The sole elevator in the brand new Hunters Point Queens Public Library.

A steep staircase that was quickly made off-limits by librarians because it is not safe for children.

Cracks on the fourth floor of the Hunters Point Queens Public Library.

Kevin C Downs for the New York P

A long-awaited $41-million Queens library that opened last month is plagued with an encyclopedia’s worth of issues — including leaky ceilings and a not-so-soundproof quiet room, The Post has learned.

Long Island City’s decade-in-the-making Hunters Point Library is already showing signs of wear, with a Post reporter recently eyeing large cracks on multiple floors — including one that stretched about 10 feet — and water damage in some areas.

“When it rains, we have leaks,” a librarian said, blaming the problem on an as-yet-un-opened rooftop “reading garden” with panoramic views of the city.

The new building’s sorry state is the culmination of nearly 10 years of design and construction. Plans for the branch were completed in 2010, but the ground-breaking did not come until 2015. The book-lender finally opened Sept. 24.

The lit house, designed by Steven Holl Architects, came under fire earlier this month because a fiction section could only be reached by a steep staircase — in violation of federal accessibility requirements.

Staffers have since moved the tomes, but that area is now just dead space. A frustrated librarian said she didn’t know if it would be remodeled “but we won’t be putting any books there again.”

“We might turn [it] into sitting areas, but no one knows yet,” she said.

Queens Library spokeswoman Elisabeth de Bourbon said the branch is assessing the situation with the architects and the city’s Department of Design and Construction, which oversaw and managed the project.

But that’s not the only design flaw librarians have had to deal with.

A curved wall in the children’s section resembling a quarter-pipe skateboard ramp had to be blocked off by rolling bookshelves to make sure kids didn’t hurt themselves climbing it.

Stairs in another children’s section were also blocked off with pieces of wood as a safety measure, before the building opened, De Bourbon said.

The structure’s acoustics are also inadequate, with the simple act of pulling out a chair on the fifth-floor generating a raucous, echoing screech.

“It’s loud I know,” said a man sitting nearby when a reporter moved the chair. “They didn’t think about that. You’d think they would put some kind of padding down.”

A supposed “quiet room” also isn’t soundproof. A reporter inside could hear footsteps, coughing, and even a broom sweeping outside the room.

One librarian said she wished the building was designed less like a museum or gallery — and more like a library.

“I would have liked more space, more shelves. As any public librarians would agree, more space,” she said. “I’d like for the floors to be open where you can see everyone and everything. It is best for their safety and our safety, too.”

The DDC said the roof is complete, and will open after its inspected by the Buildings Department, but did not respond to specific questions about the other issues.

De Bourbon said DDC is working on minor work that remains outstanding and that the branch is addressing any issues that come up with the agency.