The logo I’ve always used for the site is an image of the National Archives Building. Amazingly, Congress did not approve such a building until 1926. The architect was John Russell Pope, who also designed the Jefferson Memorial and the National Gallery of Art. Ground was broken in 1931 and the building was mostly completed by 1935. According to the online history:
By the time President Herbert Hoover laid the cornerstone of the building in February 1933, significant problems had arisen. Because the massive structure was to be constructed above an underground stream, 8,575 piles had been driven into the unstable soil, before pouring a huge concrete bowl as a foundation. Another difficulty arose over the choice of building materials. Both limestone and granite were authorized as acceptable, but construction began during the darkest days of the Great Depression, and suppliers of each material lobbied fiercely to have the government use their stone. Ultimately, as in the other Federal Triangle buildings, limestone was used for the exterior superstructure and granite for the base.
As the National Archives notes, not only was the structure built in a troublesome location, but archives have special needs, further complicating the construction:
Constructing the National Archives was a mammoth task. Not only was the building the most ornate structure on the Federal Triangle, but it also called for installation of specialized air-handling systems and filters, reinforced flooring, and thousands of feet of shelving to meet the building’s archival storage requirements. The building’s exterior took more than 4 years to finish and required a host of workers ranging from sculptors and model makers to air-conditioning contractors and structural-steel workers.
Here’s a shot similar to the one used for the site logo.