Within weeks after the Sept. 11, 2001, terrorist attacks, the Smithsonian Institution began collecting a wide range of artifacts recovered from the three sites where the hijacked planes went down.

In an exhibit opening Sept. 3, the National Museum of American History will let visitors get much closer for a more intimate experience. The museum plans to depart from the usual glass-covered displays and assemble the objects on open, uncovered tables.

“September 11: Remembrance and Reflection” contains about 60 objects from the World Trade Center in New York, the Pentagon and Shanksville, Pa.

“The objects come from collectors and donors and, more importantly, people who were there,” said Cedric Yeh, curator of the Sept. 11 collections. In 2002, the museum was designated as the official archives for Sept. 11 materials....