EXPANSION FOR STUDYING THE TOPOLOGICAL PROPERTIES OF STRUCTURES

The idea of expansion has a long history in mathematics and structures. In mathematics, Whitehead [1] used an expansion process for the charcterization of topological spaces. In structural analysis, Müller Breslau and Henneberg [2,3] emplyed simple expansion for the classification of trusses. In this paper, the latter idea is generalized and applied to the calculation of degree of statical indeterminacy (DSI) and degree of kinematical indeterminacy (DKI) of different types of skeletal structures, such as rigid-jointed planar and space frames, pin-jointed planar trusses and ball-jointed space trusses. Such a calculation not only simplifies the evaluation of DSI and DKI, but it also provides an insight to the problem of the formation of self equilibrating stress systems required for an efficient analysis of structures by the force method.

Keywords:

Expansion , union intersection theorem , graph theory , structures , degree of statical indeterminacy , degree of kinematical indeterminacy