Master thesis of Tom Godthelp

The definition ‘Reciprocal Frame’ (RF) applies to structures that are feasible by means of circulating compression or tension interactions between their constituent members.

RFs can create curved geometries by using straight members, can span longer distances than the individual member length, can be joined using low tech techniques, and have proven their applicability in times when the availability of materials, especially timber, was scarce. Where historical RF applications seemed to be induced by material shortages, complex examples of today have an investigative and aesthetic function. 

In RF design, the member height correlates to the geometrical structural design. Until now, a combination of RF form finding that regards both beam depths and structural design of connections has not yet been developed. Although researchers developed computational form finding methods to create geometrical solutions and described the global structural design, computational complexity may have prevented a direct inclusion of detailing in the overall design.

In this context, the following research is established:

’The goal of this research is to develop a computational design to production tool for vaulted timber reciprocal frame structures using an optimized connection typology and sustainable timber-based material’

The completion of this goal could:

• Offer A scientific basis for analysis and design;
• Make RF design more accessible to the designers pallet;
• Create New and practical structural applications;
• Contribute To a next generation of sustainable timber structures.

To accomplish this goal, a parametric model to be referred to as ‘The Timber Reciprocal Frame Designer’ (RFD) is developed in the Rhino/Grasshopper environment. It is suited to design three- and four-member RF assemblies from any arbitrary NURBS surface. 

Eccentricities between members that may result or are generated from this surface correlate to detailing and beam depth causing the need to be controlled. Therefore, a method has been established that allows this control and results in direct geometrical solutions. Among geometrical equations, fictional beam stiffnesses in combination with initial strains are used to derive the geometrical shape.

A geometrical shape is supplemented in the RFD with standardized timber detailing and beam dimensions that are checked, and if necessary adjusted to satisfy stress and deformation regulations. An experimental validation of the design to production process is made by means of a full-scale model, built in cooperation with the timber industry. In conclusion, the RFD provides a tool in which designs can be produced by using industry standard machines stimulating structural designers to add RFs to their design pallet. I hope that the presented work could encourage new structural applications and could contribute to a next generation of sustainable timber structures.

Figure names:

Figure 1: The definition of eccentricity and its influence on geometry
Figure 2: The structural principle of a Reciprocal Frame
Figure 3:  Nine possible RF designs made with the RFD
Figure 4: Full scale model made with CAM and Hundegger machine to test the feasibility of RF detailing
Figure 5: 3D printed 1:20 scale model