It depends on where you live, but if the household only has a single $40k income they would likely be lower-middle class in most of the country. I know people that are raising kids on that, though I wouldn't recommend it. It would only work in a very high cost-of-living area if you were single, though if you have kids you'll receive significant government subsidies. It will only support a simple and unambitious lifestyle but it won't be terrible by any means.
You'll live in a small house or suitable apartment, you'll cook at home almost all the time using inexpensive ingredients, and you'll take inexpensive vacations. You won't have any fancy stuff, aside from one or two special "nice" things, and the stuff you do have you'll use for as long as it is feasible to do so. The most challenging expense will be transportation, because you'll rely on your car and cars are prone to significant random and variable expenses.
Savings won't be enough to cover retirement but you will have a modest amount, you'll mostly be relying on Social Security. Even poor people often have a very modest amount of savings. I know a single mother who amassed $20k savings on a $30k income just by saving for many years.
The ugly part, and one of the main reasons I would not recommend raising a family this way even though I know how, is the social consequences because it comes with a lot of class signals. People in this class are often treated quite shabbily by people that live in the expensive coastal cities, which will impact your kids.