A museum dedicated to the events of 11 September 2001 will open in New York City this May.

At each stage of the design process, which incorporated objects from the World Trade Center, the museum had to consider what was appropriate to display and find a balance between commemoration and education.

New York-based Davis Brody Bond is the lead architectural firm on the project and worked in conjunction with Oslo-outfit Snøhetta, which designed the pavilion for the museum's main entrance.

The 9/11 Memorial Museum will cost US$24 (£14, €17) to enter, although admission to the 9/11 Memorial, which has attracted 11.5 million people since opening two years ago, will remain free.

The museum and the memorial together cost US$700m (£418m, €508m) to construct. The museum is divided into two main exhibition spaces. In Memoriam sits below the footprint of the south tower and commemorates the combined 2,983 people killed in the 9/11 attacks and the 1993 bombing of the World Trade Center.

The other main exhibition space, which sits under the footprint of the north tower, will provide visitors with access to the historic assets preserved at the World Trade Center site. The museum will display both the monumental artefacts associated with the events of 9/11 and look at the human element through narrations of the stories of those affected.

Speaking to delegates at Arts Council England's No Boundaries conference in York and Bristol, via a live feed from the US, museum director Alice Greenwald said: “All museums that document events defined by unimaginable personal loss and collective trauma face challenges during the planning stage – the 9/11 museum was no exception.

“The work to create the museum took place within the context of intense public scrutiny, divergent expectations of what would be appropriate to present at such an emotionally charged site and the daunting responsibility of constructing a narrative that would codify a history not yet written.”