Affinity Properties of Truss Model Nodes

Strut and tie models consist of axial force members which react on one another and on external supports through nodes, i.e. they are trusses. An analysis of a truss problem is normally entered by reducing it to a line diagram of member centrelines representing the lines along which the stress resultants in the members are intended to act. When forces are concentrated in a line diagram the nodes vanish and become points thus ensuring that member forces are concurrent and that moment equilibrium is satisfied at the nodes and this simplifies the problem to one which produces a tractable model. When fleshing out the results of a truss analysis in order to size members in structural design we use the line diagram to locate the centroidal axes of members, implicitly assuming that it is necessary to maintain the concurrence of axial forces in order to ensure moment equilibrium of nodes. For strut and tie models each node must be detailed so that it is capable of transferring the forces between members. The finite widths of the members generate a common area which is satisfactory as a real node for three force cases but not necessarily for multi-force cases in which case complex nodes have been proposed [1] [2]. We will show that there is a node model in which member forces are not concurrent but moment equilibrium is automatically satisfied in which tithe shape of the boundary is affine to the polygon of forces for the members meeting at the joint. Marti noted to the author [3] that the affinity property presented in this paper is a general statement about properties that he had used in some of his solutions [4], [5].