2. force graph

The form graph has a dual graph associated to it. This dual graph is defined below, and after the equilibrium is computed this dual graph transforms in the force diagram of the problem.

Dual graph

The dual graph of the single panel truss is depicted below. It is created by following the spaces of the form diagram.

This topology is also described by a connectivity matrix C* defined below:

Dual relationships

The following immage shows the form and the dual diagrams side by side. Both diagrams have the same number of edges.

The faces of the force diagram are related to internal vertices in the form diagram

With such relations, the equilibrium of each node of the form diagram is related to a closed polygon in the force diagram. The following images show these relation for the internal nodes of the form diagram:

Diagram orientation

As obeserved above, the dual diagram will generate edges that are perpendicular to the original edge sin the form diagram. However, up to a rotation of 90˚ this relationship can be changed, and how instead of perpendicular the edges in equilibrium will be parallel.