I've come across several of these buildings - most recently yesterday (see prior post). There is a Carnegie Library in Antwerp, OH, near to our town.
Carnegie libraries (1,689 in the U.S.) were funded and built between 1883 and 1929 with money donated by businessman and philanthropist Andrew Carnegie who earned the nickname "Patron Saint of Libraries".
In the early 20th century, a Carnegie library was often the most imposing structure in hundreds of small American communities from Maine to California. Most of the library buildings were unique, displaying a number of architectural styles. Each style was chosen by the community and the architecture was typically simple and formal, welcoming patrons to enter through a prominent doorway, nearly always accessed via a staircase, symbolizing a person's elevation by learning. Outside every library was a lamppost or lantern to symbolize enlightenment.
Nearly all of Carnegie's libraries were built according to "The Carnegie Formula", which required matching contributions from the town that received the donation. It must: demonstrate the need for a public library; provide the building site; provide ten percent annually of the cost of the library's construction to support its operation; and, provide free service to all.
The design of the Carnegie libraries encouraged ommunication with the librarian. It also created an opportunity for people to browse and discover books on their own. Before Carnegie, patrons had to ask a clerk to retrieve books for closed stacks.
While hundreds of the library buildings have been converted into museums, community centers, office buildings and residences, more than half of those in the U.S. still serve their communities as libraries over a century after their construction, many in middle- to low-income neighborhoods. (resource: Wikipedia)