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This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. The resulting planar graph can be then used as a base for the assembly of the 3D force diagram, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples show how to take advantage of the bi-directional manipulation of the diagrams in the structural design process.

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This article presents a computer-aided design framework for the generation of non-standard structural forms in static equilibrium that takes advantage of the interaction between human and machine intelligence. The design framework relies on the implementation of a series of operations (generation, clustering, evaluation, selection, and regeneration) that allow to create multiple design options and to navigate in the design space according to objective and subjective criteria defined by the human designer. Through the interaction between human and machine intelligence, the machine can learn the nonlinear correlation between the design inputs and the design outputs preferred by the human designer and generate new options by itself. In addition, the machine can provide insights into the structural performance of the generated structural forms. Within the proposed framework, three main algorithms are used: Combinatorial Equilibrium Modeling for generating of structural forms in static equilibrium as design options, Self-Organizing Map for clustering the generated design options, and Gradient-Boosted Trees for classifying the design options. These algorithms are combined with the ability of human designers to evaluate non-quantifiable aspects of the design. To test the proposed framework in a real-world design scenario, the design of a stadium roof is presented as a case study.