Computational Form-Finding of Tension-Integrated Spanning Structures with Polyhedral Graphic Statics

DISSERTATION

This dissertation advances a computational form-finding framework for tension-integrated spanning structures within the context of polyhedral graphic statics (PGS). While compression-only funicular systems are efficient under gravity loads, architectural floors and beams often encounter asymmetric or service loads that induce bending and tension. The framework incorporates tensile elements via post-tensioning and designed tension paths, resulting in equilibrium with compression and structurally informed designs for spanning systems. The research develops computational methods, including the extension of Geometric Degrees of Freedom (GDoF) to manipulate force distributions and merged force diagram operations that expand the topological design space of PGS. These approaches are validated through physical prototypes, including funicular beam systems and a 3-meter bridge, demonstrating practical applications, supported by an interactive web-based platform for broader accessibility. Beyond theory, the research integrates advanced fabrication through 3D concrete printing and explores lightweight anticlastic geometries, enabling new applications in beams and floor structures while achieving 30-50% material reduction compared to conventional approaches by systematically integrating tension elements into PGS workflows and providing designers with intuitive computational tools for form-finding.

Hua Chai