## Abstract

In the 19th century methods of graphical statics - systematized and published by Carl Culmann in 1866 – were used to study in more detail the relationship between form and force flow. Historically, they were superseded by analytical methods, due to the relative ease of numerical calculations and the increasing importance of experimentation the developing discipline of engineering with its need for precision. Nowadays, however, with the availability of digital tools and the possibility of visualization of geometry in 3D space there is a re-emerging

interest within architecture in graphic statics. It is because of this that a visual dialogue about force flow based on graphic statics should be fostered because these methods offer a simple yet precise way to discuss the geometrical dependency of form and forces. The extended graphical statics (EGS) is part of an ongoing process of extension of the methods of graphic statics to the third dimension in order to overcome some of the limitations of Culmann’s approach.

Similar to the situation in 2D it is possible to show, that by using the EGS in 3D any finite constellations

of forces in general position can be reduced to a couple of forces, which represent all forces in intensity, direction and position. With that method the construction remains always spatially without any need for projections and always independent of any global coordinate system, necessary for numerical approaches. Like in 2D there are two linked diagrams, a form diagram and a force diagram, which mean that modifications in one diagram force an adjustment in the other diagram. With that method the dependency of form and forces in 3D can be seen without using projections and an active and synthetic designing process could begin. In previous research it has already been shown, that EGS allows considering the internal forces of a complex surface by using static determinate space trusses, which can be calculated graphical. These

trusses can be summarized and three dimensional stress fields can be generated using CAD programs like e.g. Rhino in combination with Python and Mathematica.

In continuation of this research it is shown how EGS can be used to explore the 3D equilibrium by constructing a (trial) funicular polygon-net, which has to be seen as the 3D likeness of the (trail) funicular polygon in 2D. This netlike structure works as a closed system, so that every single cable of the net is determined. As in 2D, this funicular system helps to find out the ‘neuralgic’

points of a structure, so that with a few information the entire system can be considered. Using this method, important structural information of complex free forms can be examined that enables a geometrical and physical form finding process without using relaxation processes or FEM.

interest within architecture in graphic statics. It is because of this that a visual dialogue about force flow based on graphic statics should be fostered because these methods offer a simple yet precise way to discuss the geometrical dependency of form and forces. The extended graphical statics (EGS) is part of an ongoing process of extension of the methods of graphic statics to the third dimension in order to overcome some of the limitations of Culmann’s approach.

Similar to the situation in 2D it is possible to show, that by using the EGS in 3D any finite constellations

of forces in general position can be reduced to a couple of forces, which represent all forces in intensity, direction and position. With that method the construction remains always spatially without any need for projections and always independent of any global coordinate system, necessary for numerical approaches. Like in 2D there are two linked diagrams, a form diagram and a force diagram, which mean that modifications in one diagram force an adjustment in the other diagram. With that method the dependency of form and forces in 3D can be seen without using projections and an active and synthetic designing process could begin. In previous research it has already been shown, that EGS allows considering the internal forces of a complex surface by using static determinate space trusses, which can be calculated graphical. These

trusses can be summarized and three dimensional stress fields can be generated using CAD programs like e.g. Rhino in combination with Python and Mathematica.

In continuation of this research it is shown how EGS can be used to explore the 3D equilibrium by constructing a (trial) funicular polygon-net, which has to be seen as the 3D likeness of the (trail) funicular polygon in 2D. This netlike structure works as a closed system, so that every single cable of the net is determined. As in 2D, this funicular system helps to find out the ‘neuralgic’

points of a structure, so that with a few information the entire system can be considered. Using this method, important structural information of complex free forms can be examined that enables a geometrical and physical form finding process without using relaxation processes or FEM.

Original language | English |
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Title of host publication | Structures and Architecture: New concepts, applications and challenges |

Editors | Paulo J. de Sousa Cruz |

Pages | 1735-1742 |

Number of pages | 8 |

ISBN (Electronic) | 978-0-415-66195-9 |

Publication status | Published - 2013 |

MoE publication type | A3 Part of a book or another research book |