Reciprocal diagrams in membrane structures: An intuitive form-finding approach

This paper establishes a connection between reciprocal form and force diagrams and edge cable-supported membrane structures under isotropic stress. While various form-finding techniques exist for tensile membrane structures, reciprocal diagrams provide an intuitive graphical approach that is particularly effective during early design stages. The study introduces the foundational concepts of reciprocal diagrams, outlines their construction for membrane and cable elements, and explores their application to isotropically stressed membranes. The relationship between form and force diagrams is analyzed, highlighting the similarities between different graphical conventions. A method for three-dimensional form-finding is presented, starting with planar equilibrium informed by force densities and iteratively updating these densities to achieve isotropic stress. Several case studies are discussed, demonstrating the method’s capability to accurately calculate geometry and stress distributions compared to reference solutions. This work contributes to the field by offering a clear, visual approach to form-finding in membrane structures, combining graphical methods with computational techniques to simplify design and analysis processes.