An armory originally was a place to store arms, and could be any old building. Many pre-1900 armories look like fortresses, as in the Army of the First Corps of Cadets in Boston.
Beginning about 1900, however, a larger, distinct, half-barrel style of armory became very common. Examples:
Because of their huge interiors, many of these armories later doubled as sports arenas. The University of Illinois ran indoor track in their armory for many years, and the Minneapolis Armory was once home to the Minneapolis Lakers.
Why the unique half-barrel style? And why only during that time period?