BRACING RECTANGULAR FRAMEWORKS

This paper describes the economical placing of diagonal braces in the walls and ceiling of a rectangular one story building. It begins with the definition of the structure geometry of a graph embedded in Euclidean space: a combinatorial geometry (matroid) on the set of potential braces. When the embedded graph is a plane grid of squares the geometry is graphic. Then, for example, minimal rigidifying sets of braces correspond to spanning trees in a complete bipartite graph. The methods used in the plane case are extended to analyze how sets of wall and ceiling braces in a one story building can be dependent.