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Architecture, Structures and Construction (2025) 5:8
https://doi.org/10.1007/s44150-025-00126-6
ORIGINAL PAPER
Designing and prototyping of a reconfigurable segmented fan
concrete shell as a flooring system
Mishael Nuh1
·Robin Oval2
·John Orr1
Received: 27 August 2023 / Accepted: 30 December 2024
© The Author(s) 2025
Abstract
A significant portion of the environmental impact of a building’s superstructure lies in its structural flooring. By leveraging
funicular forms such as thin concrete shells, a materially and carbon-efficient alternative to bending-active flooring systems
can be attained. In addition, through segmentation and the use of dry jointed interfaces, a segmented concrete shell allows
for ease of disassembly compatible with circular economy principles for the built environment. This paper presents a novel
segmented concrete shell flooring system that leverages the symmetry of revolution of the classical fan vault form to facilitate
future design flexibility through increased reconfigurability. The design and form-finding of the segmented fan concrete shell
are detailed through the use of an evolutionary algorithm and finite element analysis. Quarter-scale prototypes were digitally
fabricated using a robotic concrete spraying process which were then assembled and tested to assess its structural potential,
evaluate the limitations, and identify areas of future work. An embodied carbon analysis demonstrates that the system provides
a mass and embodied carbon saving compared to conventional flooring systems while adding approximately a 20% embodied
carbon premium over a comparable non-reconfigurable segmented shell flooring system. Rephrased, the proposed system
provides a positive embodied carbon saving if enabling design flexibility through reconfiguration increases the life-span of
the system by at least 20%. Through this work, it is shown that a segmented fan concrete shell presents a viable lightweight
and carbon-efficient flooring system which has the potential to become a sustainable alternative that enables disassembly,
reuse, and even reconfigurability for circular construction provided further research and development to address its current
limitations for adoption in industry practices.
Keywords Circular construction ·Reconfigurable systems ·Sustainability ·Concrete structures ·Digital fabrication ·
Form-finding
Introduction
Thin-shell vaulted concrete and masonry structures
Vaulted structures such as arches and shells present a materi-
ally efficient means of spanning large distances using low/no
tensile capacity materials such as concrete and masonry. This
BMishael Nuh
men30@cantab.ac.uk
Robin Oval
r.oval@tudelft.nl
John Orr
jjo33@cam.ac.uk
1Department of Engineering, University of Cambridge,
Cambridge, UK
2Faculty Of Civil Engineering and Geosciences, Delft
University of Technology, Delft, Netherlands
is achieved by resisting loads through membrane action as
opposed to bending; tensile stresses which can lead to crack-
ing and brittle failure can be avoided, and internal tensile
reinforcement can be altogether excluded. Such structures
have been prevalent historically 1) when it was the only
means of spanning large distances before the advent of steel
reinforcement and pre-tensioning for masonry and concrete
(e.g., cathedral vaults, masonry arches, etc.), 2) where stone
was more widely available compared to wood, or 3) when
labour costs were low compared to material costs and mate-
rial efficiency often results in cost savings (e.g., thin concrete
shell forms of Nervi [1] and Candela [2]). However, as
labour costs increased, the extensive falsework and form-
work required to build and assemble such structures became
cost-prohibitive to fabricate, and the simple but inefficient
prismatic forms–such as rectangular beams and flat slabs–
became more preferred.
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Recently,t here has been a growing interest in re-evaluating
vaulted funicular forms as a sustainable construction prac-
tice by minimizing the material usage and embodied carbon
of a structure [3–6]. This is in part driven by new digital
fabrication techniques which facilitate the construction and
assembly of these structures at an affordable cost. Building
floors are of particular interest for this as they comprise a
large part of the material and embodied carbon of a typical
building’s superstructure [7,8]. It should be noted that the
use of thin-shell forms for roofs and flooring systems is not
new; there are various precedence for it, a prominent set being
the timbrel masonry vaults built by the Guastavino Fireproof
Construction Company used in over 1000 buildings primar-
ily in the United States with one of its advantageous being
its fire resistance [9]. One of the recent digital fabrication
approaches is to print or fabricate the formwork and subse-
quent formers (often using clay, foam, or plastic) which is
then cast with concrete [4,10,11]. A different approach is
to use digital fabrication to extrude and place the material
itself such as through sand 3D printing [5], extrusion-based
printing [6], and also robotic concrete spraying [12,13].
Regardless of the method, the goal is to employ roboti-
cally assisted techniques in order to reduce the labour costs
associated with the fabrication of curved thin shell forms.
The compression-only behaviour of funicular forms makes
them suitable for disassembly and reuse, allowed by simple
reversible joints, in order to aid in the formation of a circu-
lar economy for the built environment. However, these forms
are generally bespoke, lacking repetition and modularity, and
therefore present challenges for reconfigurability.
Further challenges are present with the construction of
funicular systems in regards to their assembly. Traditional
masonry requires the erection of a support structure which is
often as geometrically complex as the final structure itself.
This results in two structures being constructed: a support
structure (which is later disassembled) and the final shell. In
order to enable funicular structures to penetrate the commer-
cial market and to be adopted by industry practices, this issue
must be addressed to avoid extraneous labour costs.
Circularity and reuse of concrete structures
Structural reuse presents challenges both to the design and
construction aspects of a building project. In the prior, the
design of structures needs to be governed by the existing
stock of members, thereby presenting a reversal in thinking
which traditionally details new component member sizes and
specifications based on the design and analysis performed
(alsotermedasaform follows availability design process
[14]). As most designs are not formulated with the intent for
disassembly, reuse, and reconfiguration, this presents diffi-
culties for designers who wish to employ these pre-existing
members. For example, spans of the new structure will then
be dictated by the spans (and designed loading) of the avail-
able stock. Allowing for a degree of flexibility within the form
of new builds with the intent of facilitating future builds will
help ease this constraint. The advantages concerning sustain-
ability are clear in that reusing structural components reduces
both material usage, and retains the energy and embodied car-
bon already put in to manufacture the original components.
The extended lifespan of these components is limited only
by durability concerns; when well protected and in a safe
environment, there are no technical limitations that prevent
components from being continuously reused. It should be
noted, however, that liability concerns (whether arising from
actual durability concerns or merely from its perception)
present additional barriers and may require a novel case-
by-case approach to discussed between project parties and
insurance companies [15,16].
For concrete, the material poses further challenges com-
pared to other conventional building materials such as steel
and timber due to the lack of mechanical fasteners. Cast-in-
place concrete results in monolithic interfaces and pre-cast
members typically rely on grout and mortar to connect differ-
ent components, all of which result in monolithic structures
which are not easily dismantled. Despite these challenges
which have posed hurdles to some concrete reuse projects in
the past [17–20], there is great potential in concrete reuse in
terms of cost and embodied carbon savings, with many of
the hurdles identified as largely transitional [16]. Develop-
ing and employing structural systems that are designed with
disassembly and reuse in mind will help to ease this transi-
tion and make the construction method more appealing for
designers.
Funicular forms that employ membrane and arch action
have the potential to alleviate these issues, both for the reuse
of existing structures and for designs that facilitate reuse and
circularity in the future. By avoiding the need for internal
reinforcements, interruption of the pre-existing tensile rein-
forcement which may be necessary when cutting concrete
members becomes non-problematic. This was demonstrated
to great effect in the Re:Crete bridge which used concrete
blocks sawn from cast-in-place concrete members to create
an arch footbridge, using internal post-tensioning within and
a tie to resolve the external thrust [21]. For designs enabling
future reuse, funicular forms have the potential to minimize
grouting and mortar use as segments do not need to have
mortar in order to maintain their form and stability as the
interfaces are held together through compressive forces – the
simplest way to transmit forces. This was highlighted as a
possible advantage for various segmented funicular structure
prototypes ranging from bridges [6] to segmented funicu-
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Architecture, Structures and Construction (2025) 5:8 Page 3 of 26 8
lar floors [5,12]. In addition, the thrust is often resolved
through the use of external ties which can also be post-
tensioned. Because these tension members are external (as
opposed to being embedded within concrete flat slabs and
beams for bending), it makes disassembly much simpler.
However, funicular structures pose challenges for reconfig-
uration in a reuse case with a scenario different from the
previous one in terms of spans, supports, and loads; the seg-
mentation and geometry of the forms are not conducive for
spanning different distances compared to what they were
initially designed and form-found for. While not a prerequi-
site for reuse, enabling designers to have extra flexibility in
their design will help to lower the barrier to adopting compo-
nent reuse with reconfiguration. Additionally, the form-found
geometry of funicular structures often lends itself to multiple
unique geometries for its segments which presents challenges
for manufacturability at larger scales as well as for reuse (a
lower number of unique segments means that replacements
for damaged segments can be more easily sourced). As such,
there is space to investigate whether a lightweight funicular
structure can be designed such that it enables 1) disassembly,
2) reuse, and 3) reconfiguration for different spans.
Problem statement and research objectives
Segmented thin-shell concrete floors present a structural
system that has potentially large benefits for sustainability–
previous works have demonstrated that vaulted thin-shell
concrete structures can be a materially and carbon-efficient
structural form [3–5]. However, as their segmentation and
form do not have reconfiguration or component reuse as
their primary objective, reuse of these shells dictates that
the span of the shell be maintained, restricting designers
and disincentivizing component reuse. The work detailed in
this paper aims to leverage the structural form to create a
design that also facilitates reuse through ease of disassembly
and also by affording some design flexibility in the future
through reconfiguration. All of this will be driven through
recent digital fabrication advances to reduce the traditionally
labour-intensive fabrication process for thin-shell concrete
structures. Finally, translating the digital and engineering
design work into the physical prototyping stage combined
with structural assessment is necessary in order to demon-
strate the viability of the flooring system and elucidate any
shortcomings that may arise from manufacturing and physi-
cal constraints. In particular, the complexity of the assembly
process compared to more developed and well-adopted sys-
tems, such as precast slab construction, are assessed through
assembly of the prototype system. However, as the primary
focus of the work is on the manufacturability and structural
performance of the shell; assembly considerations, while
acknowledged to be of great importance, are only assessed
and left as future work.
Contribution
This paper details the concept, design, fabrication, and
prototyping of segmented fan concrete shells. The work
demonstrates the potential of leveraging funicular forms for
building systems compatible with circular economy princi-
ples and adds to the growing body of test data for segmented
concrete structures. In Section “Design”, the design of the
structure is detailed, along with the form-finding and opti-
mization work performed to arrive at the final structure which
is designed for disassembly and reconfigurability. Details
regarding the fabrication of two quarter-scale prototypes
measuring 2 m by 2 m using automated robotic concrete
spraying are provided in Section “Fabrication and assembly
of scale prototypes”. These prototypes were then tested under
asymmetrical point loads until failure (Section “Structural
load testing”), with the test modelled using nonlinear finite
element analysis in Section “Structural numerical analysis”.
A sustainability assessment is detailed in Section “Embodied
carbon comparison”. Lastly, conclusions and future work is
outlined in Section “Conclusions and future work”, high-
lighting areas of further development required to address
current limitations, stressing the barriers towards industry
implementation.
Design
Fan vaults and segmentation
Form and geometry The fan vault presents a unique shell
geometry due to its local radial symmetry at each conoid
which offers some particular advantages for standardisation
and modularisation of the segmentation and prefabrication.
The geometry itself can be divided into two distinct parts: the
conoids which are created by revolving a generating curve
around the column axis and the spandrel which fills the space
in between the conoids (shown overlaid over a photo of a fan
vault in Ely cathedral in Fig. 1). There are a variety of clas-
sifications of fan vault geometries based on how the conoids
intersect [22]. For this work, it will be limited to the geome-
try where the conoids only intersect each other at points (i.e.,
no intersections which will cause the conoid geometry to be
truncated) with a flat spandrel used to span the distance in
between. This is in order to avoid truncating conoid segments
and to maintain a high degree of repeatability between seg-
ments to ease fabrication (lower number of unique moulds
and geometries to fabricate) and reuse (damaged segments
can be more easily replaced).
The use of the flat spandrel to span the curved conoids
takes the thrust surface outside of the geometry, thereby
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Fig. 1 View of a fan vault in Ely cathedral with various parts highlighted (right)
requiring some bending capacity within the spandrel. How-
ever, due to the thrust generated by the conoids, compressive
stresses results in a pre-stressing effect on the concrete mem-
ber, reducing the requirements for tensile reinforcement to
properly resist the bending forces.
Segmentation Membrane analysis performed by Heyman
[23] demonstrates that, under a radially symmetric load case,
the principal stress directions align with the hoop and strip
direction of the conoids. For shells and masonry, it is desir-
able that the interface between segments be aligned to these
directions as that results in minimal shear stress transfer,
minimizing the risk of slippage. As such, the segmentation
of the conoids of the fan vault can be performed along the
hoop and strip directions. This results in a highly repeti-
tive and simple segmentation plan. While it is recognized
that this highly idealized radially symmetric loading differs
from the one stemming from the actual loads from the span-
drel due to radial symmetry being limited to a single conoid
in the realised geometry [22]–in fact, even under its own
self-weight the spandrel will cause uneven loading on the
conoids–any segmentation plan will only be optimal for a
certain load case combination and pattern. Considering the
advantages that the simpler segmentation plan has for reuse
and repeatability, it was selected as the basis for the seg-
mented fan concrete shell flooring system. This difference
between the idealised uniform radial loading and the true
loading will result in friction and shear forces developing at
the interfaces which must be resisted. Such shear forces also
occur for other asymmetrical floor loads. This is resolved
through the inclusion of shear keys which also has the added
benefit of aiding in the assembly process by aligning seg-
ments together. The shear keys are formed such that the upper
segments have protrusions that rest on the lower segments,
shown in Fig. 2.
Reconfiguration The repeatability and simplicity in the
segmentation plan of the fan vault geometry allow for recon-
figuration and flexibility in reuse; different distances can be
spanned using the same pieces by removing conoid seg-
ments and/or adding a new spandrel. Some examples are
illustrated in Fig. 3. While structurally a shorter span will be
more amenable to reconfiguration, an increase in span dis-
tance can potentially be achieved through strengthening and
retrofitting of the original segments and interfaces (through
the addition of mechanical fasteners to allow for some tensile
capacity across interfaces) in order to increase their capac-
ity. Alternatively, the design and form-finding process can be
performed for a larger span than what is needed to accommo-
date future increases in spans. To minimize embodied carbon,
maintaining the same span by reusing as many components
as possible and reclaiming the spandrel would be ideal. How-
ever, by allowing for a degree of flexibility within the system,
it incentivizes designers to reuse the building components
which increases the chances of enabling circularity for the
flooring system. Additionally, as vaulted structures main-
tain their form and stability through compressive forces at
Fig. 2 Shear keys on segments which helps to resist slipping and aid
in assembly
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Architecture, Structures and Construction (2025) 5:8 Page 5 of 26 8
Fig. 3 Example reconfiguration of a segmented fan concrete shell by removing components (red) and adding new ones (green)
the interfaces between segments, the segmented fan concrete
shell can be constructed without any grout or mortar allowing
for ease of disassembly for reuse. The simple and repeated
pattern of the segmented fan concrete shell also facilitates
fabrication due to the lower number of moulds and unique
pieces that need to be manufactured and catalogued: fewer
casting frames can be made of higher quality, precision, and
durability to reuse them multiple times.
Fabrication constraints The fabrication process that will be
used for the prototypes introduces constraints that must be
considered in the initial design phase. Manufacturing of the
prototypes will be carried out using the Automated Robotic
Concrete Spraying (ARCS) process [13] which deposits
glass fibre reinforced concrete (GFRC) onto a fabric sur-
face bounded by planar wooden formwork. This means that
the curvature of the segment boundaries (when viewed from
above) must be zero. Modifications to the segmented fan con-
crete shell were carried out in order to account for this; as
opposed to revolving around the column axis, the generat-
ing curve profile is instead extruded to fill each strip region
(illustrated in Fig. 4). The resulting segment interfaces are
therefore contained in planes parallel to the vertical axis, not
to the local normal of the shell. This also causes the spandrel
to have a polygonal boundary as opposed to an arc bound-
ary. Structurally this causes further deviation from Heyman’s
membrane analysis which will result in increased shear forces
at the interfaces.
Finite element analysis methodology
Preliminary analysis of the shell for optimization purposes
was performed in Karamba3D [24] – a Grasshopper [25]
plugin which can perform linear elastic finite element analy-
sis using shell elements. However, as the interfaces between
the segments are to remain ungrouted, this introduces non-
linearities and complexities (both due to the concrete material
and interlocking compression-only interfaces thanks to the
shear keys) which a monolithic finite element analysis using
shell elements is not capable of fully capturing [26]. For
instance, determining that the structure will fail based on
the presence of tensile stresses is too conservative as plas-
tic hinges will form at the interface which will redistribute
the loads to other parts of the shell. With respect to buckling,
ignoring the effects of the interface results in an overestimate
of the load capacity of the structure [27].
In order to address this and find a balance between a
detailed non-linear finite element analysis (which would not
be compatible with the optimisation process due to its large
computational requirements) and a simplistic monolithic and
linear-elastic finite element analysis (which does not ade-
quately represent the structure), a novel analysis approach
was formulated which combines linear-elastic finite ele-
ment analysis with a custom joint modelling technique to
enable hinging behaviour. The analysis method is detailed in
Appendix A.
Fig. 4 Rationalization of
geometry to accommodate
fabrication process
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Shell form-finding and optimisation
Form-finding was performed using the Wallacei Grasshopper
plug-in [28] which implements the NGSA-II multi-objective
evolutionary algorithm [29] to converge close to an optimal
solution. For the segmented fan concrete shell, two objectives
were optimized for: minimised mass and maximised buck-
ling load factor. Minimum mass is desired as this is a good
proxy for the embodied carbon of the structure. Because the
analysis method (detailed in Section “Finite element analy-
sis methodology” and Appendix A) is expected to produce
an overestimate of the buckling load factor, this was also
included within the multi-objective optimization in order
to provide a range of optimized solutions. This optimized
Pareto front can then be used to select the minimum mass
solution given a minimum acceptable buckling load factor.
The choice of a minimum acceptable buckling load factor
depends on the fabrication and assembly tolerances which
results in imperfections [30,31] as well as how much of an
overestimate of the buckling load factor the analysis pro-
duces. This depends on the amount of segmentation within
the shell: smaller amounts of segmentation and interfaces
mean that the buckling load factor computed is less overes-
timated due to being closer to a pure monolithic structure. A
more detailed non-linear finite element analysis [32] of select
candidates from the final structure can provide an estimate
of the amount of overestimation from the optimisation pro-
cess and can be used to inform the selection of a minimum
acceptable buckling load factor.
The parameters of the evolutionary algorithm (i.e., popu-
lation size, crossover probability, mutation probability, and
number of generations) must be appropriately selected. The
convergence speed of the optimisation process is affected
by the choice of these parameters and, consequently, will
affect the results of the algorithm. Converging too rapidly
will result in designs which converge too quickly at a local
optimum while converging too slowly will require many gen-
erations to properly converge. Tuning such parameters is a
time-consuming process, with many relying on heuristics
[33–35]. For the segmented fan concrete shell, the default
settings for the Wallacei plug-in were used for the popu-
lation size (50), crossover probability (90%), and mutation
probability (2%). The number of generations was set to a
high number and the algorithm was stopped once conver-
gence was deemed to be obtained (i.e., minimal difference
and improvement between generations).
Geometry parametrization
The segmented fan concrete shell flooring system was
parametrized in order to prepare for form-finding. Firstly,
the span of the shell was selected to be 8 m as the maximum
design span. The depth is of 800 mm (from the middle of the
spandrel to the middle of the base of the conoids), yielding a
span-to-depth ratio of 1/10. While this is larger than typical
depths of structural floors, the curved profile allows room for
services to be integrated within the structural depth (similar
to the concrete shell floor detailed in [12]), compensating for
the added depth premium. The depth of 800 mm is also com-
parable to a 300 mm thick flat slab combined with a typical
500 mm height service zone and has been used by other works
as a reasonable depth for a curved flooring system [3]. Raised
flooring will need to be added to the shell in order to cover the
integrated services and also to create a level surface on top
of the curved shell. Segmentation was performed every 1 m
along the projected length of the conoids in the strip direc-
tion and divided into 3 strips per conoid. The exception is
the region near the corner which is a single monolithic piece
extending 2 m away from the columns, as it is envisioned
that the minimum span for a flooring system will not be less
than 4 m.
The thrust surface is set as the medial surface of the
vault. The geometry can be defined by setting the midline
curve of the conoids and the thicknesses at various loca-
tions, totalling 7 parameters. It was determined that a planar
Bézier curve with two intermediate points and thicknesses
defined at the base of the conoid, the top of the conoid, and
the spandrel provides sufficient resolution while not encum-
bering the form-finding process with excessive parameters.
The extremity points are fixed, to link the column and the
spandrel. For the thickness in between the top and bottom
conoid thicknesses, a linear interpolation was used. In addi-
tion, all thickness values are constrained to be within 20 mm
to 100 mm. The lower bound of 20 mm is set by fabrica-
tion constraints, as it would correspond to a 10 mm thick
shear key. The upper bound of 100 mm is set higher than
for a common shell thickness-to-span ratio of 1:00, which
is 80 mm here, and for a common slab thickness-to-span
ratio of 1:30, which is 100 mm here, as the spandrel as a
diagonal span of 3.2 m between the conoids. A schematic
of the parametrized geometry is shown in Fig. 5, with its 7
parameters (3 thicknesses tbot ,ttop, and tspandrel, and 4 UV-
coordinates p1u,p1v,p2u, and p2v). The steel ties are set
as a constant M24 steel bar designed to resist the horizontal
thrust forces based on preliminary analysis of typical thrust
forces occurring in such spans. Including the steel tie area as
another parameter would unnecessarily increase the search
space for optimization purposes while yielding little benefits
as steel bars typically come in discrete sizes.
Model statics system
Computation of the buckling load factor objective value is
performed by finite element analysis using Karamba3D using
the method described in Section “Finite element analysis
methodology” and Appendix Ausing custom joints. A rep-
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Architecture, Structures and Construction (2025) 5:8 Page 7 of 26 8
Fig. 5 Parametric geometry model of the segmented fan concrete shell flooring system
resentative model is shown in Fig. 6. Nodes in the corner
support were restrained vertically and allowed to translate in
the XY plane freely. This is to allow the steel ties which are
connected to the corners to be engaged. To prevent the whole
structural model from rigid body motions, the node in the
middle of the spandrel area is constrained from translating
in the XY plane and from rotating about the vertical axis.
This does not affect any of the structural results except for
the buckling load factor analysis which cannot be properly
performed with rigid body degrees-of-freedoms present.
A load combination including the self-weight, an imposed
dead load of 1.0 kPa, and a live load of 1.5 kPa (selected as
it is more representative of actual loads experienced in office
type buildings [36]) was used. The live load was applied
over the entire projected area as it was found to likely be the
governing load pattern from a preliminary analysis. When
other area loadings were applied which can produce a lower
buckling load factor depending on the geometry (e.g., a live
loading applied only to one half), the difference was minor
enough that it did not warrant the inclusion of other load
combinations in the optimisation process. Instead, these load
combinations should be analysed for the optimised solutions
that the algorithm produces. Based on mesh sensitivity anal-
ysis, a coarse triangular mesh size of 100 mm was selected,
and the loads were applied over 10 load steps. While better
convergence was seen with a finer mesh size, the selected
mesh density provided a balance of computational speed and
accuracy for form-finding which requires the computation of
numerous models and geometries. Each model took approx-
imately 2 min to run on the computer setup used.
Material properties and limits
Two materials will be used to construct the segmented fan
concrete shell: one for the spandrel and one for the conoids.
For the unreinforced flat spandrel, a conventional concrete
mix with a target characteristic strength of 30 MPa at 28 days
was used. For the conoids, the automated robotic concrete
spraying (ARCS) process [13] was used to fabricate them
as they had curvature and variable thickness. The process
involves spraying glass fibre reinforced concrete (GFRC)
onto a curved surface bounded by a wooden frame. Typical
material properties of components fabricated using ARCS
are provided in [13] and were used for the analysis and form-
finding. To simplify analysis at the form-finding stage, all
segments were modelled using the GFRC material (of which
most of the shell except the spandrel consists). Material prop-
erties of the GFRC and steel ties used are listed in Table 1.
In addition to obtaining the buckling load factor from the
analysis, solutions are constrained and only considered valid
if they pass ULS strength requirements. This includes 1) the
steel tie utilization, 2) the GFRC tensile utilization, and 3) the
Fig. 6 Karamba3D finite
element model used for
form-finding showing locations
of custom joints (red) and
restraints (blue)
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Table 1 Material properties used for form-finding
Properties GFRC1Steel
Young’s modulus [GPa] 19.9 210
Poisson ratio 0.2 0.3
Weight [kg/m3] 2000 8000
1Obtained from [13]
GFRC compressive utilization for which the limiting values
are listed in Table 2. For the stresses within the shell, the
95th percentile values were used in order to exclude areas
of stress concentration in the analysis which is an artefact
of the finite element meshing and will redistribute in reality
through plastic behaviour, thanks to the ductility provided by
the glass fibres.
Results
The optimization yields a family of Pareto front solutions
which presents the minimum mass geometry given a mini-
mum acceptable buckling load factor under the applied load
combination. The performance of select generations is shown
in Fig. 7. It can be seen that the population converges onto
the approximate optimal Pareto front quite quickly, within 10
generations. This suggests that future optimization and form-
finding may be able to be carried out much faster by reducing
the overall number of generations. The full optimisation pro-
cess took approximately 1 week of computation time. Much
of this time was spent early in the process whereby inad-
missible candidates (i.e., violating ULS requirements) were
excluded and not added to the pool of accepted candidates
in the generation, thereby requiring additional model gener-
ation and computation to reach the pool size of 50.
The results of the last generation are shown in Fig. 8, with
candidates with minimum acceptable buckling load factors
of 2, 4, and 10 shown in red, green, and blue respectively.
Overall, most candidates have similar curve profiles, being a
shallow concave curve. This is to be expected given the thin-
ness of the shell and shallowness from the restricted depth:
the thrust surface is bounded by the cross-sections at the
Table 2 ULS requirements considered for form-finding
ULS require-
ments
Characteristic
strength value
Material partial factor
Steel tie util. 830 MPa 1.15
GFRC tensile
util.1
5.74 MPa 1.5
GFRC compres-
sive util.1
31.2 MPa 1.5
1Obtained from [13]
ends of the conoid and, combined with the small weight of
the conoid segments, leads to a low curvature for the thrust
surface. The main differences arise from the thickness, where
higher buckling load factors can be achieved by increas-
ing the overall mass. In general, optimized solutions have a
higher conoid thickness at the base compared to the top com-
bined with an increase in spandrel thickness. This is akin to
the effect that a pendant has on traditional gothic fan vaults;
by having a large enough spandrel weight, the compressive
forces exerted on the conoids are increased and, with suffi-
ciently large values, tensile stresses in the hoop directions
are eliminated [23].
A minimum acceptable buckling factor of 10 was chosen
to accommodate for the non-linearities unaccounted for by
the analysis method as well as any fabrication and assem-
bly imperfections (which can have a significant impact on
the performance and capacity of segmented vaulted struc-
tures [30–32]). The objective values and the parameters of
the selected candidate (along with those with minimum buck-
ling load factors of 2 and 4) are listed in Table 3.
As can be seen, the selected design has a thickness that
varies from 100 mm to 75 mm within the conoid and has a
jump in the spandrel thickness to 86 mm. The Bézier curve
profile concaves downwards slightly as expected from the
shell. In addition, overall ULS material utilization remains
low, with the tensile stresses in the concrete governing.
Again, this is similar to masonry structures where the com-
pressive stresses are quite low compared to the capacity of
the material itself. For thin shell structures such as these, the
utilization becomes slightly higher due to the lower cross-
sectional area but remains well within the limits. Under
localised point loads, higher tensile stresses arising from
localised bending and punching shear will occur. In such
cases, membrane action throughout the shell will help to
reduce these localised tensile bending stresses. However, fur-
ther analysis and checks will be required to design against
local failure under concentrated loads. For the shell, the mag-
nitude of concentrated loads applicable for typical flooring
(Qk=2.7kN as per BS EN 1991-1-1:2002 [37]) is not
expected to govern over the global buckling failure mode
induced by area loads.
In the optimisation algorithm, the stress utilisations are
treated merely as constraints: candidates that have utilisation
greater than 100% are excluded. Including this stress utili-
sation in the optimisation process would allow for a more
optimised design which increases overall material strength
utilisation. For example, maximising the mean GFRC mate-
rial utilisation on top of maximising the buckling load factor
and minimising mass would provide insights into how much
extra material is ‘wasted’ (with respect to material utilisa-
tion). This would enable the design to fully leverage the
fabrication process to fabricate a variable-thickness shell that
places just enough material where needed. However, this
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Architecture, Structures and Construction (2025) 5:8 Page 9 of 26 8
Fig. 7 Objective values of the population within select generations from the optimization process
would add another dimension to the selection of an opti-
mal candidate: rather than a simple 2-parameter Pareto front
(evident in Fig. 7), a 3-parameter Pareto surface is created. In
addition, the extra computational power required to perform
this analysis may prove to be unnecessary as such shells are
likely to be governed by stability and buckling behaviour as
opposed to their material capacity.
Fabrication and assembly of scale
prototypes
Based on the form-found design, quarter-scale prototypes of
the segmented fan concrete shell flooring system were fab-
ricated in order to assess their viability and to determine
any limitations and shortcomings of the system concern-
Fig. 8 Details regarding the population at the final generation of the optimization algorithm
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8 Page 10 of 26 Architecture, Structures and Construction (2025) 5:8
Table 3 Properties of the selected full-scale candidate from the optimisation process
Val u e s
Minimum buckling load factor 2 4 10
Objective values
Mass15.25 t (82.0 kg/m2) 6.70 t (105 kg/m2) 10.8 t (169 kg/m2)
Buckling load factor 2.02 4.09 10.2
Parameters
Conoid thickness – bottom [tbot ] 56mm 87mm 100mm
Conoid thickness – top [ttop] 29mm 33mm 75mm
Spandrel thickness [tspandrel] 47mm 52mm 86mm
Bézier point 12[p1] (2.00, 0.46) m (2.75, 0.57) m (1.94, 0.43) m
Bézier point 22[p2] (2.79, 0.62) m (3.04, 0.64) m (3.48, 0.70) m
Maximum ULS utilization
GFRC – compressive 30.2% (6.28 MPa) 28.6% (5.94 MPa) 23.7% (4.93 MPa)
GFRC – tensile 90.1% (3.45 MPa) 95.8% (3.67 MPa) 87.3% (3.34 MPa)
Steel ties 64.3% (464 MPa) 62.3% (449 MPa) 67.7% (489 MPa)
1Calculated using uniform GFRC weight of 2000 kg/m3
2U, V coordinate system shown in Fig. 5
ing physical constraints and manufacturing processes. These
prototypes measured 2 m by 2 m in span and have depths of
200 mm. All dimensions were scaled to a quarter of the full-
scale design except for the thicknesses which were scaled
only by half. This choice to only scale the thickness by half
is for two reasons. Firstly, the volume and dead weight of the
shell decreases at a greater rate compared to the decrease in
span length. As such, the thickness must be increased in order
to compensate for the scaled-down geometry for stress rea-
sons. While the stability of the shell under its own self-weight
is maintained if scaled uniformly, the added self-weight will
also aid in counteracting any imbalanced loading that will
inevitably be experienced during assembly and instrumenta-
tion. Secondly, manufacturing tolerances will have a much
bigger effect the thinner the shells are–a minimum scaled
thickness of 19 mm would have been too sensitive to the
fabrication process’ tolerances, particularly in forming the
shear keys that are only half the thickness of the shell and are
therefore kept to at least 10 mm as experienced during the
development of the fabrication process.
Two shells were fabricated with differing segmentation
plans in order to investigate the effects of the number of
segmentations on the overall structural behaviour. The main
difference between the two shells is the segmentation of the
hoops: in the first shell, the conoids are split into three seg-
ments along the strip direction while in the second shell,
the upper two conoid hoops are merged. The first shell was
tested multiple times as the sprayed conoid segment experi-
enced little damage between tests–only a new spandrel was
installed due to cracking and fracture. A schematic of the
quarter scale prototype, as well as the locations of the load-
ing plate, are shown in Fig. 9. Variations between the two
shells are highlighted in red.
Fabrication of the concrete segments can be divided into
two stages: spraying of the conoids using GFRC and cast-
ing of the flat spandrel using a conventional concrete mix.
Spraying the spandrel was not performed as it was unnec-
essary due to its flat profile and allows for the use of larger
aggregates (thereby reducing the embodied carbon density
of the concrete mix per unit volume). Preliminary finite ele-
ment analysis of the tests demonstrated that an unreinforced
spandrel will experience localised cracking due to the con-
centrated loading, but that this will not greatly affect the
overall failure mode of global buckling. In addition to the
concrete segments, steel corner supports constructed from
angles were made onto which the concrete segments sim-
ply rest with no padding or mechanical connection. M12
threaded steel ties were bolted to steel corner supports which
the concrete segments rest on in order to resolve the horizon-
tal thrust.
Robotic spraying of conoid segments
The conoid segments were fabricated using the Automated
Robotic Concrete Spraying (ARCS) process [13], shown in
Fig. 10. This fabrication process consists of two parts: the
actuated pin-bed which allows for a desired curved surface
to be created and a concrete sprayer which is controlled by
a robotic arm that then deposits the GFRC onto the target
curved surface. The target spraying area is bounded by a
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Architecture, Structures and Construction (2025) 5:8 Page 11 of 26 8
Steel support
Added extra base plate for 2nd shell/3rd test
2000
Flat spandrel
2000
20 cm x 20 cm
loading plate
2000
200
18 mm thick shear keys
M12 Steel Ties
Grade 8.8
Upper conoid hoops merged
for 2nd shell/3rd test
500
Sprayed conoids
Conoid 1
Conoid 3
Conoid 2
Conoid 4
Fig. 9 Diagram of quarter scale prototype tests, with variations and modifications between sets highlighted in red with units in millimetres
wooden frame constructed out of 18 mm thick phenolic ply-
wood with the shapes cut out using a CAD-guided CNC
router. These wooden frames also contain the negative shapes
of the shear keys which, when sprayed into, form them. Each
conoid quarter was sprayed together during one spray session
and demoulded the next day. This limitation on the amount
that could be sprayed at once was mainly due to the limited
area of the pin-bed mould and the reach of the robotic arm.
The GFRC sprayed onto the wooden frames consists of a
cement slurry which is pumped and aerated by the machine,
and combined at the end with chopped alkali-resistant glass
fibres. The recommended mix from the manufacturer of the
concrete sprayer machine (Power-Sprays) was used. This was
due to the sensitivity of the sprayer to the cement slurry’s
rheological properties and the additives used. Further testing
should be performed in order to investigate how to tune the
mix to reduce the comparatively high cement content (and
embodied carbon density) per unit volume. Quantities of the
materials used within the GFRC mix are listed in Table 4.
The nominal weight of the mix was found to be 2000 kg/m3.
The trajectory planning approach for ARCS involves
slicing the shell with curved slices [38]. As spraying was
performed in layers, the fibres were deposited and oriented
randomly but with the plane of the layers (i.e., generally
aligned with the direction of membrane stresses within the
shell). From previous investigations [13], it was observed
that the achieved thickness of the shell deviates near the
boundary regions due to excessive connecting paths and lim-
its in the acceleration of the robotic arm for turning. As such,
the thickness of the sprayed material for the smaller upper
Fig. 10 Spraying of a quarter of the conoid segments for the 1st shell prior to (left) and after (right) the GFRC is deposited
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8 Page 12 of 26 Architecture, Structures and Construction (2025) 5:8
Table 4 Material quantities used for GFRC spraying per meter cubed
Material Quantity
CEM II cement 795 kg
Kiln-dried sand [max 1 mm agg.] 795 kg
Polycure [curing agent] 80 L
Flowaid [super plasticiser] 4 L
Pumpaid [pumping aid] 4 L
Wat e r 1223 L
AR glass fibre25%
1Adjusted to achieve the desired slump of 3 to 4 based on BS EN 1170-
1:1998
2Fibres chopped to 25 mm at spraying head
conoid segments (which have a small ratio of surface area to
boundary length) was greater than what was designed. Excess
material was removed manually and a thickness correction
factor of 75% was applied for later sprayings of the upper
hoop segments of the 1st shell. This was found to not be an
issue for the 2nd shell due to the larger segments, and the
correction factor was removed.
Fabrication of flat spandrel
The flat spandrel was cast using a conventional concrete mix
designed using guidance from [39] to achieve high worka-
bility (to ensure a good finish on the shear key interfaces)
and a characteristic 28 days strength of 30 MPa. This yields
a water-cement ratio of 0.53 and a cement:sand:gravel mass
ratio of 1:1.14:3.09. A maximum aggregate size of 10 mm
was used for the gravel. Similar to the conoids, the formwork
of the spandrel contains negative shapes of the shear keys as
formers. No reinforcement was included in the spandrel as
it is designed to be held in compression through the arch
action of the shell. However, this yields a potentially brit-
tle form for handling, transportation, and storage purposes.
As such, the addition of minimum reinforcing bars or other
reinforcements (e.g., glass fibres, steel fibres, etc.) may be
required for a full-scale structure outside the controlled lab-
oratory environment.
Assembly
Assembly of the shell proceeds akin to a traditional masonry
vault: the segments are placed in their correct locations with
the use of falsework which is only decentered once the entire
structure is completed. This is necessary as the shell’s stabil-
ity relies on membrane action and is only truly stable once
fully assembled–a condition which is even more important
for ungrouted segmented vaulted structures that cannot rely
on mortar strength. However, compared to tile vaults, the
segments used for the segmented fan concrete shell flooring
system are relatively large. As such, there is no need to cre-
ate an intricate wooden falsework; here, the use of props is
sufficient to place the segments at their appropriate height
and location. A similar strategy was successfully used previ-
ously with another segmented concrete shell flooring system
consisting of nine large segments [12].
The assembly process is illustrated in Fig. 11. First, the
segments are placed on wooden props and adjusted to their
correct height. The steel ties are then tightened in order to
engage arch action. Lastly, the props can be removed one at
a time. Disassembly of the structure proceeds in the reverse
order of the assembly process. This was successfully per-
formed for Shell 1 which was disassembled and reassembled
prior to the first test. The disassembly process was found to be
much faster compared to the assembly process as segments
need not be aligned and placed in their correct position and
heights. In addition to this, Shell 1 was reassembled a second
time with a new spandrel for further load testing after the ini-
tial test, demonstrating that reuse is possible by combining
old and new components with no extra complexity. While not
as direct of an assembly process compared to conventional
precast slabs, the use of discrete props presents an improve-
ment to traditional funicular and masonry construction which
typically involves the construction of a geometrically com-
plex secondary support structure.
Due to tolerance issues, the fabricated segments did not fit
perfectly together. This was caused by small deviations in the
fabrication of the wooden frame and shearing deformations
from the relatively soft corner of the frame, amounting to a
maximum of 10 mm. Using a more precise and stiffer steel
formwork would enable higher accuracy while also enabling
Fig. 11 Assembly process of the segmented fan concrete shell, proceeding from left to right
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Architecture, Structures and Construction (2025) 5:8 Page 13 of 26 8
reuse, as the wooden formwork warped and degraded after
several casts. In order to allow the shell to stand, a fill material
was added in between the segments once they were placed on
the props which helped to close the gaps and allow contact to
form while still allowing for disassembly. For the first shell,
fine sand was used to fill the gaps for the first test (MN1) and
mortar was used for the second test (MN1M). As the strength
of the mortar was not of great concern (rather its role as a
filler material was its main purpose), MN1M was decentered
merely a day after the mortar was applied and then tested
within a week resulting in an overall weaker mortar which
has not developed all of its strength. For the second shell,
the deviations caused by tolerance issues were too great and
fine sand could not adequately be used. As such, only mortar
was used to fill the gaps for the last shell and test (MN2M).
This use of mortar does limit the disassembly potential of
the prototype shells. However, it was performed in order to
proceed with the assembly and further testing of the fabri-
cated pieces. When scaled up in an off-site prefabrication
plant process, these deviations and tolerance issues are not
expected to have as large of an impact compared to what
they have on these quarter-scale prototypes. For example, a
typical formwork dimension deviation for precast concrete
of 2.5 mm [40] is comparatively smaller for the full-scale
design of the segmented fan concrete shell compared to the
scale prototypes where the smallest segments are less than
500 mm in side lengths.
Once assembled, 3D scans were taken of the shells which
were used to measure their thicknesses and for analysis pur-
poses. The results of this are provided in Appendix B.
Structural load testing
Methodology
Testing of the shell was performed at the National Research
Facility for Infrastructure Sensing at the University of Cam-
bridge. A total of three tests were carried out, two using the
first set of sprayed conoids (MN1 and MN1M) and one using
the second set of sprayed conoids (MN2M). In addition to
differences in the segmentation of the conoids, the tests var-
ied with the material used to fill the gaps: either sand or
mortar (the latter is denoted by the addition of -M at the end
of the label). An asymmetric point loading was applied on
the shell (offset 500 mm towards an edge), whose purpose is
to induce an instability failure rather than a punching failure
which would have been induced by a central point load. Dur-
ing the test, displacements of the jack and the segments were
monitored using an LED tracking system. A displacement-
controlled loading was applied at a slow rate of 1 mm/min.
In addition, the strains of the steel ties were recorded using
strain gauges and displacements at the middle edges of the
shells were measured using linearly varying displacement
transducers (LVDTs) (Fig. 12).
Material tests
For each set of sprayed segments, a set of material testing
samples was fabricated by spraying a 40 mm thick flat panel
and cutting out prisms and cubes [13]. Bending tests were
performed on four prisms measuring 40 mm thick and 50 mm
Fig. 12 Assembled MN1 shell prior to testing
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8 Page 14 of 26 Architecture, Structures and Construction (2025) 5:8
wide tested in four-point bending over a 300 mm span as per
BS EN 1170-5:1998 [41]. Two values were extracted from
the tests: the cracking stress ( ft,lop) which is the stress at the
extreme tensile fibre at which non-linearities due to cracking
first appear and the ultimate tensile strength ( ft,ult ) which
is the maximum tensile stress at the extreme tensile fibre.
In addition, eight 40 mm cubes were tested in pure compres-
sion (adapted from compression tests of mortar prisms tested
under 40 mm by 40 mm square loading plates as per BS EN
1015-11:2019 [42]), ensuring that the loading is parallel to
the plane of the sprayed fibre (i.e., same loading direction as
would be experienced by the sprayed conoid segments). From
this test, the stiffness of the material (Ec) and the ultimate
compressive strength ( f
c) were obtained by taking the tan-
gent stiffness and the maximum stress of the loading curves.
In addition to the GFRC tests, standard 100 mm concrete
cubes were cast and tested in compression for each flat span-
drel cast. The ultimate compressive stress ( fc) was obtained
from the tests while the stiffness of the spandrel was interpo-
lated based on BS EN 1992-1-1 [43]. The tests were spread
out such that values were obtained for 28 days after the cast
and on the same days as the tests, except for shell MN1M
which did not have any separate material tests performed for
the conoids.
The mean values of the properties are listed in Table 5.
Note from the values listed, the variability of the material
properties, especially the conoid material’s stiffnesses, is
quite large, despite the same GFRC mix being sprayed. Such
variability is likely from the manual mixing and machine
calibration process involved: for each spraying session, the
machine is recalibrated manually to obtain a target glass fibre
content and the cement slurry’s water content is adjusted to
achieve a desirable slump. In addition, premature spalling
and localised crushing were prevalent within the cube sam-
ples for Shell 2, leading to unrealistically low compression
stiffness values, further exacerbated by the displacement
tracker targets spalling off the cover (for example, the 0.53
GPa stiffness value for segment 3’s material samples were a
result of this latter issue). This was likely due to fabrication
issues of the test panels which occurred with Shell 2; it was
observed that the cement slurry had started to set as a longer
time was taken between spraying the conoid segments and
the test panel compared to with Shell 1. This resulted in a
mean difference of 49.2% between the 28-day compressive
Table 5 Mean material properties from tests
Seg. # Tests Compression cube Bending prism
Ec,comp f
cEc,bend ft,lop ft,ult
[GPa] [MPa] [GPa] [MPa] [MPa]
Shell 1
28 days 1 4/2 34.9 36.4 10.1 9.12 11.1
2 4/2 31.4 38.9 13.6 8.88 11.4
3 4/2 20.6 30.1 8.54 9.07 11.1
4 4/2 11.6 26.6 6.61 7.08 8.48
MN1 1 4/2 42.4 44.0 11.2 8.23 9.99
(test day) 2 4/2 30.5 43.2 10.3 8.66 10.3
3 4/2 15.1 26.7 11.8 9.79 12.3
4 4/2 27.5 20.4 8.20 7.47 8.12
S20 33
241.4 – – –
MN1M1S10 33
245.4 – – –
Shell 23
28 days 1 2/1 14.4 41.0 8.81 9.53 13.5
2 2/1 12.7 30.1 4.74 8.68 10.4
3 2/1 0.53 28.6 7.06 7.71 10.1
26 days 4 2/1 25.0 42.2 11.9 9.79 9.86
MN2M 1 6/3 6.89 34.4 11.4 10.5 13.1
(test day) 2 6/3 6.28 27.3 8.24 7.63 9.43
3 6/3 9.84 34.3 12.0 8.75 11.9
4 6/3 14.1 43.4 12.3 9.02 12.1
S10 32
233.4 – – –
Conoid numbering matches Fig. 9
1MN1M did not have sprayed material tests
2Spandrel stiffnesses interpolated based on BS:EN1992-1-1
3Premature spalling and localised crushing of cube specimens observed
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Architecture, Structures and Construction (2025) 5:8 Page 15 of 26 8
Fig. 13 Load against
displacement of jack for the
three shell tests
stiffnesses of the two shells, despite identical mix designs
being used. Based on this, the results of the material tests on
sprayed samples of Shell 2 are not expected to be represen-
tative of the actual sprayed conoids.
Results
MN1 and MN1M were tested 28 days after the spandrel was
cast while MN2M was tested 27 days after. The displacement
of the jack is plotted against the load applied for all three tests
in Fig. 13. The displacement is set at zero for when the load
starts to be applied (i.e., when the jack starts to touch the
loading plate on the shells).
MN1 and MN1M
The MN1 and MN1M tests both exhibit very similar
responses; an initial linear response is observed with a soft-
ening and further ductile behaviour. This was accompanied
by cracking near the load plate at the spandrel early in the
loading, which demonstrates hinge formation. A maximum
load of 1.40 kN and 1.37 kN was measured for MN1 and
MN1M respectively. This is equivalent to merely 35% of the
self-weight of the shells. No visible signs of damage and
cracks were observed in the conoid segments throughout the
test.
For both MN1 and MN1M, it was observed that a large
slip between segments caused a drop in the applied load of
the jack. This is to be expected for MN1 as the fine sand
used as fill had minimal shear strength; as the load increases
and the stresses transferred across the interface increase, the
interfaces will slip. However, this does not cause collapse
as the shear keys prevent further slips from occurring. For
MN1M, the low strength of the mortar will act similarly to
the fine sand used which also has minimal shear strength.
Both tests exhibit similar stiffnesses and final collapse loads.
This suggests that the fill material (sand or mortar) does not
have a significant impact on the structural behaviour of the
shell.
During the assembly stage and testing of both MN1 and
MN1M, the ties experienced significant bending and the cor-
ner supports exhibited large rotations, shown for MN1M in
Fig. 14. This is a direct consequence of the corner supports
being too light as well as the fact that the thrust of the shell
Fig. 14 Visible support rotation and tie bending accompanied by a visible collapse of the arch (left) and cracking of the spandrel underneath the
load plate (right) observed during the MN1M test
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8 Page 16 of 26 Architecture, Structures and Construction (2025) 5:8
Fig. 15 Lifting of spandrel from conoid segments due to tilting (left) and cracking of the spandrel underneath (right) observed during the MN2M
test
is not perfectly aligned with the resultant forces of the ties.
This affected the behaviour of the shells during the test in
two ways: 1) the corner supports allow for greater displace-
ments of the corner segments due to the additional rotation,
resulting in a less stiff response compared to a structure with
non-rotating supports and 2) the failure of the shell is pri-
marily caused by the corner elements slowly slipping on the
rotated corner supports, spreading the shell and inhibiting
arch action. In addition to this, the tie strains measured from
strain gauges applied on one side of the ties included bend-
ing and did not properly reflect the average axial strain of the
ties. For the next test (MN2M), larger corner supports were
fabricated to minimise the rotation and lifting of the corner
supports. Moreover, an additional strain gauge was added to
each tie opposite the original strain gauge in order to allow
the calculation of the average axial strain in the tie.
After the peak of the tests has been reached, the shell
exhibits ductile behaviour. Visually, it can be seen that most
of the arches within the shell have collapsed (i.e., significant
deformations are present and interfaces between segments
showed visible hinging rotations). However, the shell is able
to resist further jack displacement as each of the segments is
still able to rest on each other, allowing the collapsed indi-
vidual arches to remain intact as a full shell.
MN2M
For MN2M, a significantly higher collapse load of 9.17 kN
was measured, equivalent to 231% of the self-weight of the
shell. From Fig. 13, the shell can be seen to exhibit an almost
linear response past the initial slipping phase, with a softening
response caused by cracking of the spandrel at 4.5 kN. The
shell then exhibits some non-linear response in the form of
softening and a decrease in load. No visible cracks or damage
were observed up until 4.5 kN, where a small crack running
across the spandrel was observed (shown in Fig. 15). Notably,
the crack that was found directly under the load plate in MN1
and MN1M at low loads was not observed in MN2M. Similar
to MN1 and MN1M, ductile behaviour can be observed past
the peak load. It is at this ductile phase that large cracks start
to appear in the bottom surface of the spandrel: a new one
under the loading plate and an enlarging of the crack running
from the spandrel corner with the load plate to the opposite
corner, shown in Fig. 15.
The tie forces and the displacements of the LVDTs placed
at the corners of the spandrels 200 mm away from the edges
are shown in Fig. 16 alongside results from FE analysis
(which is discussed in Section “Structural numerical analy-
sis”). Similar to the load-displacement behaviour of the jack,
the tie forces and LVDT displacements increase almost lin-
early with the load. Once peaked, the tie forces for all the ties
start to decrease until they fall to zero, which correlates with
the overall decrease in load applied by the jack. The LVDT
displacements display the tilting behaviour of the spandrel;
while displacement tracked near the edge closest to the load-
ing plate continues to increase slowly, the other corners of the
spandrel start to lift upwards. This suggests that the spandrel
is not being supported by all segments any longer, but rather
Fig. 16 LVDT displacements
(left) and tie forces (right) for
MN2M from test and FE
analysis
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Architecture, Structures and Construction (2025) 5:8 Page 17 of 26 8
that it is being supported at set points and pivoting around
them.
Structural numerical analysis
Nonlinear finite element analysis (NLFEA) of the scale pro-
totypes was carried out using LS-DYNA. The modelling
approach is detailed in [32] and utilizes contact surfaces to
allow stresses to transfer between discrete segment parts.
Solid tetrahedral elements were used which were meshed
from the 3D scanned geometry obtained after assembly (B).
A mesh sensitivity analysis demonstrated that an equivalent
element size of 15 mm was adequate for convergence. The
Continuous Surface Cap Model (CSCM) was used to model
the concrete material, with the stiffness and compressive
concrete strengths adjusted to match those obtained from
material tests. The tensile strength of the CSCM material is
lower compared to that observed in the sprayed GFRC due to
the lack of fibre reinforcement (approximately 4 times lower
compared to test values). However, this was left as is to avoid
further parameter tuning of the complex material model and
since minimal tensile stresses are observed in the FE analysis
within the conoid segments, suggesting that additional ten-
sile capacity will not affect the behaviour of the shell under
this highly asymmetric loading meant to induce instability.
The cracks that were observed were limited to the spandrel
which is a typical unreinforced concrete mixture with low
tensile strength, matching the CSCM model well.
Loading was applied in two stages. First, a preloading
phase was performed which applies the self-weight of the
shell. This allows the contacts to appropriately engage and
also models the assembly stage of the shell: the structure sup-
ports its self-weight prior to the application of the localised
point load. After this preloading phase, a displacement-
controlled loading was applied at a variable maximum rate
starting at a low 0.01 mm per load step (as contact between
the loading plate and the shell is formed) and increasing to
1.00 mm per load step, with LS-DYNA allowed to adjust this
based on the rate of convergence of the previous load step.
The corner supports of the shell were treated as rigid
bodies due to their much higher stiffness compared to the
concrete shell. These corner supports were prevented from
rotating and moving vertically, only being allowed to move
along the plane of the floor. Tie elements were used to rep-
resent the M12 ties in the shell.
Results
MN1 and MN1M
The results of the FE analysis of MN1 and MN1M were
almost identical. This is as expected as the geometry and
thickness distributions of both shells are very similar, as
shown in Fig. 22. As such, only the FE analysis results of
MN1 are included here for brevity. Comparison of the tie
strains was also excluded as the measured tie strains are
affected by the bending strains observed in the ties while
the FE model employed tie elements which only resist axial
forces.
The load applied by the jack was plotted against the jack
displacement from the experimental results alongside results
from both MN1 and MN1M in Fig. 17. As can be seen, the two
tests exhibit a much less stiff response and also a much lower
maximum load capacity compared to the 10.5 kN obtained
from the FE analysis. This is to be expected due to the rotation
of the corner supports resulting in a lower stiffness as the shell
is allowed to spread without fully engaging the axial stiffness
of the ties.
To investigate this further, the model was modified to
allow rotation in the corner supports by capturing the contact
between them and the flat ground. The ties were also changed
from tie elements to beam elements, with one end fixed to
the support to allow moment transfer while the other side
was left pinned. These end conditions mimic the end condi-
tions of the ties in the experiment as one side was threaded
Fig. 17 Load displacement curves of load jack from FE analysis plotted alongside experimental results for MN1 and MN1M (left) and MN2M
(right)
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8 Page 18 of 26 Architecture, Structures and Construction (2025) 5:8
through the corner supports while the other was attached by a
single bolt. The FE analysis of MN1 performed with support
rotations included predicts failure at the self-weight preload-
ing phase, with difficulties in converging when only 57.4% of
the self-weight has been applied due to the precarious contact
between the corner supports and the corner conoid segments.
This demonstrates reliance of the structural capacity and sta-
bility on the support conditions; with MN1 and MN1M, the
rotating corner supports both reduce the stiffness and max-
imum load capacity of the shell. The rotation also creates
instabilities in the contact surfaces as the corner elements
now do not rest well on the supports, creating difficulties for
the FE analysis to converge.
MN2M
As previously stated, the material tests performed on the
test date of shell MN2M exhibited premature failure in the
compression tests due to localised spalling and delamination
which are specific only to the test panel. As such, the material
properties will not be representative of the actual stiffnesses
of the conoid segments in the shell. In order to accommodate
for this, two different FE models were created based on 1) the
material properties taken from the material tests and 2) nom-
inal 28-day material properties of the sprayed GFRC [13].
The load applied by the jack was plotted against the jack
displacement from the experimental results alongside the two
FE models in Fig. 17. As can be seen, the stiffness observed
in the linear portion of the experimental test is quite closely
matched by the stiffness of both FE analyses, with a per-
centage difference of 31.1% and 39.2% for the models with
material tests properties and the nominal 28-day material
properties respectively. The increased conoid segment stiff-
ness used in the 28-day FE model shows a significant increase
in the collapse load of 10.4 kN compared to 5.65 kN, which
translates to a percentage difference of 12.6% and 47.5%.
As the failure mechanism in the FE analysis is through an
instability similar to buckling, it was expected that a higher
material stiffness would result in a higher collapse load. Past
the load peak, the implicit analysis scheme used has difficul-
ties converging and finding a suitable equilibrium solution.
In the actual physical test, this instability will result in a read-
justment of the load paths and a slow ductile failure (an effect
of the displacement-controlled loading used).
The tie forces and the vertical displacements of the nodes
in the first FE model are plotted alongside experimental mea-
surements in Fig. 16. The increases are mostly linear, and the
gradients agree well with those measured. For the tie forces,
the starting forces applied by the ties in the experiment do
not match the forces in the FE model which resists the thrust
from gravitational loads. This is due to the manner in which
the ties were tightened in the structure; the ties are slowly
increased until the shell lifts slightly off of the supports. As
the shell starts to settle initially, the initial tie forces will
vary and may not exactly match those observed from the FE
model.
Discussion
Due to the aforementioned difficulties with manufacturing
tolerances at the interfaces and the rotating support condi-
tions of one of the shells, it is difficult to assess whether the
FE analysis methods described in [32] can be used to prop-
erly capture the behaviour of the segmented fan concrete
shell prototypes. However, these uncertainties present barri-
ers and difficulties for any analysis methods, and as such are
challenging to assess regardless of the methods used. Further
testing of prototypes will be required in order to improve the
test data and limit the number of variables that affect the
structural performance of the shell.
Regardless, some trends can be extrapolated from the FE
analysis, especially for MN2M where the issue of rotating
supports is not present. The collapse load is shown to be
sensitive to the stiffness of the conoids themselves, with the
model using the more realistic 28-day properties providing
a closer match compared to the model using material prop-
erties obtained from material tests which failed prematurely.
The ductile post-peak behaviour of the shell is difficult to
capture using the implicit analysis scheme utilised for the
FE analysis. If it is desired to model this, an explicit anal-
ysis scheme may be utilised, although this requires further
investigation and validation.
The FE analysis of the MN1 and MN1M demonstrated the
potential capacity of these shells when no support rotations
are allowed. The rotating supports in the experiment signif-
icantly reduce the structural capacity of the structure due to
increased spreading. Attempts to model this behaviour in the
FE analysis resulted in models that were not stable enough
to support their own self-weight. In real life, this instability
can result in a slip which results in the structure resettling
into a stable configuration and being able to resist more load.
However, this is difficult to capture numerically in an FE
analysis. Regardless, the weak structural stability of MN1
and MN1M is well demonstrated by the low maximum loads
of the shells in the experiments compared to both MN2M
and the predicted FE analysis (under non-rotating supports).
Due to the rotating supports, not much can be concluded
regarding the effects of the segmentation on the structural
behaviour of the shells based on the tests. However, some
conclusions can be extrapolated from the nonlinear numer-
ical analysis. The load capacity between the models shows
similar collapse loads, although Shell 1 exhibits a less stiff
response. This is because the collapse mechanism under this
asymmetric loading does not rely on the formation of the
hinges at the additional interfaces present in Shell 1. Under
a different load case–the worst case being a direct point load
123
Architecture, Structures and Construction (2025) 5:8 Page 19 of 26 8
at the location of the interface–it is expected that the addi-
tional interface will result in a drastic drop in load capacity.
In addition, a higher number of interfaces will exacerbate
any tolerance and fabrication issues which is present–a fac-
tor which is difficult to account for numerically in the implicit
analysis scheme used [32]. As such, it can be concluded that
increased segmentation will affect the structural performance
negatively, although further investigation is required to quan-
tify the extent under various load cases.
Embodied carbon comparison
An embodied carbon comparison between the segmented
fan concrete shell flooring system compared to conventional
flooring systems is detailed herein. Firstly, it must be stated
that the embodied carbon of the shell drops drastically if the
segments are reused. With the lack of steel reinforcements
inside the segmented fan concrete shell minimising durabil-
ity concerns, the components can potentially be continuously
and indefinitely disassembled and reused. However, such
promises of potential reuse in the future are not assured (as
demonstrated from previous case studies [44]) and should
not be used as an argument to justify a significant embod-
ied carbon premium. Furthermore, it is acknowledged that
the following presents merely one facet of sustainability for
comparing various structural options. Assembly considera-
tions and labour effort, which adds to the overall energy, cost,
and embodied carbon, are outside of the scope of this com-
parison. Compared to conventional precast slab construction,
the segmented fan concrete shell is likely to perform worse
in this aspect. However, further work involving large-scale
assembly, prototyping, and refinement of the assembly pro-
cess is required to properly quantify the effects of this. As
such, this simplified analysis can be viewed as a means of
assessing the sustainability potential of a novel structural sys-
tem at the early stage of development and to evaluate whether
there is potential for further development and work.
The analysis was performed using a cradle-to-gate bound-
ary (equivalent to Modules A1 to A3 of the BS EN 15978
[45] life cycle stages). Four flooring systems were selected
to be compared: 1) a flat reinforced concrete slab, 2) a voided
hollow deck concrete system, 3) a thin-shell concrete flooring
system also fabricated using GFRC (the ACORN shell [12]),
and 4) the segmented fan concrete shell. Calculations were
performed based on a span of 8 m by 8 m using the same
ULS load combination used for form-finding purposes. It
should be noted that an 8 m by 8 m is not optimal for flat and
voided slabs to reduce their embodied carbon effects [46].
However, this span was used for comparison purposes with
the segmented fan concrete shell which has been designed
for this particular span. Conversely, the ACORN shell was
form-found against a 4.5 m by 4.5 m span distance. However,
this was not modified as it would require redoing the original
form-finding process of the ACORN shell [12]. Furthermore,
the false flooring has not been included in the embodied car-
bon comparison. This is a requirement to create a flat surface
for the shells, but is only optionally employed in conven-
tional slab construction depending on building usage and
other requirements. For this simplified analysis, it is assumed
that all options will utilise false flooring as it is a relatively
common system employed in office-type spaces to contain
services.
The material of the concrete (for the flat slab, voided
slab, as well as the flat spandrel) is taken to be C30/37 class
concrete with 35% cement replacement. Conventional steel
reinforcement is taken to have a yield stress of 500 MPa.
Design of the flat slab was carried out as per Eurocode 2
and the voided hollow deck system was designed as per
a manufacturer’s recommendations [47]. The high-density
polyethylene (HDPE) bubbles used to form the voids were
assumed to have a uniform thickness of 5 mm. Raised floor-
ing is excluded from the calculations as it is assumed that
all the flooring systems considered will employ it in order
to accommodate services. Embodied carbon impacts of the
various materials are listed in Table 6and the total mass and
embodied carbon of each flooring system is shown in Fig. 18.
The mass and embodied carbon impacts of the ACORN shell
were taken directly from [12].
From the analysis of embodied carbon of the four floor-
ing systems, it can be seen that the two shells have the
least embodied carbon per floor area, with the ACORN
shell and the segmented fan concrete shell having a reduc-
tion of 27% and 13% compared to the flat slab alternative
respectively. These savings are quite modest compared to
the mass reduction, having only 15.9% and 28.5% of the
mass of the reference flat slab design. The cause of this
difference is rooted in the high embodied carbon of the
sprayed GFRC mix, mainly due to its high cement content
and lack of larger aggregates. Further work to tune the mix
to improve its sustainability (e.g., using cement alternatives
or reducing the cement content) will allow for a signifi-
cant reduction in the embodied carbon of the shell. Despite
this, the analysis demonstrates that funicular flooring systems
are a lightweight and sustainable alternative to conventional
flooring systems.
Comparing the ACORN shell and the segmented fan con-
crete shell, the ACORN shell is shown to be both lighter and
to have less embodied carbon. This is to be expected as the
ACORN shell is not designed for reconfigurability (although
it is compatible with disassembly and reuse [12]). The con-
strained form-finding and design approach of the segmented
fan concrete shell produces a mass premium of 79% and an
increase in embodied carbon of 19%. The smaller difference
in the embodied carbon density is due to the use of the lower
embodied carbon density of the concrete mix of the flat span-
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8 Page 20 of 26 Architecture, Structures and Construction (2025) 5:8
Table 6 Embodied carbon
factors of materials Material1Embodied carbon factor Source
[kgCO2e/kg]
Standard
C30/37 with 35% cement replacement 0.103 [48]
Reinforcement bars/steel ties 0.76 [49]
Plywood formwork 0.681 [50]
Voi d e d s l ab
HDPE 1.93 [51]
Segmented fan concrete shell
Individual GFRC components
Cement 0.832 [50]
Sand 0.00747 [50]
Polycure FT (curing agent)21.67 [50]
Flowaid FT (super plasticiser) 1.88 [50]
Pumpaid FT (thixotropic pumping aid)21.67 [50]
Alkali resistant glass fibre 3.00 [52]
Combined GFRC mix 0.626
1Materials coloured to match those used in Fig. 18
2Taken from the average factor of concrete admixtures
drel compared to the ACORN shell which is made entirely
from sprayed GFRC.
Regardless, the disassembly, reuse, and reconfiguration
potential of the segmented fan concrete shell (demonstrated
through the assembly and disassembly of Shell 1) combined
with its savings in embodied carbon presents an improvement
over the conventional flooring systems analysed. Beyond the
flooring system itself, the low mass results in far lower loads
on the columns and footing, allowing material and embodied
carbon savings elsewhere within the superstructure and sub-
structure of the building. This highlights another advantage
of a lighter funicular flooring system outside its disassembly
and reuse potential.
When considering reuse and circularity (i.e., Module D of
the BS EN 15978 [45] life cycle stages), the potential for fur-
ther reduction drastically increases, potentially offsetting the
majority of the Module A embodied carbon depending on the
amount of segments reused, with 72% of it initially coming
from reclaimed concrete floor modules. However, promises
of future reuse should not be relied upon to justify a higher
embodied carbon cost as they may not be realised [44] and
are dependent on factors outside of the designer’s control
at the end of the building’s lifespan (e.g., social acceptance,
state of economics, political climate, etc.). The segmented fan
concrete shell however facilitates this reuse option without
requiring it to make it a sustainable option, making it a flex-
ible and sustainable flooring system, with potential to reuse
all or part of the structural components if designed durably.
If a more sustainable mix is utilised to fabricate the conoid
segments (take the C30/37 concrete as a reference), the
embodied carbon density of the segmented fan concrete shell
drops drastically from 86.4 kgCO2e/m2to 19.4 kgCO2e/m2,
a 78% reduction. However, the GFRC material presents
advantages for fabrication purposes (as it is a necessary
Fig. 18 Comparison of mass
and embodied carbon of various
flooring systems with ACORN
data taken from [12]
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Architecture, Structures and Construction (2025) 5:8 Page 21 of 26 8
component of the robotically sprayed fabrication process to
produce variable thickness thin-shell concrete [13,38]) and
the inclusion of glass fibres helps to increase the durability
of the components, especially for transportation, storage, and
assembly purposes. Regardless, this demonstrates the bene-
fits of the form independent of the material and shows that
there is space for further sustainability improvements in the
design.
Conclusions and future work
The proposed segmented fan concrete shell contributes to the
search for a materially and carbon-efficient flooring system
that is compatible with disassembly, reuse, and reconfigu-
ration. Scale prototypes of the form-found geometry were
fabricated and tested in order to evaluate the structural per-
formance of the system and identify any limitations and
deficiencies of the proposed system. The work herein adds
to the growing literature of thin shell flooring systems as a
sustainable alternative and contributes experimental test data
that can be built upon.
Compared to the ACORN shell (another form-found thin-
shell concrete flooring system), the added constraint of
designing for reconfiguration adds a mass and embodied
carbon premium to the segmented fan concrete shell floor-
ing system. However, the system remains a more carbon and
material-efficient alternative to flooring systems where bend-
ing dominates, and the choice to design for reconfiguration
merely adds a 19% embodied carbon premium over a compa-
rable segmented shell flooring system. Whether the ability to
easily reconfigure the flooring system for future reuse cases
is worth this premium should be decided upon by the client,
designer, and/or construction parties weighing in other fac-
tors of the project.
The load tests highlight the sensitivity of the segmented
fan concrete shell system to support conditions as well as fab-
rication tolerances. In the first set of shell tests, the supports
experienced significant rotations which resulted in increased
spreading and a drop in the stiffness of the structure. In com-
parison, the larger corner supports of the second shell test
contributed to the drastically higher load capacity and stiff-
ness observed; factors which could not merely be attributed
to the differences in segmentation layout. Further testing and
prototyping are required to provide further validation of the
finite element analysis methodology utilised as well as to iso-
late fabrication and testing factors that affect the structural
performance of the shells.
Further work is required to investigate whether the cur-
rent dry joint interface with shear keys is the appropriate
interface type for shells. Mechanical fasteners may allow
for more reliable and predictable force transfer while also
being able to be disassembled. Unbonded post-tensioning
could also present another viable means of compressing the
segments together while being reversible. In addition, fur-
ther work is required to tune the embodied carbon of the
GFRC mix to better translate the material and mass sav-
ings into embodied carbon savings. Outside the structural
behaviour and sustainability factors, investigations into the
fire safety performance of the shell (because of fire-resistance
of glass fibres, and by protecting the steel ties), integration
of mechanical services (through standard raised floors), as
well as acoustics (by breaking the smooth geometry with
structural ribs or non-structural acoustic panels) are needed
in order to bring the system closer to implementation in
practice. The existence of historical precedence of shells as
flooring systems in buildings (e.g., Guastavino’s tile vaults,
etc.) suggests that these are more than likely solvable design
problems rather than barriers that will impede the proposed
system from practical viability. Lastly, constructability and
assembly considerations must be addressed. Compared to
conventional precast slab construction, the assembly pro-
cess of the segmented fan concrete shell is more involved,
leading to higher labour costs and energy usage. The use
of discrete props as opposed to a complex support structure
already presents an improvement over conventional masonry
construction, but falls short of the rapid erection rate of mod-
ern precast construction. This may potentially be solved by
manufacturing a standardised support structure which can be
reused throughout an entire building project, provided similar
spans and loading requirements. The use of a curved surface
onto which a false floor must be installed on also presents
added difficulty in the assembly process. The development of
a custom false floor system or integration of a flat top surface
onto the shell itself may help to address this. As such, the
problems present with funicular construction and its adop-
tion in industry practice (that being increased labour costs
compared to precast funicular construction) largely remains.
However, there are avenues and options which needs to be
further explored which may address these challenges. Never-
theless, the segmented fan concrete shell presents a potential
means of enabling a lightweight and carbon-efficient flooring
system that is compatible with component reuse and circular
economy principles.
Appendix A Form-finding analysis method
A novel custom joint interface modelling approach was
developed to explicitly capture the behaviour of the joints,
inspired by similar interface modelling approaches used for
rigid block analysis [53]. The behaviour of the joint is illus-
trated in Fig. 19 and is implemented in Grasshopper3D [25]
relying on Karamba3D [24] as the solver. The interfaces are
modelled using stiff beam elements connected at the extra-
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8 Page 22 of 26 Architecture, Structures and Construction (2025) 5:8
Fig. 19 Schematic of custom joint behaviour which allows opening and closing of hinges
dos and intrados locations by nodes. The choice to use stiff
beam elements is due to the lack of rigid beam elements in
Karamba3D. In the presence of tensile forces at the ends of
these beam connections, the joint is allowed to open, thereby
allowing hinges to form. If an open joint is detected to dis-
place such that the joint will close (i.e., the shells start to
penetrate each other), the joint is then closed by reconnect-
ing the beam connections. Using this approach, the joint is
able to hinge at either end, close when needed, and also fully
detach (if tension is registered at the beam connection at an
already hinged joint). This nonlinearity is dealt with using an
iterative and incremental analysis method based on the lin-
ear elastic analysis solver within Karamba3D. The loads are
incrementally applied and at each load stage, the hinge states
are modified until they are converged (i.e., no tensile forces
are transmitted across interface nodes and no penetrations
exist which suggests that the hinges should be closed). Unlike
a fully non-linear analysis, the initial geometry and stress
state are not modified at each load stage, merely the hinge
and interface states. In addition, slipping between segments
is not captured, only hinging and fully opening behaviour.
Nevertheless, the devised analysis method provides a bal-
ance between a fast and simple linear elastic analysis and a
fully non-linear analysis using contact surfaces which makes
it compatible with population-based optimization algorithms
and approaches (which was used as a form-finding strategy
in Section “Shell form-finding and optimisation”).
The modelling approach was validated by modelling a 5-
segment catenary arch with a cross-section of 100 mm by
100 mm spanning 5 m with a depth of 1 m. The material is
taken to be similar to conventional concrete with a density of
2400 kg/m3, a Young’s modulus of 30 GPa, and a Poisson
ratio of 0.15. A downward point load is applied on the cen-
troid of the second segment on the left until failure. While
this structure is essentially a 2D problem, it was modelled
in 3D with several shell elements spanning the out-of-place
direction’s length. This was because the analysis method
is targeted towards 3D structures and shells as opposed to
arches. The geometry and loading of this arch are shown in
Fig. 20.
Fig. 20 5-segment catenary arch used to validate the custom joint model
123
Architecture, Structures and Construction (2025) 5:8 Page 23 of 26 8
The results of the analysis are shown in Fig. 21 (blue)
alongside results from a nonlinear finite element analysis
(NLFEA) using contact surfaces (red) [32] and the collapse
load obtained from thrust line analysis (black). It can be
seen that the custom joint model provides a collapse load
in between the values obtained from NLFEA and the thrust
line collapse analysis. This is reasonable as the NLFEA is
able to account for the geometrical non-linearities that arise
as the load increases, leading to a lower stiffness as the load
increases and an overall lower collapse load. Conversely,
the thrust line analysis assumes completely rigid segments.
In this case, where the segments are quite large and slen-
der relative to conventional masonry bricks or voussoirs,
this assumption results in an overestimation of the collapse
load. The custom joints used in the Karamba3D analysis
provide a balance between these two analysis methods by
allowing hinges to form and, as such, capture some of the
non-linearities of the structure without having to perform a
fully non-linear analysis.
Looking at the buckling load factor as the load is increased
shows that the analysis method is also capable of predicting
the loads and location at which hinges will form; once a hinge
forms, the buckling load factor drops significantly. Capturing
the drop in buckling load factor from the presence of hinges
presents another advantage of the modelling approach com-
pared to a fully connected linear elastic analysis which would
yield unconservative results for a segmented structure.
Appendix B 3D scans
3D scans were taken of the shell each time it was fully assem-
bled. Using this data, the thickness distribution of the shell
can be obtained and compared to the designed geometry’s
intended thicknesses. The results of this are shown in Fig. 22.
As MN1 and MN1M were constructed from the same set of
conoid segments, the thickness distribution is almost indistin-
guishable. Overall, the thicknesses of the conoids are greater
than intended. This is a common trend for segments sprayed
using the ARCS fabrication method [13]. The thickness of
the first conoid sprayed for MN1 and MN1M located in the
bottom left can also be seen as higher compared to the rest of
the conoids as they were fabricated prior to the 75% thickness
correction factor being applied. The deviations compared to
the intended thickness (normalised by the maximum thick-
ness of 50 mm) are also shown in Fig. 22. Visible here is the
characteristic grid caused by the sagging of the fabric form-
work on the actuated pin-bed’s grid of carbon fibre strips.
The variations in thickness between the different conoids of
a shell (despite having the same robotic spray path trajec-
Fig. 21 Comparison between results obtained from the custom joint model, an NLFEA, and thrust line collapse for the 5-segment catenary arch
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8 Page 24 of 26 Architecture, Structures and Construction (2025) 5:8
Fig. 22 Thickness of designed shells compared to 3D scan data and the deviations from the designed thickness, normalised by the spandrel thickness
of 50 mm
tory) are due to the variations caused by the calibration of
the machine settings which are performed manually for each
separate spray session.
Acknowledgements The authors would like to acknowledge and
thank the contribution of NRFIS staff Ricardo Osuma-Perdomo, Phil
McLaren, Martin Touhey, and Pieter Desnerck who aided in the fabri-
cation of the prototypes.
Author Contributions Mishael Nuh: Conceptualization, Methodology,
Software, Validation, Investigation, Visualization, Writing - original
draft. Robin Oval: Writing - review & editing, Supervision. John Orr:
Writing - review & editing, Resources, Supervision.
Funding The work presented in this paper was part of the ACORN re
search project funded by UK Resea rch a nd Innovation (E P/S031316/1).
Additional funding was provided by the Cambridge Trust.
Data Availability Additional data related to this publication are avail-
able at the University of Cambridge data repository at the following
link doi.org/10.17863/CAM.96375.
Declarations
Conflicts of Interest On behalf of all authors, the corresponding author
states that there is no conflict of interest.
Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing, adap-
tation, distribution and reproduction in any medium or format, as
long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons licence, and indi-
cate if changes were made. The images or other third party material
in this article are included in the article’s Creative Commons licence,
unless indicated otherwise in a credit line to the material. If material
is not included in the article’s Creative Commons licence and your
intended use is not permitted by statutory regulation or exceeds the
permitted use, you will need to obtain permission directly from the copy-
right holder. To view a copy of this licence, visit http://creativecomm
ons.org/licenses/by/4.0/.
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