## Graphical Methods

In engineering practice graphic statics has a long tradition and master builders, such as Robert Maillart and Gustave Eiffel used this method to design their outstanding structures. Besides the well-known advantages of graphic statics with the intuitively readable diagrams, this method further provides the possibility to change either the form or the force diagram. Changing the force diagram is beneficial for optimizations, because it leads to less parameters. Compared to FEM-Programs graph statics is a relatively easy way to deal with zero bars by just keeping two vertices of the force diagram in just one place. In graph statics one particular force diagram can be constructed for each form diagram. Every bar in the form diagram has a corresponding, parallel line in the force diagram, where the length of the line corresponds to the magnitude of the force. With the modern computational possibilities and the implementation of algebraic graph statics in the TrussPath tool the disadvantage of the time-consuming drawing of the force diagram can be rectified. For further informations the Algebraic Graph Statics paper is recommended.

## Load Path

The load path theory is a very powerful tool to assess the efficiency of a truss structure. It is very easy and fast to apply, so that it can be used in an early design stage in the form-finding process. Only the length and the force in every bar is required to compute the load path. This fact offers the combination with graphic statics, because in the form and the force diagram all required data is already available. With the following formula the total load path, which is directly related to the amount of required steel, can be computed:

$$ LP_{ traditional }=\sum{ }{ }{L _{Form,i }*L_{ Force,i } } $$

In the last decades new researches on the load path in combination with graphic statics have been done by Skidmore, Owings & Merrill LLP (SOM). They used it to improve stiffening structures of super tall skyscrapers, where buckling can be avoided structurally (see links).

## Buckling

For the most truss structures, like bridges, buckling can not be avoided and is design-determining. Therefore it was implemented in the TrussPath tool according to the Swiss Code. Because of the innumerable possibilities to apply a real cross section from a table, it is impossible to compute it automatically. That is why a fictional circular hollow section, with a certain thickness/diameter ratio and steel quality, is assigned to every bar in the TrussPath tool. For every cross section a buckling indicator (\(\chi_{ k }=\frac{ \sigma_{ k } }{f_{ y } }\)) can be computed according to the Swiss Steel Building Code (SIA 263). Considering buckling the total load path can be calculated by following extended formula:

$$LP_{ buckling }=\sum{ }{ }{L _{Form,T,i }*L_{ Force,T,i } }+\sum{ }{ }{}\frac{L _{Form,C,i }*L_{ Force,C,i } }{ \chi_{ k,i } }$$