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The examples in Fig. 4 show how funicular structures such as half arches can stand in equilibrium by introducing tension elements. This structural principle to create large cantilevering structures is illustrated in Fig. 5 using simple graphic statics. Graphic statics is based on two diagrams: a form diagram, representing the geometry of the pin-jointed structure, and a force diagram, also referred to as (Maxwell-) Cremona diagram, representing the equilibrium of the internal and external forces of the structure (Cremona 1890). The power of graphic statics is based on its inherent bidirectional capabilities; one can either use the form diagram to construct the force diagram, or apply the inverse process and construct parts of the form diagram from an intended force diagram, i.e. either form or force constraints can drive the design exploration (Kilian 2006). Geometrically, the relation between the form and force diagram is called reciprocal (Maxwell 1864). Graphic statics also allows to mutually use compression and tension elements which can be easily identified based on their individual direction in the form and force diagram.

Fig. 5 shows the form and force diagram of a funicular arch in compression (a) and the same structure cut in half, with one half flipped horizontally (b). The equilibrium of each node in the form diagram is represented by a closed force vector polygon in the force diagram. Note that the upper ends of both arch segments (b) are in static equilibrium considering the appropriate reaction forces. These reaction forces can either be guaranteed by horizontal supports such as buttresses on both sides or by using a tension tie connecting both ends (Fig 5b).

Fig. 5 (a) Form and force diagram of a closed funicular arch in compression; (b) two, tied half arches in static equilibrium (tension forces marked in blue)