friends and family for help before turning to AFAC.

The nonprofit agency will allow anyone who shows up at its Shirlington warehouse to leave with a box of food once. For subsequent visits, they have to receive a referral from Arlington County. The clients have to show that they are Arlington residents and they qualify for help, typically because of low or no income.

While the economy has recovered from the worst days of the recession and the number of families that sought food assistance dropped to 1,550 last week, Meng said some needs will not cease.

“Most of our population is finding jobs, but they’re not very good jobs. So even if they get jobs, they still need us,” he said. “In the case of the elderly and disabled,they’re always going to need us.”