ArticlePDF Available

The Canopy: A Lightweight Spatial Installation Informed by Graphic Statics

Authors:

Abstract and Figures

This paper illustrates the design and fabrication process of the temporary installation The Canopy, developed as part of the fib Symposium on Conceptual Design of Structures 2021. The geometry of the perforated hanging membrane that forms The Canopy is the result of seamless integration between the disciplines of architecture and structural design, which was one of the driving inputs for the entire process. Particularly, the use of geometry-based models and graphic statics allowed activating the interplay between these disciplines. This was the key to balancing the relationship between architectural spaces and structural requirements, and to informing the multifaceted design exploration of The Canopy from conceptual design to construction.
Content may be subject to copyright.
Citation: Wang, S.; Bertagna, F.;
Ohlbrock, P.O.; Tanadini, D. The
Canopy: A Lightweight Spatial
Installation Informed by Graphic
Statics. Buildings 2022,12, 1009.
https://doi.org/10.3390/
buildings12071009
Academic Editors: Oleg Kapli ´nski,
Agata Bonenberg, Wojciech
Bonenberg and Marco Lucchini
Received: 20 June 2022
Accepted: 12 July 2022
Published: 14 July 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
buildings
Project Report
The Canopy: A Lightweight Spatial Installation Informed by
Graphic Statics
Shuaizhong Wang * , Federico Bertagna, Patrick Ole Ohlbrock and Davide Tanadini
Department of Architecture, ETH Zurich, 8093 Zurich, Switzerland; bertagna@arch.ethz.ch (F.B.);
ohlbrock@arch.ethz.ch (P.O.O.); tanadini@arch.ethz.ch (D.T.)
*Correspondence: shuaizhong.wang@arch.ethz.ch; Tel.: +41-77-977-6840
Abstract:
This paper illustrates the design and fabrication process of the temporary installation The
Canopy, developed as part of the fib Symposium on Conceptual Design of Structures 2021. The
geometry of the perforated hanging membrane that forms The Canopy is the result of seamless
integration between the disciplines of architecture and structural design, which was one of the
driving inputs for the entire process. Particularly, the use of geometry-based models and graphic
statics allowed activating the interplay between these disciplines. This was the key to balancing
the relationship between architectural spaces and structural requirements, and to informing the
multifaceted design exploration of The Canopy from conceptual design to construction.
Keywords:
temporary installation; architecture and structure; structural design; graphic statics;
lightweight structure
1. Introduction
The Canopy (Figure 1) is a temporary lightweight installation made of wide perforated
fabric strips hanging from steel cables inside the Kiesofenhalle, a former cellulose factory
in Attisholz, Switzerland. The project aimed at creating a venue for the 3-day event of the
International fib Symposium on “Conceptual Design of Structures” [
1
], which was held in
September 2021 and hosted over 150 participants. In conjunction with the conference, an
exhibition explored the Swiss contribution to structural design looking at design methods
and exemplary projects. Particular emphasis was given to the use of physical models for
form-finding and graphic statics, represented by the work of renowned Swiss engineers
such as Heinz Isler (1926–2009) and Robert Maillart (1872–1940).
Figure 1.
The front elevation of The Canopy as seen from the reception desk. Photo by Shuaizhong Wang.
Buildings 2022,12, 1009. https://doi.org/10.3390/buildings12071009 https://www.mdpi.com/journal/buildings
Buildings 2022,12, 1009 2 of 17
The objective of this paper is to illustrate the design, fabrication, and erection processes
of The Canopy. Drawing inspiration from the work of Sekler [
2
], this paper elaborates on
the strategy to integrate and balance the relationship between structure, construction,
and tectonics. These three aspects are addressed from three perspectives throughout The
Canopy’s design process: conceptual design, fabrication and assembly, and final spatial
expression. The paper shows the instrumental role of graphic statics in unfolding the
relationship between form and forces and thus in reconciling spatial artistic needs and
structural requirements from the conceptual design phase. Graphic statics provides an ideal
medium for integrating the design of structure, construction, and tectonics, with the aim
of fostering a collaborative and creative interaction between architecture and engineering.
The Canopy’s design process exemplifies the significance of this collaboration.
2. Background
The Kiesofenhalle is a former industrial hall located inside the industrial estate of
Cellulose Attisholz AG, a company that operated for over 100 years in the paper production
industry. The company was founded in 1881, merged with the Balsthal paper mill in 1914,
and finally was acquired the German company Hakle in 1983 [
3
]. Since the end of 2016,
in collaboration with the municipality of Riedholz and the Canton of Solothurn, the area
has gone through radical transformation that aimed to turn it into a mixed-use artistic and
cultural district while preserving the original cultural values of the industrial buildings [
4
]
(Figure 2a).
Figure 2.
(
a
) Aerial view of the industrial complex Cellulose Attisholz AG in 1924,
©
Walter Mittel-
holzer/ETH Library (http://doi.org/10.3932/ethz-a-000492184 (accessed on 30 May 2022)); (
b
) The
interior of the Kiesofenhalle today. Photo by Shuaizhong Wang.
The overall size of Kiesofenhalle (Figure 2b) exceeds 3000 m
2
and reaches a maximum
height of 17.5 m. The hall served as a storage for raw material whose chemical properties
greatly enhanced the risk of corrosion of metal elements. For this reason, even the roof
slender trusses are in fact made of concrete, thus remarking the strong industrial expression
of the hall. Furthermore, the building’s exceptionally tall scale and large, continuous
south-facing windows contribute to the creation of an almost sacred spatial experience
similar to a modern concrete church.
The enormous size of the hall called for a series of interventions that would frame the
space and create a human-scale venue to accommodate the different functions required by
the organizer of the conference. In particular, it was necessary to separate the hall into a
conference space, an exhibition area, and a registration and catering area.
Apart from a limited amount of time for on-site assembly—only three days—another
requirement was to intervene on the existing structure as little as possible. This excluded
the possibility of using the existing roof trusses as supports, or anchoring elements to the
ground. Moreover, the possibility to introduce high external forces in the walls was also
Buildings 2022,12, 1009 3 of 17
limited. Because of these constraints, the design was defined as a lightweight structure
made of parallel steel cables and perforated fabric strips hanging from above. The undulat-
ing geometry of the fabric allowed for a continuous generation of vertical partitions and of
horizontal surfaces with different heights above ground. Thanks to this simple logic, the
elements could be pre-fabricated off-site and easily transported and assembled in the given
time frame. In this sense, the combination of cables and textile elements represented a
suitable way to generate the desired spaces, while complying with the given requirements,
as demonstrated by several reference projects [58].
In response to the conference’s functional requirements, the hall was divided into
three main areas based on different privacy levels: a public area with registration desks
and a catering area; a semi-public exhibition area; and a relatively intimate auditorium for
lectures and discussions (Figure 3). In the auditorium, the height of the fabric had to be
higher than 4.8 m to avoid obstructing the projector but less than 7 m in order to create the
feeling of an enclosed space. Conversely, the more public character of the exhibition and
reception areas called for more open spaces, with fabric heights reaching up to 11 m above
ground. The division between these three functional areas was achieved solely through the
geometry of The Canopy. As better explained in Section 4.1.1, by manipulating the lower
boundary line of the fabric sags, it was possible to create a subtle spatial division between
the different areas, thus suggesting a new spatial order to the enormous hall. Aspects
related to the acoustics of the diverse spaces were not considered as integral part of the
design process since the Symposium program did not include parallel sessions, and the
catering and exhibition areas were not used during the presentations.
Figure 3.
Floor plan and functional planning. The hall was divided through the sole use of hanging
fabric strips into three areas characterized by different levels of privacy.
Based on the design concept, to achieve the sensation of lightness and a floating
effect, The Canopy’s supporting structure had to be designed to be as invisible as possible.
Therefore, when conceiving the structural system, we sought to minimize both the size
and number of components. The slender and clear supporting structure for The Canopy
was made of simple steel cables. The catenary line that they draw as they span over the
hall recalls the historical methods of form-finding using hanging models, also relating to
the content of the exhibition. The use of hanging models as a design tool to determine
the optimal form for structures is a technique used by many architects and engineers,
especially before the introduction of analytical methods. Antoni Gaudí(1852–1926) already
used the hanging model as a three-dimensional design tool to determine the optimal form
Buildings 2022,12, 1009 4 of 17
for structures subjected to purely compressive loads at the turn of the 20th century, and
ultimately obtained the structural form of the Sagrada Familia [
9
]. Later on, the Swiss
engineer Heinz Isler has been a key protagonist in the use of this technique to determine
the optimal shape for shell structures [
10
]. For them, the physical model entails not only a
method for determining the ideal shape, but also a method of thought and operation [
11
].
Similarly, graphic statics was used as a key method in the design of The Canopy.
3. Methodology
In the design process of The Canopy, the simultaneous requirements related to form
and forces were reconciled using graphic statics. Graphic statics is a set of geometric
rules that allow unfolding in a diagrammatic way the relationship between the form of a
structure in static equilibrium and the forces within it [
12
14
]. Several scientists contributed
to the development and formalization of graphic statics starting from the 16th century.
Interestingly, many of the early works related to graphic statics make use of the hanging
models under given loads to illustrate the basics of the method [
15
17
] (Figure 4a). Graphic
statics was eventually formalized and expanded by the German engineer and ETH Professor
Karl Culmann in his two volumes of Die Graphische Statik [
18
] (Figure 4b). His work on
graphic statics significantly influenced renowned Swiss engineers such as Robert Maillart
(1872–1940) [
19
], and this legacy remains an integral part of the teaching of structures at
ETH Zurich to these days [
20
]. The use of graphic statics as the structural design tool for
the canopy is a tribute to this legacy.
Figure 4.
(
a
) Stevin’s diagrams illustrating equilibrium states for a cable under different loads, and the
corresponding internal forces using graphic statics [
16
]; (
b
) Culmann’s introduction of the polygon of
forces and funicular polygon [18] (p. 513).
It is worth mentioning that this approach is radically different compared to conven-
tional Finite Element Analysis (FEA) software for structural engineering. In fact, unlike
graphic statics, FEA software is based on analytical models that are solved through numeri-
cal techniques [
21
]. When used for design purposes, FEA shows several shortcomings as it
generally tends to conceal the relationship between form and forces. This often hinders
the possibility to operate on a conceptual level and to create an effective dialogue between
Buildings 2022,12, 1009 5 of 17
architects and engineers [
20
]. Conversely, the diagrammatic nature of graphic statics offers
a common ground between disciplines and an effective design tool for the conceptual
design phase of a structure [
22
]. Additionally, it also facilitates the early integration of the
art and technology of structures as part of the architectural design process by reducing
the design of load-bearing structures to basic equilibrium concepts and by translating
calculations into simple geometric operations [23,24].
In addition to its visual nature, the constructive and generative nature of the vector-
based operations of graphic statics enables easy integration with digital design methods
that began to emerge in architecture in the early 2000s [
25
28
]. Digital implementations
of the method allowed for overcoming the inherent limitations of manual applications
and proved effective for the creation of architectural spaces informed by form and forces
simultaneously [
29
31
]. A simple digital implementation of graphic statics has also been
used in the design of The Canopy for rapid form-finding and calculation of forces using
Grasshopper3D.
4. Case Presentation: Structure, Construction, and Tectonics
To elaborate The Canopy’s design and fabrication methods, this paper utilises Eduard
F. Sekler’s critical aspects of structural design to dissect its embedded structural think-
ing: structure, construction, and tectonics [
2
]. In his article, Structure, Construction, and
Tectonics, Sekler defines structure as an “intangible concept” that is “realized through
construction and visualized through tectonics” [
2
]. Thus, structures are bonded to the
construction technique and the perceptual representation of the tectonic form (Figure 5).
Based on this understanding, the following section of the paper describes how graphic
statics was used to inform the design in order to facilitate early collaboration between the
architects and engineers.
Figure 5.
The graphical representation of the relationship between Structure, Construction, and
Tectonic from the concept of Eduard Franz Sekler.
4.1. Structure: A Lightweight and Minimal Intervention
The most challenging aspect of intervening in the building was transforming the over-
scale floor height into a human-scale exhibition and lecture space with the least amount
Buildings 2022,12, 1009 6 of 17
of means. This led to the main design concept: designing a small, nested space within
the building with a limited height above ground that separates three functional areas
with varying dynamic and static partitioning. Due to the spatial qualities of the original
structure, it was decided early on to create this enclosure out of a translucent or perforated
material. As such, the installation would limit the space while preserving the context of
the surrounding scene. The three main functional areas were identified based on the main
entrance’s location, located in the south-east corner of the building (Figure 3).
The project was conceived as a lightweight spatial installation, a translucent, abstract,
white fabric canopy that floats within the hall in a gradual wave pattern. Each fabric fold
corresponds to the axis of the building’s original concrete trusses, achieving geometric and
visual continuity. While defining the space beneath it, the fabric separates the different
functions of the private density through the fluctuating height changes of the fabric in the
vertical direction, linking the entire space in a holistic and continuous form while meeting
the requirements for the conference activities. The free-falling, hanging form of the fabric
seeks to recall the image of paper rolls that were once produced at Attisholz and the logic of
the catenary curve as a pure structurally-informed shape. This interplay between form and
force was also addressed repeatedly in the exhibition that was organized in conjunction
with the conference.
From the beginning of the design process, the diagrammatic nature of graphic statics
allowed for the intuitive expression, rapid communication, and visual definition of these
structural forms during the design brainstorming phases (Figure 6).
Figure 6.
(
a
) The early canopy design concept based on graphic statics describing how to use
compression element in the center and tension elements on both sides to create a covering surface;
(b) Sketches of the canopy’s different hanging methods according to different functional use.
Due to the enormous size of the canopy, with the fabric sagging up to 6.5 m, the choice
of fabric properties such as porosity, weight, and elasticity had a significant impact on the
final result. To simulate the material as realistically as possible, several 1:1 mock-ups were
built and tested (Figure 7). In particular, these tests showed that fabrics that were too light
could not easily result in a precise catenary geometry for the lack of sufficient self-weight.
Heavier fabrics, despite generating cleaner catenary lines, proved to be excessively opaque,
Buildings 2022,12, 1009 7 of 17
thus considerably weakening the desired architectural image and the relationship with the
context. Additionally, fire safety represented an additional requirement that excluded the
possibility to use several types of materials. The final choice was a polyethylene 2-m wide
white mesh of 5 mm and a weight of 0.1 kg/m2.
Figure 7.
Physical suspension mock-up of different fabric materials. The analysis of diverse physical
models allowed finding the desired balance between weight and translucency of the fabric. Photo by
Shuaizhong Wang.
Before the detailed design of the hanging structure, a crucial design step was to
decide whether to suspend the fabric using longitudinal or transversal rows of cables in
the Kiesofenhalle. Even though the building footprint is symmetrical in its short section,
the north side of the façade is almost entirely closed with a solid retaining wall, whereas
the south side of the building has stunning continuous windows that give the building
a sense of breathing. Due to the shorter transversal distance, the first test comprised an
array of parallel cables along this direction (Figure 8a). However, the presence of windows
heavily limited the freedom in choosing locations for the hanging structure’s anchor points.
Moreover, because of the inevitable sagging of the cable when spanning, it was difficult
to maintain the same height for fabric strips that belong to the same row. This would
have called for the need to add a second array of cables in addition to the main one,
which would have significantly affected the simplicity and abstraction of the overall form.
Therefore, we ultimately decided to suspend the fabrics along the building’s longitudinal
axis (Figures 8b, 9and 10). This decision results in four direct benefits:
1. It provides more freedom in the placement of anchor points on the walls;
2.
The anchor points of each cable are placed further away one from each other, thus
evoking a sense of ambiguity due to The Canopy’s incomprehensible structural logic
as users cannot see both arrays of anchor points simultaneously;
3.
The cables span the entire 94.5-m-long hall, elongating The Canopy longitudinally,
expanding the covered area, and enhancing the dialogue with the building;
Buildings 2022,12, 1009 8 of 17
4.
The longitudinal anchorage allows the lower portion of the fabric to remain horizontal
in the vertical direction while slightly lifting the sides due to its own sagging, giving
the sides of the building a geometry that follows the interior circulation more closely.
Elevation (West wall)
Cable anchor point
Figure 8.
(
a
) Spanning the cables along the short side of the building would have called for a
secondary structure to keep the top part of the fabric strips on the same height; (
b
) Conversely, when
the cables span the longitudinal direction, it is possible to avoid the need for this secondary structure.
Figure 9.
Axonometric diagram of the relationship between the structural model and the order
of the existing building. In its final configuration, the cables were suspended along the building’s
longitudinal axis, thus eliminating the secondary structure and giving more freedom for the placement
of anchor points on the walls.
Buildings 2022,12, 1009 9 of 17
Figure 10. The plan and section drawings of The Canopy.
4.1.1. Form-Finding through Graphic Statics
After the definition of the hanging direction, graphic statics was used to investigate
the geometry of the cables that would support the fabric strips, as well as to control the
forces in the supports. The Canopy’s catenary line is not just a formal translation of the form
diagram of graphic statics. Instead, it is an attempt to retrace the design logic of graphic
statics as a method and integrate it with the site and functional needs of the conference.
Therefore, the interaction and synergy between the force diagram and the form diagram
were used in many ways as the leading logic in designing the structures of The Canopy.
The use of graphic statics allows for a clear illustration of the relationship between form
and forces to control the relationship between the height of each fabric strip, as well as
their length. Figure 11 shows the final geometry, as well as two variants with a slightly
lower (Variante 1) and higher (Variante 2) cable. The corresponding force diagrams show
the change of the force F in the cable connected to the counterweight according to the
three different geometries. It is worth mentioning how the force in the cable is extremely
sensitive to changes in cable height and vice-versa. Thanks to the use of graphic statics, this
dependency between design parameters (i.e., depth of the cable sag, force in the cable, and
reaction forces) is represented in an explicit manner. The manipulation of form and force
diagrams represented an extremely important design tool that allowed controlling the form
of the cable and the resulting forces in the walls jointly. The geometric lower boundary of
the installation is determined by the separation function that the fabric needs to provide.
The final design is, therefore, a tradeoff that enhances the expressiveness of the canopy and
its functional aspects, while keeping the forces under control.
Buildings 2022,12, 1009 10 of 17
BCDEFGHIJ
1
F
F
F
K
A
Fromtheforcediagram:
F≈370kg
F1≈180kg
F2≈815kg
10
500
Variante1Finaldesign
Lowerboundary
Finaldesign
Finaldesign
Formdiagram
50
m
5
10
20
50
Forcediagram
100
kg
Lowerboundary
200
Pulley
Variante2
Lowerboundary
2
2
F
1
F
F2
Figure 11.
Graphic statics unfolds the relationship between the shape of The Canopy (Form diagram)
and the forces acting in the cable and supports (Force diagram). For each element in the Form
diagram, there is a corresponding segment in the Force diagram, whose length is proportional to
its internal force. The figure shows a superposition of form and force diagrams for three different
options. The mutual relationship between Form and Force diagrams shows in an explicit way that
even small changes in the form of the cable greatly affect the internal forces in it and vice-versa.
For instance, a reduction in the sag of the cable (Variante 2) would result in deeper sags for the
fabric—which enhances the spatial effect of the strips—but it would also result in extremely high
reaction forces that might create problems when anchoring the cable to the walls.
Buildings 2022,12, 1009 11 of 17
Because of the undulating form, the weight distribution at each point where the fabric
and the cable are connected were different. The magnitude of the force at each connection
point informed the geometry of the cable and, consequently, the relative height between
each strip and the adjacent strip of the fabric. This necessarily results in an iterative form-
finding process in which the shape of the fabric and the cable are interdependent. Thanks
to the use of parametric tools (i.e., Grasshopper3D), it was possible to instantly update the
relative relationship between the form of the fabric and the force on the cable, as well as
provide immediate feedback on the magnitude of the force and the corresponding form.
As a result, the folding positions of the ten fabrics waves corresponded to the positions of
the concrete trusses on the roof, and the precise control of the forces enabled the structural
elements to be as thin as possible, thus enhancing the dialogue between The Canopy and the
existing structure.
Due to production and transportation constraints, the longest dimension of a fabric
roll was limited to 75 m. Therefore, we implemented a simple optimization algorithm to
approximate as closely as possible the relationship between the desired undulating form
and the total length of the fabric, in the attempt to minimize the need for cuts and overall
material waste. This optimization problem was solved using Galapagos [
32
], a native
Grasshopper3D component.
4.1.2. Structural Detailing
Once the overall force distribution pattern was determined, it was necessary to develop
a connection system between extremely thin steel cables (
5 mm) and aluminum pipes
(
17 mm) on which the fabric is folded. The system had to be easy to produce and it
had to allow for simple adjustments on site also considering that neighboring pipes might
result in misalignments along the vertical direction. For this reason, the joint between the
cable and the pipes was designed as a hook that is pin-jointed to the pipes in order to
guarantee the necessary tolerances with respect to vertical movements. The connection
between fabric strips and pipes was solved using 3D printed holders to be screwed directly
onto the pipe (Figures 12 and 13). To meet the constraints of a three-day construction period
and a one-day dismantling period, The Canopy was designed in such a way that all the
components could be pre-fabricated and partially pre-assembled in the workshop. The
following section illustrates the pre-fabrication process and how the assembly was then
carried out on site.
1
1
7
4
2
3
4
5
2
6
1 - Aluminium Pipe (d = 17 mm)
2 - Custom made fork piece (casted)
3 - Custom made hook (laser cut)
4 - Custom made fabric holder (3D printed)
5 - Self-tapping screw
6 - Tightening screw
7 - Pin
8 - Steel cable (d = 5 mm)
9 - Fabric
7
8
4
1
9
5
6
2
5
2
1
4
9
8
3
5
70 mm
50 mm
70 mm
60 mm60 mm
Figure 12. The structural detail drawings of the fabric, pipe, and cable connections.
Buildings 2022,12, 1009 12 of 17
Figure 13.
(
a
) The detail of the joints’ final expression; (
b
) The joints become invisible from a distance.
Photos by Shuaizhong Wang.
4.2. Construction: A Convenient and Flexible System
The Canopy’s entire structure was pre-fabricated at ETH Zurich and partially assembled
before transporting it to the site. The components of the nodes were custom made-using
3D printing and laser cutting, and pre-assembled onto the pipes (Figure 14a). This made it
possible to quickly hang and adjust them on-site during construction. To ensure that the
fabric folding position could be precisely measured and that the aluminum pipes could be
fastened without creating creases or discoloration of the fabric from repeated fabrication
processes, a customized rolling machine was developed at the Raplab at ETH (Figure 14b).
This allowed for precise measurements of the fabric strips and for an easy installation of
the pipes at the right location along the strips.
Figure 14.
(
a
) The 3D-printed and laser-cut elements for the joints (Photo by Alessandro Tellini);
(
b
) The rolling machine for measuring the fabric strips and for the installation of the pipes developed
at the Raplab (ETH Zurich) (Photo by Giulia Boller).
Eventually, the 10 fabric rolls—with pipes already installed on them—were transported
on site. At that point, 11 pairs of anchor points were installed on both walls. Due to the
structure’s extreme lightness, the anchor points for the cable consisted of 22 mm threaded
bars and stainless steel rings. The 22 anchor points represent the sole direct intervention on
the existing structure.
The stainless steel cables were connected on one end directly to the anchor points
on the wall, whereas the other end is redirected to a set of counterweights placed on
Buildings 2022,12, 1009 13 of 17
the ground using a pulley. The counterweights were created on site using sandbags. To
facilitate the assembly process, the counterweights were equipped with a hand-operable
winch to control the length of the cables, and thus their height above ground. Once the
cables were arranged, the 10 fabric strips were unrolled on the ground and connected to
the cables using the hooks (Figure 15a). The erection process consisted of a simultaneous
rise of the 11 cables until they reached their final position (Figure 15b). The overall erection
process was carried out in less than two days, whereas the final disassembly required only
three hours, including the process of rerolling the fabric for future reuse.
Figure 15.
The 10 fabric strips were first unrolled on the ground and connected to the cables (
a
). The
entire system was later lifted into the final position through a set of hand-operable winches located at
the ground level (b). Photos by Shuaizhong Wang.
4.3. Tectonic: An Abstract Floating Cloud
Due to the in-depth consideration of the structure, the final expression of The Canopy
appears as a temporary cloud floating in the Kiesofenhalle in a pure and ethereal way,
showing ever-changing levels of transparency as the user moves in the space. The user’s
perception is challenged, as the structural logic is not evident at first glance. This was
achieved thanks to the extremely thin cables that almost disappeared in the height of the
hall. This ambiguous structural expression also invites users to discover and explore the
entire installation from all sides, inadvertently echoing the conference’s intention to refine
and stimulate conceptual thinking about structures through a multidisciplinary exchange.
Furthermore, the long side of The Canopy, with its gaps between the fabrics, exposes as
much as possible of the original walls, thus defining the scale of the space primarily in terms
of height. This enhanced the existing architectural quality of the space and gave it new
life subtly and reverently, swiftly transforming it into a new functional space (Figure 16).
Interestingly, the Kiesofenhalle is also used for cultural events and exhibitions, and it featured
an indoor immersive light show that was displayed at the end of the conference (Figure 17).
Although it was not considered in the design process, such a unique lighting condition
greatly enhanced the floating image of The Canopy.
Buildings 2022,12, 1009 14 of 17
Figure 16.
(
a
)The Canopy as seen from the entrance of the Kiesofenhalle; (
b
) A side view showing
the partitioning elements between the lecture hall and the exhibition area; (
c
) The relatively small
height of The Canopy above the lecture hall allowed creating an intimate space at human-scale;
(
d
) The exhibition area under The Canopy; (
e
) A view of the entire installation from above; (
f
) The
superposition of several layers of fabric in space created very diverse levels of transparency that
stimulated user curiosity and interaction with The Canopy. Photos by Shuaizhong Wang.
Buildings 2022,12, 1009 15 of 17
Figure 17.
(
a
) Some of the lighting situations greatly enhanced the ethereal character of The Canopy;
(
b
)The Canopy reacting to the immersive light show present in the venue. Photos by Shuaizhong Wang.
5. Discussion
The final materialization of The Canopy demonstrated that all the design intentions,
functional requirements, and site constraints were met. The thinking process behind
this project reflects the interaction between form and force, creating a space of “Strong
Structures” [
33
] through a synergy of structure, construction, and tectonic aspects with
an extremely lightweight and minimal intervention. The Canopy ultimately succeeded
in providing an attractively proportioned and functionally partitioned temporary space
for the conference, always respecting the existing space in which it was immersed. By
considering the structure from multiple scales and perspectives, the design concept and
the intended function of the space are achieved.
The use graphic statics enabled simultaneous control of form and forces during each
design phase, and helped to reconcile structural constraints, functionality, and spatial
expression of the factory building. The development of the form and force diagrams in
2D, as in the case of The Canopy, is in fact very simple to the point that it can also be
conducted by hand. However, the development of a 3D structure soon results in more
demanding graphical constructions as the geometric complexity significantly increases.
This might represent the sole limitation of the method proposed in this paper, meaning
that three-dimensional applications are often possible only with the help of 3D modelling
software or specific digital implementations.
Finally, the workflow of The Canopy shows that the pursuit of structural art is not about
letting the structure’s sound overshadow the building itself [
34
]. We can instead find an
interdependent and solid balance between the two by utilizing the proper design medium
and process [
35
,
36
]. Obviously, achieving this equilibrium requires multiple iterations
of the design process instead of allowing the structure to realize the building’s form in a
“post-rationalization” manner.
6. Conclusions
This paper described the design, fabrication, and erection process of The Canopy, a
temporary spatial installation created as part of the International fib Symposium on “Con-
ceptual Design of Structures”. The Canopy is the result of a multidisciplinary design process
in which spatial, structural, and functional needs were reconciled using graphic statics. The
diagrammatic and intuitive nature of graphic statics enabled the rapid communication and
definition of structural concepts using both qualitative hand-sketches in the conceptual
design phase and digital implementations of the method in the form-finding stage. The
diagrammatic and cross-scale nature of graphic statics also clarifies the subsequent detail
processing and construction process, enabling the structural concept to be systematically
linked to the construction, thereby harmonizing the relationship between structure, con-
struction, and tectonic in the design and reinforcing their relevance. The design process
Buildings 2022,12, 1009 16 of 17
of The Canopy demonstrates the significance of collaboration and the use of common and
practical design methods in structural design such as graphic statics. In fact, without the
establishment of an effective common ground between architects and structural engineers
The Canopy’s final spatial expression would not have been possible.
At the end of the conference, the company currently managing the Kiesofenhalle ex-
pressed the desire to preserve The Canopy and reuse it for future events. The Canopy is
currently stored in the warehouse adjacent to the hall and will be re-erected in the hall to
recreate, with extremely simple means, that space-within-a-space that allowed a radical,
yet respectful transformation of the Kiesofenhalle.
Author Contributions:
Conceptualization, S.W., F.B., P.O.O. and D.T.; methodology, S.W., F.B. and
D.T.; formal analysis, F.B. and D.T.; writing—original draft preparation, S.W.; writing—review and
editing, F.B., P.O.O. and D.T.; visualization, S.W., F.B. and D.T. All authors have read and agreed to
the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Not applicable.
Acknowledgments:
The authors would like to thank the whole team involved in the design, fab-
rication, and construction of The Canopy, and all the people who made it possible to realize this
project. Special thanks to Giulia Boller, Ueli Oskar Brunner, Philippe Hilger, Joseph Schwartz (ETH
Zurich); Enrique Corres, Diego Hernandez, and Aurelio Muttoni (EPF Lausanne); Alessandro Tellini,
Christian Egli, Fabio Meier (Raplab, ETHZ); Pierluigi D’Acunto (TU Munich); Marco Bahr (Schwartz
Consulting); Fabian Graber (Jakob AG).
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Conceptual Design of Structures, Switzerland. 2021. Available online: http://conceptualdesign2021.com/ (accessed on 30
May 2022).
2.
Sekler, E.F. Structure, Construction, Tectonics. In Structure in Art and Science; Kepes, G., Ed.; Braziller: New York, NY, USA, 1965;
pp. 89–95.
3.
Geschichte der Cellulose-Fabrik Attisholz. Available online: https://attisholz-areal.ch/informationen/geschichte/ (accessed on
30 May 2022).
4.
75 Jahre Cellulosefabrik Attisholz AG. vorm. Dr. B. Sieber. Schweizerische Bauzeitung. 25 August 1956, pp. 509–510. Available
online: https://www.e-periodica.ch/digbib/view?pid=sbz-002:1956:74::480#2796 (accessed on 30 May 2022).
5.
Chilton, J. 7—Tensile structures—Textiles for architecture and design. In Textiles, Polymers and Composites for Buildings; Woodhead
Publishing Ltd.: Cambridge, UK, 2010; pp. 229–257.
6.
Ney & Partners. Covering of the Courtyard of the Carrédes Arts in Mons/Ney & Partners + AgwA, ArchDaily. 12 October
2014. Available online: https://www.archdaily.com/555329/covering-of-the- courtyard-of-the-carre-des-arts-in-mons-agwa-
ney-and-partners (accessed on 10 July 2022).
7.
AD Editorial Team. ‘Sunyata: The Poetics of Emptiness’: The Indonesian Pavilion at the 2018 Venice Biennale, ArchDaily. 18
June 2018. Available online: https://www.archdaily.com/895626/sunyata-the-poetics-of-emptiness-the-indonesian-pavilion-at-
the-2018-venice-biennale (accessed on 10 July 2022).
8.
Josep Ferrando Architecture. Barcelona Building Construmat Ephemeral Space/Josep Ferrando Architecture, ArchDaily. 8
October 2019. Available online: https://www.archdaily.com/926011/barcelona-building-construmat-ephemeral-space-josep-
ferrando-architecture (accessed on 10 July 2022).
9. Huerta, S. Structural Design in the Work of Gaudí.Archit. Sci. Rev. 2006,49, 324–339. [CrossRef]
10.
Boller, G.; Chilton, J. Heinz Isler’s Experimental Approach to Form Finding. In Candela Isler Müther—Positions on Shell Construction;
Beckh, M., del Cueto Ruiz-Funes, J.I., Ludwig, M., Schätzke, A., Schützeichel, R., Eds.; Birkhäuser: Basel, Switzerland, 2020;
pp. 98–109.
11. Kotnik, T.; Schwartz, J. The Architecture of Heinz Isler. J. Int. Assoc. Shell Spat. Struct. 2011,52, 185–190.
12. Allen, E.; Zalewski, W. Form and Forces: Designing Efficient, Expressive Structures; Wiley: Hoboken, NJ, USA, 2010.
13.
Muttoni, A. The Art of Structures: Introduction to the Functioning of Structures in Architecture; EPFL Press: Lausanne, Switzerland, 2011.
14.
Saliklis, E. Structures: A Geometric Approach: Graphical Statics and Analysis, 1st ed.; Springer International Publishing: Cham,
Switzerland, 2019.
15. Stevin, S. De Beghinselen der Weeghconst; Franciscus Raphelengius: Leiden, The Netherlands, 1586.
16. Varignon, P. Nouvelle Mécanique ou Statique; Chez Claude Jombert: Paris, France, 1725.
Buildings 2022,12, 1009 17 of 17
17.
Maxwell, J.C. On the calculation of the equilibrium and stiffness of frames. Lond. Edinb. Dublin Philos. Mag. J. Sci.
1864
,427,
294–299. [CrossRef]
18. Culmann, K. Die Graphische Statik; Meyer und Zeller: Zürich, Switzerland, 1866.
19.
Billington, D.P.; Doig, J.W. The Art of Structural Design: A Swiss Legacy; Princeton University Art Museum: Princeton, NJ,
USA, 2003.
20.
Schwartz, J. Structural Theory and Structural Design. In Cooperation: The Engineer and the Architect; Flury, A., Ed.; Birkhäuser:
Basel, Switzerland, 2012.
21.
Zienkiewicz, O.C.; Taylor, R.L.; Zhu, J.Z. The Finite Element Method: Its Basis and Fundamentals; Butterworth-Heinemann: Oxford,
UK, 2013.
22. Muttoni, A.; Schwartz, J.; Thürlimann, B. Design of Concrete Structures with Stress Fields; Birkhäuser: Basel, Switzerland, 1997.
23.
Kotnik, T.; D
0
Acunto, P. Operative Diagramatology: Structural Folding for Architectural Design. In Proceedings of the Design
Modelling Symposium, Berlin, Germany, 28 September–2 October 2013; pp. 193–203.
24.
Kramer, S. Operative Bildlichkeit. Von der ‘Grammatologie’ zu einer ‘Diagrammatologie’? Reflexionen über erkennendes ‘Sehen’.
In Logik des Bildlichen: Zur Kritik der Ikonischen Vernunft; Heßler, M., Mersch, D., Eds.; Transcript Verlag: Bielefeld, Germany, 2009.
25.
Block, P.; Ochsendorf, J. Thrust Network Analysis: A New Methodology for Three-Dimensional Equilibrium. J. Int. Assoc. Shell
Spat. Struct. 2007,48, 167–173.
26.
Rippmann, M.; Lachauer, L.; Block, P. Rhino VAULT—Interactive Vault Design. Int. J. Space Struct.
2012
,27, 219–230. [CrossRef]
27.
Ohlbrock, P.O.; D’Acunto, P. A computer-aided approach to equilibrium design based on graphic statics and combinatorial
variations. Comput.-Aided Des. 2020,121, 102802. [CrossRef]
28.
Yuchi, S.; D’Acunto, P.; Jasienski, J.; Ohlbrock, P.O. A new tool for the conceptual design of structures in equilibrium based on
graphic statics. In Proceedings of the International fib Symposium on Conceptual Design of Structures, Attisholz, Switzerland,
16–18 September 2021; pp. 75–82.
29.
Zastavni, D. The Structural Design of Maillart’s Chiasso Shed (1924): A Graphic Procedure. Struct. Eng. Int.
2008
,18, 247–252.
[CrossRef]
30.
Fivet, C.; Ochsendorf, J. The Graphic Statics behind the Collier Memorial. In Proceedings of the IASS Symposium, Boston, MA,
USA, 16–20 July 2018; pp. 1–8.
31. D0Acunto, P.; Jasienski, J.; Ohlbrock, P.O.; Fivet, C.; Schwartz, J.; Zastavni, D. Vector- based 3D graphic statics: A framework for
the design of spatial structures based on the relation between form and forces. Int. J. Solids Struct. 2019,167, 58–70. [CrossRef]
32. Rutten, D. Galapagos: On the Logic and Limitations of Generic Solvers. Archit. Des. 2013,83, 132–135. [CrossRef]
33.
Wang, S.; Kotnik, T. Embodied structural ambivalence: A neurophysiological perspective on structural expression. In Proceedings
of the International fib Symposium on Conceptual Design of Structures, Attisholz, Switzerland, 16–18 September 2021; pp. 23–30.
34.
Billington, D.P. The Tower and the Bridge: The New Art of Structural Engineering; Princeton University Press: Princeton, NJ, USA, 1985.
35. Nervi, P.L. Aesthetics and Technology in Building; Harvard University Press: Cambridge, MA, USA, 1965.
36.
Wang, S.; Kotnik, T.; Schwartz, J. Redefining Structural Art: A Neuroaesthetics Perspective on the Art of Structural Design. Archit.
Struct. Constr. 2022,2, 3–16. [CrossRef]
... GS finds applications across various fields of mechanical analysis. It can be employed for analyzing the impact of moving vehicle loads on bridge structures using influence line analysis [18], assessing the stress distribution in complex industrial machinery components [19], and performing performance analysis in maritime engineering, among others. In the realm of structural analysis in construction, Strut-and-Tie Models (STM) are models established for reinforced concrete structures using GS [20,21]. ...
Article
Full-text available
Timber has long been extensively employed within the construction industry as a famous, environmentally friendly, and low-carbon material. Considering that construction constitutes one of the most significant contributors to carbon emissions throughout the entire life-cycle of a building, there is an urgent desire to incorporate timber into this domain. Nevertheless, the use of timber faces inherent challenges stemming from its anisotropic nature, a result of the natural growth of timber fibers, which makes it challenging for it to function as a primary load-bearing material in coping with the various complex stresses inherent in architectural applications. Numerous designers have attempted to address this limitation through over-sized members and reinforcement at joints; however, none have satisfactorily resolved this issue in an economical manner. In this article, we introduce the Strut-and-Tie models (STM) from Graphic Statics (GS) and a topological optimization algorithm. This algorithm has the capability to generate a ‘load-minimizing path’ STM based on external load support conditions and the maximum structural path span. Regardless of the complexity of the initial external loads, each load transfer path in the optimized STM bears loads in only one direction, representing an optimal solution with minimal internal loads that align seamlessly with the characteristics of timber. Consequently, we endeavor to adopt this optimization algorithm to propose a structural design methodology, with the aspiration of designing structural systems that harness the unique attributes of timber perfectly and applying them to various architectural scenarios. Ultimately, we conclude that structural systems designed based on optimized STM are adaptable to diverse architectural contexts, and when applied to small-scale buildings, this method can save approximately 20% of material consumption compared to conventional timber frame structures, while in the case of mid-rise to high-rise buildings, it can lead to a material savings of approximately 5%.
... Four papers have been qualified for the structural aspects and design group. Article [3] is a good example of seamless integration between the disciplines of architecture and structural design. The geometry of a light spatial installation called Canop is discussed. ...
Article
Full-text available
The current Special Issue is a synthetic overview of 21 published articles. The contact point of architecture–art–engineering is multidimensional, and therefore, this synthesis of works takes into account three criteria: (a) research subject indication, (b) research problem identification, and (c) sublimation of the research techniques and instrumentality used. Research problems, scientific values, and utility values have been highlighted. This synthetic tripartite is intended to make it easier for the reader to find an interesting subject and instrumentality. As the topics of the articles overlap, guided by the dominant values of each article, five subject groups have been sublimated. These are: structural aspects and design, digitization, architectural heritage, aesthetics and emotions vs. engineering, and interior architecture. The characteristic values of each subject group are presented. The indicated new design and research tools do not separate but combine the subject industries; they connect the entities of the investment process.
Article
Full-text available
Structural art should not be marginalised as an integral part of structural design. By reviewing historical understandings of structural art, this article discusses the ambiguous and neglected perspective of structural art on architectural design and human perception dimensions, concentrating the attention of structural art on the question of human aesthetic perception. Based on significant changes in how art is perceived due to recent neuroaesthetics research, this article introduces recent findings from cognitive neuroscience regarding embodied perception principles, sheds new light on the aesthetic experiences inherent in the built environment, and clarifies and expands previously held beliefs about structural art. Finally, while emphasising the significance of structural art, this article attempts to provide a body-informed perspective on structural art that can aid in incorporating human neuroaesthetic perception principles during the conceptual phase of the structural design process, thereby redefining the effect of structures on architectural space and aesthetics, thus redefining structural art.
Conference Paper
Full-text available
The paper attempts to provide a neuroscientific perspective on the discussion of structural expression. Taking human perception as the clue, this article starts with the notion of strong structures, take it as the base to review and analyses the principles of structural perception under the neurophysiological perspective. Based on the findings from mirror neuron and embodied simulation, this article further reviewed the impact of embodied structural ambivalence on structural expression and human perception from the concrete example to the theoretical implication. Therefore provides a neuroscience-based scientific perspective on the research of structural expression.
Article
This article introduces a series of significant enhancements to the Combinatorial Equilibrium Modelling (CEM), a computer-aided form-finding approach to generate and control three-dimensional structures in static equilibrium based on topological considerations. In comparison to the initial formulation of the CEM, this article presents various procedures that extend the applicability of the CEM to various structural topologies and load cases, while allowing the designer to engage with different types of constraint-based optimisation problems. As described in the article, these new features of the CEM have been implemented in a digital tool for form-finding, which has been applied to a series of design examples and case studies to demonstrate the usability of the proposed approach for conceptual structural design. _____________________________________________________________________ https://authors.elsevier.com/a/1aTYk2O2yI1X%7E
Article
This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. Resulting planar graphs can be then used as a base for the assembly of 3D force diagrams, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples demonstrate the benefits of bi-directional manipulations of form and force diagrams in the structural design process. 10.1016/j.ijsolstr.2019.02.008
Chapter
In this chapter mainly tensile textile structures used for the roofing of small, medium and large enclosures are considered, although the principles outlined apply equally to façades, and to textile structures in interior design and art. Commencing with a brief history of the development of modern tensile structures, the general principles (structural efficiency, typical materials, form-finding, patterning, fabrication, installation and pre-stressing) are discussed. Physical and environmental properties and other factors that influence the aesthetic and architectural perception of tensile structures and the spaces they enclose, for example translucency, thermal performance, acoustics and lighting, are also reviewed. Case studies of selected architectural, interior design and art projects are presented to illustrate recent practice. Finally, future trends are identified and a selection of further sources of information and advice is given.