Graphic statics: projective funicular polygon

Abstract

Since its birth, around the mid-19th century, graphic statics has been through several stages, with the most recent one being its “renaissance” phase, due to mainly the development of digital graphical tools, after almost being abandoned during the last two thirds of the 20th century. The power of graphic statics rises from the reciprocity between its two main pillars, namely the force polygon and the funicular polygon. These two pillars, tend to represent in the modern era two distinct disciplines: architectural (form) and structural engineering (force). To this end, graphic statics can act as the common ground, as we move, potentially, towards the direction of the multidisciplinary master-builder approach. The majority of graphic statics applications, in its “renaissance” phase, reported in the literature is related to form-finding of axially-loaded statically determinate structures. In the current work, we suggest a so-called projective funicular polygon, that is necessary for the structural analysis of statically indeterminate beams with inclined loads that impose an axial force component to the beam. In addition, the construction of the projective funicular polygon explicitly defines the bending moments, shear forces and axial forces in the beam and therefore provides information regarding an efficient cross-sectional variation of the beam element, while the classical funicular polygon provides information regarding an efficient alternative structural form. Finally, apart from highlighting that graphic statics is a powerful tool not only for form-finding, but for structural analysis as well, it is worth emphasizing that the information provided by the polygons (force, funicular, projective) can help us generate insights in the light of geometry towards more efficient and sustainable structures.