Temporary reciprocal structures.

Reciprocal structures are composed of mutually supporting rigid elements that are short with respect to the span of the entire structure. Although reciprocal structural systems have received significant interest among architects and engineers, they are not yet commonly employed in construction. The main reason for this non-adoption, is the complexity of conceiving a structure from a module to the global scale without adapting the structure’s final global shape. As a result, two approaches have emerged for the design of reciprocal structures. The first approach takes the module as primary building blocks and the final global form emerges as a result of the module’s properties. The second approach results from adjusting the module’s properties throughout the surface of the structure to fit its predefined global shape. This work presents a complete design-to-construction workflow for reciprocal frames using a cell-based pattern algorithm. The developed parametric model explores geometry and patterning to adapt any module geometry to any free-form surface by adjusting the eccentricities between the modules. The resulting reciprocal structure is then analyzed and sized using finite elements. Finally, manufacturing layouts are generated and construction processes are discussed.

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Vocabulary and definitions of a reciprocal module

In this study, a novel cell-based method is proposed. The method allows the population of free-form surfaces with reciprocal modules. Moreover, the method is based on a parametric model, i.e. it maintains all executed operations in relationship as the model is manipulated. The input parameters for the parametric model are (i) the free-form surface and (ii) division mesh (cell pattern). In the current version of the algorithm there are two available patterns: one based on triangular cells and one based on quadrilateral cells. However, the algorithm can be extended for a wide range of cell patterns provided that the mesh division is composed of closed cells.


Continuous network of reciprocal modules on the spherical surface

Contrary to existing methods where the global final shape is a result of the module employed, the proposed method innovates by taking into account the global shape of the structure as an input parameter. Additionally, it can accommodate various cell-based patterns. The challenge in the design of reciprocal structures is handling all the non-hierarchical geometric constraints such as engagement length, eccentricities, and angles. The parametric model employed in this study uses these geometric properties to obtain the desired surface. Moreover, the parametric model includes an all-in-one tool from geometry to construction, passing through structural analysis and fabrication. The workflow was validated with the construction of a large scale prototype.

The design-to-construction workflow was validated experimentally with the construction of a 5 meter diameter reciprocal hemispherical dome at Princeton University at the occasion of the book launching event  Shell Structures for Architecture – Form finding and optimization ‘  and a temporary pavilion on the Nativity square in Bethlehem, for the first international Comics festival in Palestine.

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Book launching event of Shell Structures for Architecture – Form Finding and Optimization, at the E-quad, Princeton University. Photo by Zach Donell ©



Reciprocal pavilion on the Nativity square, Bethlehem at the occasion of the first international Comics Festival in Palestine



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