Vector-Based 3D Graphic Statics (Part II): Construction of Force Diagrams

This paper presents an approach to the extension of graphic statics force diagrams to the third dimension. The main focus is to build 3D force diagrams out of vectors, so that each edge in the form diagram corresponds to two parallel vectors in the force diagram; this pair of vectors can generally be overlapped to form one single edge. The issue of parallel vectors that cannot overlap in the force diagram is discussed for both planar and spatial geometries and a convenient arrangement of the nonoverlapping vectors is presented. Alternative ways of assembling the force diagrams and their properties are suggested. As a result, the 3D vector-based force diagrams defined in this approach are a direct extension of the 2D force diagrams, taking advantage of their strengths for early design exploration. Moreover the presented approach applies to all typologies of pin-jointed frameworks, (including self-stressed and with external loads).