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Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
10–14 July 2023, Melbourne, Australia
Y.M. Xie, J. Burry, T.U. Lee and J. Ma (eds.)
Copyright © 2023 by Markus HUDERT and László MANGLIÁR. Published in the Proceedings of the IASS Annual
Symposium 2023 with permission.
A reconfigurable construction system based on hypar timber
components
Markus HUDERTa,*, László MANGLIÁRa
a,* Aarhus University, Department of Civil and Architectural Engineering
Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark
mhu@cae.au.dk
Abstract
With the aim of contributing to a higher degree of circularity in the building construction sector, and a
more efficient use of resources, the here presented research explores the potential of upcycling scrap
wood into hypar-shaped modular construction components, to be used as basic units in reusable and
reconfigurable construction systems. The work employs empirical methods and pursues a research by
design approach. In addition to introducing a new approach toward upcycling scrap wood, we also
present a novel method for building hypar components from planar wooden pieces. Furthermore, the
paper features a design proposal for a pavilion that is intended as a contribution to the IASS 2023 Design
Competition. This pavilion is also expected to serve as a proof of concept for the above-mentioned
construction and upcycling method. We conclude with an overview of future research and an indication
of potential applications of the presented construction system. On a more general note, the work suggests
going beyond the use of shell structures as monolithic and static artefacts. By investigating reusable and
reconfigurable shell-based structures, it adds to and expands on existing research on segmented shells.
Keywords: timber and bio-based structures, modular timber structures, circular construction, hyperbolic
paraboloids, reconfigurable structures, upcycling scrap wood, conceptual design, methods and construction
technologies for sustainable shell structures, digital modelling and fabrication
1. Introduction
Reducing the environmental impact of the building construction sector has emerged as one of the prime
challenges for practitioners and researchers in Architecture, Engineering, and Construction (AEC) over
the past few years. As stated previously [1], increasing the use of timber can be one way of addressing
this challenge. Preconditions for this are short routes of transport and certified sustainable forest
management. For a truly sustainable use of timber, it is equally important to extend the service life of
wooden components as much as possible, and to unlock alternative material sources such as scrap wood.
This research explores the potential of upcycling scrap wood into modular construction components
with a hypar geometry, to be used as part of reconfigurable construction systems.
A hypar is a certain type of doubly ruled surface. According to [2], a ruled surface is defined as “a
surface generated by a moving straight line with the result that through every point on the surface a line
can be drawn lying wholly in the surface.” A similar definition is provided in [3]: “Cylinders, cones,
one-sheet hyperboloids, and hyperbolic paraboloids are surfaces that carry families of straight lines.
Thus, they could also be generated by moving a straight line.”
The capacity of hypar structures for merging load-bearing and stabilizing functionalities with
architectural qualities [4] becomes evident in numerous built examples. Depending on the construction
method and the material used, hypar structures can consist of discrete, similar, and sometimes even
identical elements. This could contribute to the reusability of their basic elements [5]. As modular
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Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
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entities or units, timber hypar components could become an alternative solution to conventional
prefabricated building components.
In addition to being based on simple straight lines, hypars have yet another compelling geometric
property. As pointed out in [6], “[…] flat quads can be created by connecting the corresponding points
of intersection of the generatrices in diagonal direction.” In [6], this property is highlighted in the context
of using glass panels as cladding for hypar steel grid shells. The here presented research investigates the
potential of employing this property for segmented timber shell components, as illustrated in Figure 1.
Figure 1. Left: Top view of a hypar with five equally spaced rulings (top) and a quadrilateral mesh based on top
of these rulings (bottom). Right: Stepwise generation of a quadrilateral mesh based on the rulings of a hypar with
a square base.
2. Design space explorations
This research explores the potential of upcycling scrap wood into modular construction components
with a hypar geometry, to be used as part of reusable and reconfigurable construction systems. The
design space of multi-hypar structures fundamentally depends on the geometry of the basic hypar unit.
So far, two different hypar geometries have been studied as a basic unit for multi-hypar configurations.
The first one approximates a Schwarz P minimal surface when multiplied twelve times, as shown in
Figure 2. This geometry can also be found in some of Ángel Duarte’s mathematics-inspired sculptures,
as well as in projects he developed together with Heinz Isler [7]. Duarte’s work was identified as a
relevant precedent while preparing teaching material for the MSc course “Tectonics in Engineering and
Architectural Design” in the fall semester of 2020. The starting point for constructing the geometry of
this hypar is a square in which a smaller and 45° rotated square is inscribed, using the midpoints of the
larger square’s edges as corners of the smaller one. Following this, the edge lines of the smaller square
are rotated up by 45° in pairs of two, using the neighboring edges as rotation axes. Then, the now inclined
edge lines are extended so that they connect and form a closed tetrahedral polyline. The four spatially
articulated edges are then mirrored around their center point. The two intersecting polylines define the
outlines of twelve identical, albeit differently oriented hypars.
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Figure 2. Two options of using patches of an approximated Schwarz P surface: in closed Schwarz P surface
condition (left) with twelve patches, and as an open configuration with six patches, to be used for example as a
pavilion (right), using planar quad meshing.
The second hypar geometry is based on a cube, meaning that the edges of the hypar surface are identical
to the diagonals of a cube’s faces. Six of such hypars can be combined into star-shaped higher-order
units, as shown in Figure 3. The possibility of doing so was observed in the outcome of a combinatorial
design workshop that was part of the MSc course “Tectonics in Engineering and Architectural Design”
in the fall semester of 2021.
Figure 3. Six identical hypars, with a hypar surface that can be inscribed in a cube, can be combined into a star-
shaped higher-order unit. This example also shows how neighboring triangular mesh faces, on the boundary of
adjacent hypars, can be merged into quads.
3. Design and fabrication of a pavilion
The here presented pavilion design is the outcome of an ongoing research project that investigates the
potential of upcycling scrap wood into modular construction components based on hypar geometry. The
construction method used takes advantage of a geometric particularity of hypars, which enables the
creation of quad meshes aligned diagonally with the rulings. Thus, it becomes possible to fabricate such
double-curved shell components from planar wooden pieces.
In addition to introducing a novel construction method, and a novel approach towards upcycling scrap
wood, the pavilion highlights the potential of using hypars as modular construction components. The
underlying hypar geometry is based on a cube. As explained above, six of such hypar components can
be combined into star-shaped higher order units, six of which are included in the proposed design. As
an entity, the pavilion displays properties similar to those of periodic surfaces, see Figure 6.
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Figure 4. Axonometric view of the pavilion design, which incorporates six higher-order units. The pavilion has
an approximate length of 180 cm, a width of 90 cm, and a height of 270 cm.
When moving around it, its appearance smoothly transitions between open and closed. Potential
applications of this modular system could be façade elements, loadbearing walls, room dividers,
skylights, or other.
For the exhibition at IASS 2023, we aim to build this pavilion, respectively demonstrator, out of scrap
wood pieces, connected with wooden dowels or similar, and partially with glue. The joints between the
higher order units will be designed to be reversible, allowing for the disassembly and future reuse of the
components, potentially in a variety of different configurations.
Figure 5. Top and side views of six different panel geometries.
3.1. Geometry and construction
The design space of modular hypar structures is partially determined by the way in which an immaterial
hypar geometry is brought into the physical world. A closed volumetric hypar can be generated by equal
distance offset, or by one-directional extrusion of the hypar surface.
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There are several methods of constructing timber shell components with a hypar geometry. The most
common approach is probably that of generating a grid shell, which can be achieved by extruding the
rulings of the hypar, or by placing straight elements on these rulings. Another method is to combine
mutually rotated layers of timber boards into assemblies similar to Cross Laminated Timber (CLT), and
to connect them to an edge beam [8, 9]. Yet another option could be steam bending, which would imply
size constraints and a relatively high consumption of energy.
The here proposed method enables the construction of segmented shells with wooden panels, which are
geometrically described as convex polyhedrons, defined by the intersecting half-spaces of their six
boundary planes.
The planar segments of a hypar are given by the diagonals of the subdivided hypar’s quad meshes. The
result is a planar quad mesh, which needs to be offset to obtain the geometry of the final segmented shell
structure. This would be relatively easy if the hypar-based mesh would be conical. Only conical meshes
have the property that their offset results in planar edge and mesh faces in equal distance, as in conical
meshes, all quads adjacent to one vertex are tangent to a common cone.
However, similar to other quad-meshes based on doubly curved surfaces, the hypar-based mesh is not
conical, which leads to flawed results when applying standard offset procedures. One way of solving
this issue is mesh adjustment, for example via the conicalize function that is part of the interactive
physics/constraint solver Kangaroo, which is included in the current version of Grasshopper. Another
option would be to chamfer the corners of the offset quads [10].
As using these options could cause fabrication challenges and increase design complexity, we apply a
method where the panels are defined as convex polyhedrons that are generated by the intersecting half-
spaces placed on their boundary planes. Two of these are the inner and outer offset planes of the origin
plane of the panel, and the four other are the boundary planes placed along the shared edges with the
neighbouring panels. These edge boundary planes are laying along common edges, and are aligned with
the average of the normal vectors of the two connected faces. It is noteworthy that in the case of
synclastic surfaces, the boundary plane of the vertex neighbour faces, located on the respective vertices,
should be added to the definition as well.
The resulting panels will share their long edges, provided they have the same thickness and their planar
edge surface. Due to the non-conicality of the basic mesh, their offset vertices will not coincide, which
is tolerable in this case. This method also enables a straightforward definition of segments made of
materials with different thickness.
3.2. Joints, connections, and assembly
The pavilion is comprised of six modules, or higher-order units. Each of these higher-order units consist
of six hypars with a low mesh-subdivision resolution. There are four main types of panels within one
higher-order unit: triangular, rectangular, rhombic, and trapezoid shapes. The rhombic and trapezoid
panels are the result of merging two or three triangular panels adjacent to the individual hypars’ edges
or corners, as indicated in Figure 4.
With a 270 cm high pavilion design, one higher-order unit has an edge length of 120 cm and consists of
60 panels. The edge length of the panels is between 16 and 30 cm, and the panel thickness is
approximately 20 mm. The segments of the higher order units are milled out of scrap wood pieces,
mainly from plywood or LVL, and optionally from solid wood boards. These pieces are glued and joined
by internal dowel-like connections, such as cylindrical dowels, biscuit connectors, or tongue and groove
joints with loose tongues. The challenge of assembling elements with various angles is addressed in the
joint design, and here with the dowel orientation, which is based on a pre-defined assembly sequence.
One possibility is to join the panels into strips, which are then merged into one half of a higher-order
unit.
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Proceedings of the IASS Annual Symposium 2023
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Figure 6. Rendered axonometric view of the pavilion.
Two halves are then glued together to form one whole. A simple formwork and tension belts are
envisioned to apply pressure on the glued surfaces during the curing process, a method that could be
applied for each edge. The joints between the higher order units will be designed to be reversible,
allowing for the disassembly and future reuse of the components, potentially in a variety of different
configurations. One option is that the modules are connected with dowel connections, and secured by
wooden wedges or screws. An alternative method is the use of mechanisms with easier access, such as
hinge- or clamp-like metal fasteners.
The final design and joinery solution also depends on the fabrication method and its constraints. The
panels can be fabricated in various ways, most favorably via 5-axis CNC milling, but possibly also with
a robotic arm, or with a traditional circular saw. The above-mentioned joinery solution describes the
current design stage of the demonstrator. Later on, we plan to develop and compare different joinery on
full-scale prototypes, mainly with cylindrical wooden dowels, biscuit connectors and finger joints.
4. Conclusion and future work
In this paper, we propose to upcycle scrap wood into hypar timber components, to be used as basic
elements of modular and reconfigurable construction systems. We provide insights on the design space
of multi-hypar structures and elaborate on the different factors that have an impact on it. We present the
design of a pavilion that implements a novel construction method for hypar shaped segmented timber
shell components, using scrap wood as material.
Currently ongoing studies investigate the potential of using hypars with irregularly spaced rulings as a
means of incorporating or adapting to material stock with specific geometric properties. We are also
preparing a survey that will inquire on the quality and quantity of wood scrap produced in selected areas
of Europe, the results of which will allow us to refine the target definition of the optimization process.
Additional studies will be required to obtain deeper insights on the structural properties of the above-
described structures, by means of numerical and experimental testing. Here it will be interesting to study
the impact of the connection details as well as the overall composition and orientation of different multi-
hypar configurations.
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Future studies will also explore the potential of double-layer configurations. Building with two layers
instead of one could facilitate the inclusion of insulation or other functions. Shifting the paneling
patterns of the two layers against each other – similar to the mutually shifted tiles in Catalan vaults [11]
– could support water and wind tightness. More importantly, this could also lead to advantages regarding
the structural performance.
Acknowledgements
The possibility of combining six cube-based hypars into star-shaped higher-order units was observed in
the outcome of an online-workshop on combinatorial design. During the workshop, the students worked
with Grasshopper and the plug-in WASP. The workshop was part of the MSc course “Tectonics in
Engineering and Architectural Design” in the fall semester of 2021, and carried out by the developer of
the WASP plug-in, Andrea Rossi.
References
[1] L. Mangliár and M. Hudert. Re:Shuffle. Paper presented at the Fifth International Conference on
Structures and Architecture, Aalborg, Denmark, July 6–8, 2022.
[2] Merriam-Webster. No date. Ruled surface. In Merriam-Webster.com dictionary. Accessed March
23, 2023. https://www.merriam-webster.com/dictionary/ruled%20surface.
[3] H. Pottmann, A. Asperl, M. Hofer and A. Kilian. Architectural Geometry: first edition. Exton:
Bentley Institute Press. 2007.
[4] T. S. Sprague. “‘Beauty, Versatility, Practicality’: the Rise of Hyperbolic Paraboloids in post-war
America (1950-1962).” Journal of Construction History, Special Issue: Construction History in
the Americas 28, no. 1 (2013): 165-184.
[5] M. Hudert, “Connecting lines: investigating the potential of ruled surface structures for circular
construction,” in Conceptual Design of Structures: Proceedings of the International fib Symposium
2021, Attisholz Areal, Switzerland, September 16-18, 2004, C. Fivet, P. D’Acunto, M. Fernández
Ruiz and P. O. Ohlbrock (Eds.), fédération internationale du béton (fib), 2004. pp. 469-476.
[6] H. Schober. “Graphic Design Principles for Grid Shells with Flat Quadrilateral Meshes.” In
Transparent Shells, edited by Hans Schober (Berlin: Ernst & Sohn, 2015), pp. 87-90. DOI:
10.1002/9783433605998.
[7] M. Ludwig. “Relations between Félix Candela, Heinz Isler, and Ulrich Müther.” In Candela Isler
Müther: Positions on Shell Construction. Positionen zum Schalenbau. Posturas sobre la
construcción de cascarones, edited by Matthias Beckh, Juan Ignacio del Cueto Ruiz-Funes,
Matthias Ludwig, Andreas Schätzke and Rainer Schützeichel, 16-23. Basel: Birkhäuser. 2020.
[8] M. Arnold and P. Aondio. “Hyperbolic Paraboloid Shells made of Engineered Wood.” Paper
presented at the Doktorandenkolloquium Holzbau „Forschung + Praxis“, Stuttgart, Germany,
March 5–6, 2020.
[9] Hyperbolisch-parabolische Schale aus Holz. Bauen + Wohnen, (17), Heft 10, 1963.
[10] I. Stotz, G. Gouaty and Y. Weinand. “Iterative geometric design for architecture.” Journal of the
International Association for Shell and Spatial Structures, vol. 50, num. 1 (2009): 11-20.
[11] G. R. Collins, “Antonio Gaudí: Structure and Form,” in Perspecta, Vol. 8 (1963), pp. 63-90, 1963.
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