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Bracing Rectangular Frameworks. I

Ethan D. Bolker and Henry Crapo
SIAM Journal on Applied Mathematics
Vol. 36, No. 3 (Jun., 1979), pp. 473-490
Stable URL: http://www.jstor.org/stable/2100966
Page Count: 18
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Bracing Rectangular Frameworks. I
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Abstract

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.

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