Minimum weight layouts of spanning structures obtained using graphic statics

The focus of this article is to identify an analytical description for the layout of a minimum volume truss that is uniformly loaded. Two different span conditions are considered: single and multiple spans. The multiple-span condition is supported at equally spaced locations. The methodology utilized for the solution of the problems takes advantage of Maxwell’s Theorem of Load Paths and the properties of reciprocal diagrams in Graphic Statics. This approach provides considerable insight in the properties of the optimal layouts for the given boundary and loading conditions. In Graphic Statics, the solution to a problem is based on tracing two related diagrams: the form and the force diagram. These obtained graphs can also be viewed as the definition of two dual structures. A force diagram created for a truss structure (form diagram) can be understood as the layout of a (dual) structure with its own loading condition. Therefore, the optimization can be conducted in either space (the force or the form). The analytical solutions obtained in this article are verified numerically using a ground structure optimization tool.