Design with equilibrium prototypes in graphic statics: a parametric approach to form-finding in early architectural education

The historical divide between engineering and architecture has perpetuated challenges in reconciling structural and design priorities. Current methods for integrating structure and architecture – form-making and form-finding – each face limitations. Form-making grants designers geometric control but relies on fixed prototypes, restricting formal diversity. Form-finding, though generative, offers minimal intervention post-initiation, limiting design control. Both approaches depend on predefined models (geometric or funicular), constraining innovation. This study proposes a diagrammatic form-finding method using equilibrium prototypes derived from Graphic Statics, which abstractly represent compression-tension relationships. These prototypes act as adaptable starting points for generating diverse structural topologies through geometric and force-based operations, avoiding reliance on fixed models. By maintaining transformable equilibrium diagrams throughout the process, designers gain dynamic control and expanded formal possibilities. The method was tested in undergraduate studios tasked with designing open-air theaters using the computational tool CEM to ensure structural equilibrium. Students produced varied, well-resolved outcomes, demonstrating the approach’s capacity to transcend conventional constraints while balancing creativity and feasibility. The findings suggest that the approach effectively bridges architectural design and structural rationality, offering an educational framework that enhances students’ ability to synthesize novel forms while maintaining structural coherence.