Vector-Based 3D Graphic Statics (Part I): Evaluation of Global Equilibrium
The evaluation of the equilibrium of a system of forces that fulfils specified boundary conditions is a core question of theory of structures. This paper reviews three methods, related to procedures introduced at the end of the 19th century, to evaluate the global equilibrium in three dimensions using graphic statics. The paper is specifically focused on one of these methods, which is grounded on the use of projections. Based on this method, a given system of forces can be reduced to three skew resultants, which are parallel to three initially chosen unit vectors. The three resultants can be composed into two resultants thanks to the construction of a simple 3D auxiliary structure or reduced to one resultant and a couple. Given the three resultants, the reactions at the supports can be evaluated according to specified boundary conditions in both cases of externally statically determinate and indeterminate systems.