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DIGITAL DESIGN AND FABRICATION OF A 3D CONCRETE PRINTED
FUNICULAR SPATIAL STRUCTURE
HAO WU1, ZIYAN LI2, XINJIE ZHOU3, XINYU WU4, DINGWEN
BAO5 and PHILIP F. YUAN6
1,3,6College of Architecture and Urban Planning, Tongji University
2,4,5School of Architecture and Urban Design, RMIT University
12032186@tongji.edu.cn, 0000-0002-0503-1696
2S3764754@student.rmit.edu.au, 0000-0002-2027-9227
3xinjie_zhou@tongji.edu.cn, 0000-0002-2543-2307
4S3701802@student.rmit.edu.au, 0000-0002-0616-6787
5nic.bao@rmit.edu.au, 0000-0003-1395-8747
6philipyuan007@tongji.edu.cn, 0000-0002-2871-377X
Abstract. In recent years, additive manufacturing (AM) and 3D
concrete printing technologies have been increasingly used in the field
of construction engineering. Several 3D concrete printing bridges were
built with post-tensioning technology. However, the current post-
tensioned 3D concrete printing projects are mostly in a single direction
of force. There are fewer cases of concrete printing funicular spatial
structures, and most funicular spatial structures are currently
manufactured by casting-in-place in formwork. This paper presents a
case of manufacturing spatial 3D concrete printed structure using post-
tensioned technology with multiple force direction. The design of the
non-parallel printing path, the joints between single units, and the post-
tensioned steel cable system in the design and research process are
discussed. A funicular spatial structure is built, and a method of
manufacturing 3DCP funicular spatial structure is proposed.
Keywords. 3D concrete printing; Robotic fabrication; Prestressed
concrete; Funicular spatial structure; Structural optimization; SDG 9;
SDG 11; SDG 13.
1. Introduction
In the last decade, 3D concrete printing has demonstrated its potential to change the
traditional construction way by printing concrete walls without conventional
formworks (Le et al., 2012), which creates new possibilities in both architectural design
and environmental protection. The application strategies for 3D concrete printing in
building construction can be generally divided into on-site printing (Scott, 2020)
(Mechtcherine, 2019) and prefabricated assembly. For prefabricated assembly 3DCP
project, post-tensioned technology is widely applied to make separated printed units
become a whole. The past five years have seen the completion of several post-
tensioned 3D concrete printing bridge projects (Vantyghem et al., 2020) (Salet et al.,
POST-CARBON, Proceedings of the 27th International Conference of the Association for Computer-
Aided Architectural Design Research in Asia (CAADRIA) 2022 , Volume 2, 71-80. © 2022 and published
by the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong.
H. WU ET AL.
2018) (Zhan et al., 2021). However, these projects are tensioned in a single direction,
which is why all are beam-like structures, namely bridges.
Typically, elements printed in concrete are achieved by extruding wet paste-
material in layers which eventually build up the desired shape, which is first described
as Contour Crafting in 2004 (Khoshnevis et al., 2004) and has been popular still now.
However, the CC technology is limited to vertical extrusion, hence yielding 2.5D
topologies (vertical extension of a planar shape) (Gosselin et al., 2016). Concrete units
printed in this way are best stressed in the vertical direction, which is why many 3D
printed structures are tensioned in one direction.
From the research of Gosselin, the method of non-parallel printing is described,
which makes it possible to realize multi-angle printing (Gosselin et al., 2016). The
arched masonry structure from BRG et al. (2021) fully demonstrates the advantages of
this printing method in building funicular spatial structure. Separated units are printed
in layers orthogonal to the main structural forces and they compress each other to form
a compression-only funicular structure. In this arched masonry structure, there are no
joints connecting the separate units, yet joint design is important in post-tensioned
spatial structures.
The research project described in this paper is committed to exploring how to
achieve post-tensioned 3DCP funicular spatial structure. Macroscopically, post-
tensioning technology has been applied to achieve the efficiency and rationality of the
structure. At the micro-level, non-parallel printing technology is applied to realize the
printing of all separated units. A set of steel plate system for positioning and a set of
post-tensioned pre-stressed steel bar system were applied. Finally, an experimental
funicular spatial structure with a range of about 6m*6m*3m was built. The project
discussed the rationality of the structural design of large-scale concrete printing
funicular spatial structure and how to use these techniques to achieve the complexity
of the printing structure.
2. Research and Prototyping
2.1. PROTOTYING DESIGN
In order to verify the feasibility of prestressed 3D concrete printed spatial structure and
to discover potential problems during installation, a simple small-scale experimental
prototype was designed, and the printing and installation tests were carried out.
Figure 1. The development of the prototyping design
This simple funicular spatial structure is designed using PolyFrame (Masoud et al.
2019), a Grasshopper plugin based on 3D graphic statics. This plug-in is good at
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DIGITAL DESIGN AND FABRICATION OF A 3D
CONCRETE PRINTED FUNICULAR SPATIAL
STRUCTURE
constructing purely compressed space structures. While in this prototype, prestressed
steel bars can be used to simulate this compressed state. It is designed into a uniform
structure composed of four identical units and four curved steel bars. The four concrete
members are compressed tightly together to form a stable structure that presses and
restrains each other. Figure 1 shows the development of the prototyping design.
2.2. PRINTING AND ASSEMBLY TEST
The segmented units are geometries with multiple direction, which means that they are
non-developable curved surface. In Lim et al.’s (2020) work, a method of printing a
non-developable curved surface is described (Lim et al., 2020). Compared to traditional
method, it required temporary fabric formwork supported by height-adjustable rods.
Lim has proposed in his theory within this technology, which is to print with saddle
and dome surface on the temporary fabric formwork. The limitation of this kind of
method is that a specific height-adjustable system is required, and each piece of printing
will consume one piece of fabric. In addition, the temporary fabric formwork has
relatively low accuracy and hard to control, which will increase the printing error and
may eventually lead to the failure of the entire structure when assembly.
In prototype design, a method of printing the base with concrete material is
proposed. As shown in Figure 2, a triangular base was designed according to the shape
of the printed segment in this experiment. This base has three inclined surfaces that
need to be printed with a specific printing path. After base printing, a piece of plastic
flim was in use to separate the unit from the base that it attaches to. With this technique,
four identical structural segments are printed.
Figure 2. Left: printing process, Mid: toolpath, Right: steel bar system
2.3. PROBLEM
Although the printed base can ensure that the inclinations of the three slope surfaces of
each unit are accurate. However, from a micro perspective, as it's shown in Figure 3,
the inclined surface of the printed base is stepped. The bottom of the final printed object
cannot fit this inclined curved surface completely, which makes the connecting surface
of the prints uneven.
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H. WU ET AL.
Figure 3 shows that because the nozzle has an unchangeable size, the printing
height of the first layer needs to be raised to prevent the print head from rubbing against
the inclined surface of the base. Therefore, the first layer of the printed component is
obviously wider, and the layer height is also different from others.
Figure 3. A micro view of the filament
Due to the superposition of the previous two reasons, the stability and accuracy of
the entire prototype structure were declined from expectation. When the printed
components were assembled, the connecting surface could not be fully attached. This
leads to insufficient assembly accuracy of the printed parts and affects structural
stability. Figure 4 describes the printing process and the assembly process.
Figure 4. Record of printing and assembly process
3. Computation design
3.1. MULTI-TOOL COLLABORATIVE DESIGN
The design result is attributed to the collaboration of two software, Polyframe, which
generates a purely compressed frame, and Ameba (Xie et al. 2016), which calculates
the volume through topological optimisation. With the help of PolyFrame, a system of
purely compressed funicular spatial structure is created upon the basis of 3D graphical
statics. Then optimization based on Ameba was introduced into the design. Some
members were set as non-designed regions under the same boundary conditions, and
then the Ameba algorithm was used, followed by 90 iterations. Figure 5 shows the
development of the design process. As a result, an efficient spatial structural system
based on mesh optimization was obtained, which predicts the basic material
distribution of the final pavilion shape and improves the feasibility of concrete 3D
printing.
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DIGITAL DESIGN AND FABRICATION OF A 3D
CONCRETE PRINTED FUNICULAR SPATIAL
STRUCTURE
Figure 5. Iterations in Ameba
3.2. SEGAMENTATION
The final structure design needs to be divided into small pieces for printing. The
direction of the force, the maximum printing height, and the maximum printable
inclination are 3 main factors that need to be considered during the segmentation
process. Finally, the whole structure is divided into 18 segments, each of which is less
than 1500mm in height. To meet the requirements of reliable printing, every segment
has at least one horizontal surface, with a maximum inclination angle no more than 45
degrees. Each column and beam are divided into two and three segments respectively.
The remaining three outward heads each become an independent piece. Each segment
is attached with one or two steel plates, which are used for positioning in assembly
process. The division of the segments, the position and the serial number of steel plates
are shown in Figure 6.
Figure 6. Segmentation
3.3. PRESTRESSED STEEL BAR
To simulate the calculation results of PolyFrame, 9 steel bars were added to this
system. Three of them are connected to the column foundation from the overhanging
ends and each beam has two steel bars. All steel bars are pre-stressed by post-
tensioning.
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H. WU ET AL.
Figure 7. Nine steel bars
3.4. POSITIONING STEEL PLATE
This funicular structure is post-tensioned in multiple force direction, which create
another difficulty in accurate positioning. The joints between single units need to be
specially designed. 3D printing concrete ink usually has good fluidity during
movement and satisfying standing behavior at static state (Zhang et al. 2018). The
printing filament is in a wet-state and maintains a certain degree of plasticity for a
certain period of time after extrusion. Exploit this property of 3DCP filaments, some
scholars have demonstrated the feasibility of implanting micro cable during filaments
deposition process (Ma et al. 2019) (Li et al. 2020). In this study, a method of
implanting steel plates as positioning joints between the units during the printing
process was employed.
Each segment has at least one steel plate, the segment in the middle of the beam has
two steel plates. The printing of a single unit is paused during the printing process and
the steel plates are then manually placed. After inserting steel plate, the printing process
is continued. The concrete and the steel plates will become a whole when concrete gain
strength.
The thickness of the steel plate processed by CNC milling machine is 4mm. There
are two kinds of holes with diameters of 20mm and 50mm on the steel plate. 20mm
holes are used for steel pipe welding during assembly. It plays the role of positioning
between segments. The 50mm hole is where the steel bar passes through. The edge of
the steel plate is designed to be zigzag, as shown in Figure 8, so that the steel plate and
the concrete printing filament can be combined more firmly. The jagged edges make
the filaments on both sides have a larger contact area. This is because, through the early
printing experiments, it was found that the steel plate with a smooth edge will cause
poor connection of the filaments separated by the steel plate. The printing segment
brokes easily at where the smooth steel plate was placed.
Figure 8. Steel plates with zigzag edges
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DIGITAL DESIGN AND FABRICATION OF A 3D
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STRUCTURE
4. Robotic fabrication
4.1. TRAJECTORY DESIGN
The final structure is a multi-directional pre-stressed structure. The segmented unit is a
multi-directional block, which cannot be printed by the traditional horizontal printing
path. As shown in Figure 9, three sets of non-parallel planes are used to cut the printed
units and then the intersected curves are connected to form the final path. Filaments are
printed in non-uniform and non-parallel layers. The printing layers are orthogonal to
the prestressed tensile direction so that the printing filaments within the structural unit
can be tightly compressed together.
Figure 9. Toolpath generation
4.2. PRINTING PROCESS
In the prototype experiment, the bottom of the printing segments was uneven which
will cause poor integrity when assembly. The accuracy of the connecting faces is not
only an important factor but also an essential guarantee for the structure stability.
To achieve good connectivity, the contact surface of each unit must be flat. Thus,
the printing strategy with the multi-directional side down in the experiment is
abandoned. Every unit is printed with one-direction side down to obtain a rational flat
surface connected with the base. This contact surface allows the unit to be stressed
evenly during the printing process to ensure stability of the final structure.
The printing process is described in Figure 10:
● Place the tray (for the convenience of subsequent transportation)
● Lay the plastic film
● Print the base and pause for a horizontal surface)
● Lay the plastic film (for the subsequent separation of the base and the unit)
● Print the first 4 layers of the unit and pause
● Manually place the steel plate
● Print the remaining part
● Manually place the 2nd steel plate (for units in the middle of the beam)
● Print the remaining part (for units in the middle of the beam)
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H. WU ET AL.
Figure 10. Printing process
4.3. ASSEMBLY
After all the printing work is completed, each unit has been cured for at least 14 days
to ensure that it has obtained sufficient early yield strength. The installation process is
as follows:
● What installed first is three pillars. The steel bars inside the three pillars are welded
to the foundation. Inside the three pillar legs, 300mm-thick mortar is poured to
connect the pillars with the embedded steel components.
● Install the second section of the column.
● The three beams are assembled on the ground respectively, and then the three beams
are hoisted up.
● The three overhanging units are put on last.
The connections between the units are installed with anti-collision strips with a
width of 30mm. The steel pipes are welded to the steel plate in the 20mm hole, and
then assembled with the other segment whose steel plate they go through to achieve
Figure 11. Record of the assembly process and final outcome
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DIGITAL DESIGN AND FABRICATION OF A 3D
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STRUCTURE
precise positioning between the units. Pre-stressed steel bars with a diameter of 15mm
pass through the 50mm hole in the steel plate and reach three overhang ends
respectively. At the end of each overhang end, 9 steel bars are tightened with nuts to
realize the post-tension of the entire structure.
5. Result and discussion
The final structure presents a relatively good surface quality. Although there are some
discordant seams in some connections, but the overall quality is within the acceptable
range of the architectural scale. The reasons for this may be:
● The error of non-parallel 3D printing is larger than that of traditional 3D printing.
● The deviation of the position of the pillars.
The method of placing the steel plate during the printing process needs to be
optimized. It is found that the filament where holds the steel plate will sightly bulge,
which declare that the method of embedding the steel plate in the concrete need further
investigation. Methods such as optimizing the zigzag design, reducing the size or
thickness of the steel plate deserve further exploration.
At present, the mainstream concrete 3d printing construction is divided into two
categories: on-site printing and prefabricated assembly. The on-site printing
technology is relatively mature and there is no segmentation problem. When it comes
to prefabricated assembly, however, there are more issues to be settled.
In general, the concrete printing segments are relatively heavy and fragile, which
leads to lots of difficulties in assembly period. In this project and the arched masonry
structure from BRG et al. (2021), although each unit was manufactured using template-
free 3D printing technology, a large amount of supports were used for positioning,
including wood scaffold, during the assembly process, which led to a significant
increase in both construction and environmental costs. Recent years, non-parallel
concrete printing becomes popular and further eliminates the limitations of complex
shapes. It is foreseeable that more large-scale 3DCP funicular spatial structures will
emerge in the near future, which will also mean more complex scaffolds are needed.
In this context, perhaps 3DCP technology needs to be re-evaluated, because the best
option for these complex scaffolds is wooden waffle scaffold.
Acknowledgements
This spatial structure is part of the result of RMIT master studio "Intelligent Force
Printing", studio leaders and all students of the studio have made great contributions to
this project.
Studio leaders: Philip F. YUAN (RMIT Visiting Professor), Dingwen ‘Nic’ Bao
(RMIT lecturer)
Teaching Assistants: Hao Wu, Xinjie Zhou, Xiang Wang
Students: Bowen Li, Da Wang, Guowei Xia, Jingyi Liu, Ruoxing Wang, Wenjie
Gai, Xinyu Wu, Yuhan Bao, Zengwei Wang, Zhangxizhi Wang, Zhengqian Peng,
Zhuohua Tan, Ziyan Li, Ziyu Zhou (Sorted by initial letter)
This research was supported by National Key R&D Program of China (Grant
79
H. WU ET AL.
No.2018YFB1306903), National Natural Science Foundation of China (Grant No.
U1913603), and Shanghai Science and Technology Committee (Grant No.
21DZ1204501).
References
Block Research Group (BRG), Zaha Hadid Architects Computation and Design Group
(ZHACODE), Incremental3D (in3D), Striatus - 3D concrete printed masonry bridge,
Venice, Italy, 2021. from https://block.arch.ethz.ch/brg/project/striatus-3d-concrete-
printed-masonry-bridge-venice-italy-2021
Gosselin, C., Duballet, R., Roux, P., Gaudillière, N., Dirrenberger, J., & Morel, P. (2016).
Large-scale 3D printing of ultra-high performance concrete–a new processing route for
architects and builders. Materials & Design, 100, 102-109.
https://doi.org/10.1016/j.matdes.2016.03.097
Khoshnevis, B. (2004). Automated construction by contour crafting—related robotics and
information technologies. Automation in construction, 13(1), 5-19.
https://doi.org/10.1016/j.autcon.2003.08.012
Le, T. T., Austin, S. A., Lim, S., Buswell, R. A., Gibb, A. G., & Thorpe, T. (2012). Mix
design and fresh properties for high-performance printing concrete. Materials and
structures, 45(8), 1221-1232. https://doi.org/10.1617/s11527-012-9828-z
Li, Z., Wang, L., Ma, G., Sanjayan, J., & Feng, D. (2020). Strength and ductility enhancement
of 3D printing structure reinforced by embedding continuous micro-cables. Construction
and Building Materials, 264, 120196. https://doi.org/10.1016/j.conbuildmat.2020.120196
Lim, J. H., Weng, Y., & Pham, Q. C. (2020). 3D printing of curved concrete surfaces using
Adaptable Membrane Formwork. Construction and Building Materials, 232, 117075.
https://doi.org/10.1016/j.conbuildmat.2019.117075
Ma, G., Li, Z., Wang, L., & Bai, G. (2019). Micro-cable reinforced geopolymer composite for
extrusion-based 3D printing. Materials Letters, 235, 144-147.
https://doi.org/10.1016/j.matlet.2018.09.159
Masoud Akbarzadeh. Andrei Nejur.(2019). Polyframe. From
https://psl.design.upenn.edu/polyframe/
Mechtcherine, V., Nerella, V. N., Will, F., Näther, M., Otto, J., & Krause, M. (2019). Large-
scale digital concrete construction–CONPrint3D concept for on-site, monolithic 3D-
printing. Automation in Construction, 107, 102933.
https://doi.org/10.1016/j.autcon.2019.102933
Salet, T. A., Ahmed, Z. Y., Bos, F. P., & Laagland, H. L. (2018). Design of a 3D printed
concrete bridge by testing. Virtual and Physical Prototyping, 13(3), 222-236.
https://doi.org/10.1080/17452759.2018.1476064
Scott, C. (2020, March 17). Chinese construction company 3D prints an entire two-story
house on-site in 45 days. from https://3dprint.com/138664/huashang-tengda-3d-print-
house/.
Vantyghem, G., De Corte, W., Shakour, E., & Amir, O. (2020). 3D printing of a post-
tensioned concrete girder designed by topology optimization. Automation in
Construction, 112, 103084. https://doi.org/10.1016/j.autcon.2020.103084
Xie, Y. M. (2016). Ameba. From https://ameba.xieym.com/
Zhan, Q., Zhou, X., & Yuan, P. F. (2021). Digital Design and Fabrication of a 3D Concrete
Printed Prestressed Bridge.
Zhang, Y., Zhang, Y., Liu, G., Yang, Y., Wu, M., & Pang, B. (2018). Fresh properties of a
novel 3D printing concrete ink. Construction and building materials, 174, 263-
271.https://doi.org/10.1016/j.conbuildmat.2018.04.115
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