Design and fabrication of optimised ribbed concrete floor slabs using large scale 3D printed formwork

This paper describes the design, fabrication, and testing process of an optimised, reinforced concrete ribbed floor slab fabricated using robotically 3D printed formwork. The design of the floor slab is based on the alignment of ribs along the trajectories of the principal bending moments. A workflow is described that generates a rib layout based on structural analysis, which is used to create a three-dimensional model of the slab. A full-scale prototype is fabricated by using an industrial robotic arm with a pellet extruder mounted as an end effector to 3D print the formwork. Reinforcement is inserted and the formwork is cast using self-compacting concrete. The successful design, fabrication, and structural testing of the full-scale floor slab prototype showed that the described workflow is suitable for realizing material-optimised, ribbed reinforced concrete floor slabs using 3D printed formwork.


Introduction
Concrete is an essential material in construction and is currently the most-used building material worldwide. Due to its extensive use, concrete also has an outsize effect on the environment, with around 8% of global CO 2 emissions resulting from the production of cement [1]. In buildings, a large amount of concrete is used in floor slabs, making up more than half of the structural mass of a multistory building [2]. Most often, concrete floor slabs are executed as flat slabs, not because of their structural efficiency but rather because of the efficiency of the planar formwork needed to cast them. In contrast, ribbed floor slabs with similar structural performance require less material due to more efficient material distribution.
The previous century has seen several examples of expressive, efficient, ribbed floor slab systems. In the 1950s, the engineer and contractor Pier Luigi Nervi built ribbed floor slabs such as the Gatti Wool Factory [3]. Nervi's ribbed floor slabs made use of his patented Ferrocement technique to produce the formwork necessary to create the ribs. This technique was economical at the time since timber and steel moulds were expensive, and low-cost labour to produce the Ferrocement moulds was readily available [4].
Another historical example of a ribbed concrete floor slab is the Zoology Lecture Hall at the University of Freiburg, designed by Hans Dieter Hecker. [5]. The floor slab, built in the 1960s, was constructed using custom-made timber formwork elements. Because of its efficient shape, the ribbed slab used less concrete when compared to a modernday hollow core slab, even though the structure was built 50 years ago. However, the costs for producing the formwork were also around four times higher when compared to modern-day standardized floor slabs [5].
Although the ribbed floor slab systems built by Nervi and Hecker are efficient in terms of material, they each required a high amount of manual labour to be constructed. As labour costs have risen and the building sector has moved towards industrial construction, these labourintensive processes are uneconomical to use in the present day. Digital fabrication with concrete could provide a solution, as it allows for the automation of labour-intensive processes. Therefore, recent advances in digital fabrication with concrete have sparked a resurgence of ribbed floor slab systems. Digital techniques for producing formwork and digital methods of depositing concrete offer opportunities for precise, automated manufacturing of ribbed floor slabs [6].
The Block Research Group at the ETH Zurich has used computer numerically controlled (CNC) cutting of expanded polystyrene (EPS) blocks to produce the formwork for a vaulted ribbed floor slab. The slab requires external ties or supports resisting the horizontal components of the vault. Several iterations of the slab system have been produced [7]. The first iteration of the vaulted floor system did not use conventional steel reinforcing bars but instead has steel micro fibres in the concrete [8]. This prototype was developed further into the HiLo slabs: two ribstiffened funicular floor slabs [7] that were built on-site as part of the EMPA NEST [9] building in Dübendorf, Switzerland. The HiLo slabs also use CNC-cut polyurethane foam to create the formwork for the ribs. Again, no conventional reinforcing bars were used, but instead, posttensioned tension ties were used as a method of external reinforcement, in addition to steel fibres in the concrete. Compared to a flat slab, the HiLo slabs are claimed to use 50% less concrete. Therefore, these floor slabs have the potential to reduce the Global Warming Potential (GWP) by a large amount. However, polyurethane is made from nonrenewable resources, making it in undesirable choice for sustainable construction, and additionally the fabrication process of the floor slab was complex due to the many manual steps involved. The Smart Slab, from Digital Building Technologies, ETH Zurich, is another project that demonstrates how digital fabrication can be used to fabricate highly complex concrete floor slabs [10]. This project, part of the DFAB HOUSE [11], also part of the EMPA NEST building, consists of eleven 7.1 meter long concrete slab elements that were joined using post-tensioning. The elements were prefabricated using a combination of formwork produced with binder jet 3D printing and CNC milling of timber. The 3D printed formworks were sprayed using glass fibre reinforced concrete, after which the ribs were cast with conventional concrete. By using binder jet 3D printing, a very high geometrical freedom can be achieved; however, it is a costly process, and the formwork elements need to be destroyed to make demoulding possible, resulting in high waste. Furthermore, the manual process of spraying concrete on complex formwork is time-consuming.
Researchers from the Graz University of Technology have used 3D concrete printing (3DCP) to produce stay-in-place formwork for a ribbed floor slab [12]. Forms defining the voids between the ribs were printed and then placed upside-down into a 8 × 3 m wooden formwork box, after which steel reinforcement was added, and the slab was cast with concrete. The resulting ribbed floor slab shows that 3DCP is a promising method for producing stay-in-place formwork. Still, it is difficult to use the presented approach to produce a slab with variable rib height (introducing curvature in the direction of the span) and thin ribs, which would be beneficial for material savings. Additionally, the issue of structural bonding of the stay-in-place formwork with the cast concrete is still largely unresolved.
TU Braunschweig uses shotcrete 3D printing (SC3DP) to print strengthening ribs onto a freshly cast straight slab [13]. This approach requires no formwork for the ribs, which is interesting from an economic and environmental perspective. However, achieving sufficient accuracy of the part, as well as achieving good surface quality, could be challenging.
Fused deposition modelling (FDM) 3D printing offers the potential to be used for the production of concrete formwork, providing geometrical freedom at a relatively low cost. The potential of this method has been explored by various institutions to produce different building elements. Previous studies that have been conducted include a concrete staircase [14], concrete columns [15,16], and a functionally integrated concrete floor slab [17]. A thorough review of projects that have used FDM 3D printed formwork is provided by Jipa and Dillenburger [18].

Scope of the study
This paper presents a novel approach for the digital design and fabrication of reinforced ribbed floor slabs by using robotic FDM 3D printed formwork, conventional reinforcement and conventional casting of concrete. In particular, this paper focuses on: (1) material and fabrication tests of the 3D printed formwork, (2) the computational design process of ribbed floor slabs, and (3) the fabrication process of ribbed floor slabs.
This section describes the scope of the study, the content, and how it builds up on previous research. Then, the design-to-fabrication workflow, used materials, and robotic setup are described (Section 3). Section 4 describes experiments that have been conducted to make the fabrication process possible. A series of experiments investigate strategies for 3D printing of the formwork (Section 4.1). Another set of experiments investigates the effect of hydrostatic pressure exerted by the freshly cast concrete onto the 3D printed formworks (Section 4.2). These experiments provide the basis for the full-scale prototype: a 2.7 × 2.7 m floor slab (Section 5). Section 6 contains the discussion and conclusion. Finally, Section 7 provides an outlook for this research.
The work presented in this paper builds upon previous research that has been conducted at the Chair of Architecture and Digital Fabrication at the ETH Zurich, more specifically, on the Eggshell fabrication process [19]. The Eggshell fabrication process combines robotic FDM 3D printing of a thin formwork with casting of a fast-hardening, set-ondemand concrete [20][21][22]. Previously, the Eggshell fabrication process has been used to produce columns [23,24], as well as beam elements [25] and has relied on hydration control to avoid bursting of the formwork due to hydrostatic pressure. Previous research has shown that it was possible to cast up to a height of 400 mm of concrete into a thin, 3D printed formwork without breaking the mould [24], as hydrostatic pressure exerted onto the formwork is limited. Therefore, when fabricating an element with a lower height, it might be possible to cast conventional concrete into 3D printed formworks without causing breakage. Thus, this research investigates the potential of using robotic FDM 3D printed formwork to fabricate optimised ribbed floor slabs cast with conventional concrete. Key considerations for the design and fabrication process were: (1) optimised structural design, (2) integration of conventional steel reinforcement, and (3) making use of a commercially available concrete mix for casting.
The entire floor slab is envisioned to be fabricated upside down (Fig. 1). The casting of the slab is thought to be in two parts: first the ribs and then the flat part of the slab. The fabrication process roughly consists of the following steps: (a) 3D Printing of formwork for the ribs, (b) inserting reinforcement into the rib formwork, (c) 3D printing a cap to close the rib formwork, (d) casting the ribs, (e) casting the solid part of the slab. A detailed description of the fabrication process is provided in Section 5.2.
For the 3D printing of the cap that closes the formwork, non-planar 3D printing is emloyed. Previous projects employing non-planar 3D printing have either printed curved layers on a curved base [26,27], or used height variation within individual layers to create curved layers on a planar base [28]. In contrast, in this study, the non-planar layers of the cap are printed on top of the planar printed formwork walls so that the formwork walls essentially acted as a inclined printing base. The potential advantage of using this approach is that complicated path planning (such as required for non-planar printing) is avoided for most of the print, as it is only required for the cap part, which represents just a small portion of the total print time.

Design to fabrication workflow
In Fig. 2, the workflow from the structural design of the slab to the design and fabrication of the formwork is outlined. First, an initial finite element analysis (FEA) considering linear elastic behaviour is performed in which the principal bending moments are calculated (a). The direction and magnitude of the bending moments are imported into the parametric modelling software Rhino Grasshopper [29,30] to allow for further manipulation. Then, lines are generated according to the direction of the principal moments (b) using the process described by Halpern et al. [3]. This process takes a starting node, obtains the maximum principal bending moment direction and draws a straight line with a specific length in the maximum principal bending moment direction. This process is repeated until a set boundary is crossed.
In the next step, the resulting lines can be used to generate a rib layout (c). A certain rib spacing, as well as rib width, can be specified. A three-dimensional model of the floor slab is generated using the rib layout (d). In this step, the height of the ribs, as well as of the slab, is set. The 3D model can then be used to perform another FE-analysis (e). A size optimisation using the evolutionary solver Galapagos [31] is performed, adjusting the width and height of the ribs with each step (f). Then, different rib layouts and rib sizes are compared, and the variant using the least amount of concrete is selected (g). A more elaborate explanation of this structural optimisation process is described by Huber et al. [32].
Once the geometry is fixed, the reinforcement can be designed (h), and a slab section is extracted for fabrication (i). Then, FE-analysis of the formwork deformations caused by the concrete casting is performed (j). This allows designing the stiffening ribs of the formwork to limit the deformations according to the allowed tolerances. Additional formwork detailing such as fixing features and stiffening ribs are added to the formwork model (k) based on the analysis of hydrostatic pressure. These steps are described in more detail in the design process of the full-scale prototype (Section 5.1). The geometry is sliced using COMPAS SLICER (l) [33], a slicing plugin within the COMPAS Python [34] framework [35]. In this step, the total printing time and the maximum overhang of the geometry can be obtained. These parameters are manually assessed by the user and if not deemed feasible (e.g. printing time is too long or maximum overhang too high), a new rib layout and 3D model can be generated. After the slicing result is approved, the robotic motion can be generated using COMPAS RRC [36] and the formwork is 3D printed (m). If the printed result is deemed successful, this completes the formwork  fabrication process. In case of an unsuccessful print, changes can be made to the geometry and the process is repeated (m -d).

3D Printing setup
The formwork fabrication setup ( Fig. 3) consists of an ABB IRB 4600-40 industrial robotic arm (e) with a maximum payload of 40 kg and a reach of 2.55 m. The robotic arm is mounted inverted to a threeaxis ceiling gantry system (d). For this project, two of the external axes were used, the Z and Y-axis.
The extruder used for 3D printing is an E25 Pellet Extruder from the company CEAD (c) with a maximum output of 12 kg/hr [37]. Unless stated otherwise, a nozzle diameter of 6 mm is used. For most experiments described in this paper, PLA NX2 from the company extrudr [38] is used as a printing material. The 3D printing material is dried at a temperature of 50 • C for at least 2 h before extrusion using a Vismec Dryplus hopper dryer (a) [39]. The printing platform (f) consists of medium-density fibreboard (MDF) plates mounted to a supporting frame of aluminium profiles.

Concrete
Two types of concrete were used throughout this study. Holcim 3708CL, a self-compacting concrete with a maximum aggregate size of 8 mm was used to cast the ribs (Fig. 1d) since a highly fluid concrete was required to fill the entire 3D printed formwork. Holcim A151EVO, a lowcarbon concrete with a maximum aggregate size of 16 mm was used to cast the solid part of the slab (Fig. 1e), as here, high fluidity was not required since the concrete could easily be compacted.

Formwork experiments
Various experiments had to be conducted to develop the fabrication process of the ribbed slab floors. First, different strategies for 3D printing of the formwork were investigated (Section 4.1). Then, the effect of hydrostatic pressure on the 3D printed formworks had to be studied (Section 4.2). These investigations were fundamental for the production of a full-scale prototype: a 2.7 × 2.7 m section of a floor slab (Section 5).

3D Printing
This section describes several experiments that were conducted to gain more knowledge on different aspects of the 3D printing process.

Material testing
The first experiments conducted aimed to compare different printing materials and evaluate their potential for large scale 3D printing of formwork. The main criterion that was evaluated was deformation due to shrinkage, as it was envisioned that this could become problematic with large prints. Typically, in FDM 3D printing, shrinkage can be controlled by using a heated chamber, but this was not a feasible option due to the large scale of the floor slab elements.
A rectangular geometry was designed with a length of 250 cm, a width of 13 cm and a height of 40 cm. The fabrication parameters were set to a nozzle size of 3 mm, layer height of 2 mm and a print speed of 70 mm/s. Three different materials were tested: polypropylene (PP), polyethylene terephthalate glycol (PET-G), and polylactic acid (PLA). The prints were fixed to the printing base by printing a fixing feature (Fig. 4, right) every 30 cm that can be screwed down to the board.
The prints using PP (Fig. 4a) and PET-G ( Fig. 4b) were not printed to the full 40 cm height due to premature failure of the print because of the deformation due to warping. Deformation was measured on the sides of the print with a ruler. The deformation was symmetrical, meaning the same deformation occurred on either side of the print.
The PP print showed warping deformation of 6 cm, and the PET-G print a deformation of 2 cm. Moreover, the fixing feature had either come loose from the wooden board or had broken due to the deformation while printing. The print using PLA (Fig. 4c) exhibited the lowest deformation: 1.3 cm. These results also correspond with the values for shrinkage given in the material specifications [38] (2% for PP, 0.5% for PET-G, and 0.3% for PLA). Since limiting deformation was the main material selection criterion, PLA was selected as the material of choice.

Cap printing
To enable fabrication of a rib with variable height (allowing the reduction of material by adapting the height according to variations in bending moments), it is necessary to create a closed, horizontal cap for the formwork. The cap will act as the formwork that shapes the ribs. To print the cap, the gap between the two formwork walls has to be bridged with the 3D printing filament. This series of experiments investigates several approaches for printing the cap part of the formwork.
First, the bridging capabilities of the 3D printing setup were tested by printing rectangular models with varying width (Fig. 5). The models were printed using PET-G, as these experiments were conducted before PLA had been selected as the preferred printing material. However, it is assumed that the printing material does not have a large influence on the bridging capabilities, as this is largely dependant on the tool path. The models consisted of four vertical walls and a flat or pitched cap with different patterns for the printing path. Sample CAP_A (Fig. 5a) and CAP_B (Fig. 5b) used a print path consisting of parallel print lines that span the shortest length of the geometry. CAP_A had a width of 20 mm, and CAP_B had a width of 40 mm. However, it can be seen that in both tests, the print lines forming the cap are sagging down and are not creating a flat, consistent cap. CAP_C (Fig. 5c) and CAP_D (Fig. 5d) show a different method of generating the tool path of the cap: using a spiral motion from outside to inside. The spiral motion showed excellent results with a width of 40 mm (CAP_C), resulting in a flat cap without sagging. However, when increasing the width to 80 mm (CAP_D), the print failed after printing six cap contours due to insufficient adhesion between the horizontal layers. Lastly, the possibility of bridging by creating a pitched cap was investigated. Using an overhang angle of 45 degrees and a spiral tool path, it was possible to achieve good printing quality for a width of 40 mm (CAP_E, Fig. 5e). In an attempt to limit the pitch of the cap, an overhang of 60 degrees was also tested for a rib width of 80 mm with successful results (CAP_F, Fig. 5f).
These tests showed that parallel print paths are ineffective in creating a closed cap as the printed filaments exhibit sagging, even with short bridging distances of 20 mm. Potentially, this could be improved by adding robust cooling systems, as has been demonstrated by others [40], but this was outside the scope of this research. Spiral, horizontal print paths are more effective but do not work well for widths of more than 40 mm. Therefore, to achieve good print quality for a cap structure, it is advised to use a cap with a pitch of 45-60 degrees.

Formwork deformation due to concrete pressure during casting
Another set of experiments investigated how the pressure exerted by the freshly cast concrete affects the formworks. Previous investigations have been conducted that study the effects of formwork pressure on vertical, column-like structures [24]. However, as the floor slab elements described in this paper consist of horizontal ribs (as well as a thin flat slab), the behaviour of these ribs during casting has not yet been studied.

Formwork deformation experiments
A series of four rib formworks were printed, and each was fully filled with self-compacting concrete (Fig. 6). In each case, the formwork deformed during casting and the deformation was measured. An overview of the results can be seen in Table 1. DEF_A was printed using PET-G, all other rib samples were printed using PLA with a layer height of 2 mm, and a layer width of 4 mm.
Sample DEF_A was printed without any stiffeners and exhibited a significant width increase at the top of 34% (9.5 cm to 12.7 cm). Therefore, DEF_B was printed with additional stiffening ribs placed every 15 cm. Like DEF_A, the formwork was fixed to a wooden plate with hot glue. This fixing method proved inadequate since the glue detached from the plate, and large deformations (5.5 cm, or a width increase of 73%) occurred at the top of the formwork. With DEF_C, additional fixing features were placed next to the stiffeners to fix the formwork mechanically using screws. The fixing features helped to fix the bottom of the formwork into place. However, a width increase of 36% was observed, which indicates that the stiffeners were not structurally activated. When monitoring the formwork more closely, it could be seen that there was a gap between the end of the stiffeners and the base plate caused by shrinkage. Due to this gap, the stiffener could rotate together with the formwork, instead of resisting the force exerted by the concrete. Therefore, in sample DEF_D, the stiffener was mechanically fixed to the base plate by screwing the end of the stiffener into the base plate. This resulted in a deformation of 0.5 cm or a width increase of just 4%.

Prediction of formwork deformations
Other than the physical experiments, an attempt was made to predict the formwork deformations during casting. The predictions were made either by a linear-elastic finite element analysis of a complete specimen's model or by modeling a single stiffening rib as a cantilever beam, with both models subjected to the hydrostatic pressure of the fresh concrete. The PLA material [41] was modeled as linear-elastic with an E-modulus of 260 kN/cm 2 (ν = 0,33) in both cases, following the recommendations of Ferreira et al. [42].
The linear-elastic analysis of the full specimen geometry was performed with RFEM [43]. For this analysis, 2D plate elements with a desired size of 25 mm were used and the above described material properties of PLA were applied. In DEF_C, the screws at the fixing tabs were modelled as free-rotating point supports, with the movement blocked in all direction at the same time. In DEF_D, the additional fixings at the tip of the stiffener to suppress shrinkage, were also modelled as free-rotating point supports, (with the movement blocked). The results match the experimentally observed deformations Δ exp of the screwed PLA specimens very well (DEF_C and DEF_D in Table 1). DEF_C results in Δ FEA = 4.52 cm ( − 4%) and DEF_D in Δ FEA = 0.44 cm ( − 12%), respectively.
The maximum deformation of the formwork modelled as a cantilever beam under a linearly increasing load is: where p is the load at the bottom of the formwork caused by the hydrostatic pressure; h is the height of the formwork; E is the modulus of elasticity and I is the moment of inertia of the stiffening rib. The concrete pressure was assumed to be linear increasing with a specific weight γ of 25 kN/m 3 , accounting for fresh self-compacting concrete. Thus, the bottom load level could be calculated with p = γ⋅h⋅swith s indicating the stiffener spacing (15 cm in DEF_D). To model ribs with linearly increasing cross-sections in a simplified manner, it is recommended to consider in Eq. (1) the moment of inertia at the lower third of the stiffening rib. This provides similar results compared to an analysis in which the variable cross-section is modelled. The evaluation of (1) gives approximately the same result Δ mod = 2⋅ w = 0.44 cm) for the mounted stiffener solution (DEF_D in Table 2) and matches the results provided by FE-analysis.
This model was further used to predict the formwork deformation measurements of differently shaped beam specimens (Fig. 7), which are presented in Huber et al. [32]. The results can be seen in Table 2. Although stiffener design varies for the different beams, the developed model gives good results. As the simplified model and FEA give matching results, it will most often be more practical to use the simplified model. These evaluations laid the basis for proper stiffener design at the final prototype discussed in the next section.

Full-scale prototype
Based on the findings of the experiments described in Section 4, a full-scale prototype could be designed, fabricated, and structurally tested to validate the workflow. A video documenting the process can be viewed here: https://vimeo.com/716061209.

Design
The design of the slab element followed the general workflow outlined in Fig. 2. This section describes some of the steps in more detail, most notably the creation of the 3D model (Fig. 2d) and the formwork detailing (Fig. 2k).
The design process of the formwork is shown in Fig. 8 and consists out of the following steps: For the purpose of this paper, we have chosen a rectangular grid of columns spaced 8 × 8 m as a starting point of the design. A custom parametric script to generate the 3D model was developed using Rhino Grasshopper and Python [34]. The script starts by taking the 2D rib layout generated from the polylines following the principal bending moments (a). The shape of the rib layout is governed by parameters describing the number of ribs, the distance between ribs, and the width of the ribs at the bottom of the slab. First, the 2D curve is discretized into a polyline. The resulting polyline is then copied vertically (b) and the original and translated polyline are lofted together to form a straight extrusion mesh (c). Another polyline is then generated, forming the pitched cap of the secondary rib formwork, with an angle of 60 degrees  Fig. 8. Formwork design workflow.
(as described in Section 4.1.2). Finally, a surface can be generated that determines the changing height of the formwork from the sides to the centre of the floor slab, to which the primary ribs' polyline points are projected (d). This 3D polyline is then combined with the original 2D polyline to create the top part of the mesh. The three meshes are then joined to form the walls of the formwork (e). At this point, the overall floor geometry can be split into sections for fabrication. For the prototype, a section of 2.7 × 2.7 m above the column is chosen and is cut out of the 3D model for further manipulation (f). Next, stiffening ribs are added to the model (as described in Section 4.2) (g). The stiffening ribs are modelled with a certain thickness, length, height, and spacing between them.
The exact geometry of the stiffeners was determined using linearelastic finite element analysis using the same assumptions and software as described in Section 4.2.2. The models and results are shown in Fig. 9. To evaluate the positive and negative effects of (i) additional stiffening because of the cap, (ii) possible delamination between the formwork walls and cap, and (iii) having the ribs connected in the middle part, several complete models were analyzed using FEA. This includes the model of the 2.7 × 2.7 m full-scale prototype with (i) no delamination (Fig. 9a), ii) a single rib cap delaminated (Fig. 9b), iii) all rib caps delaminated and (iv) the formwork without caps (Fig. 9c). The formwork was modelled with the geometry of DEF_D (Table 2), with a slightly increased thickness of 0.78 cm. The maximum formwork deformation Δ FEA = 2⋅u of 0.56 cm was found at mid-depth of the first rib field around the circular solid part (Fig. 9a). In case of delamination of the cap, a width increase of 2.50 cm at the top edge of the formwork was predicted to occur for a single rib ( Fig. 9b; +446% compared to the undamaged formwork), without significant widening of other ribs. If all rib caps would delaminate, a total deformation of 2.58 cm at the same location was calculated (+3% compared to the delamination of a single rib). If additionally the top-part of the center of the slab delaminates (Fig. 9c), a single rib would deform 2.60 cm (+4% compared to the delamination of a single rib).
Interestingly, the calculated values for formwork deformations with and without cap parts correspond precisely to those obtained from an additional model of a single rib separated from the whole formwork. This finding confirms the independence of other ribs from local cap delaminations. Additionally, this means that no severe effects in other ribs or even the whole formwork's subsequent failure must be considered. Nevertheless, the results further highlight the necessity of providing a strong connection between the formwork walls and the cap.
The last step for the geometry of the formwork walls is to cut out the holes for the reinforcing bars (h). For this, a double-layered orthogonal grid of reinforcing bars was modelled, and holes were made where the grid intersects the formwork. Then, the finished mesh of the formwork walls can be exported for slicing.
With the walls of the formwork exported, the print path for the cap of the primary ribs can be generated (i). The cap is generated as a separate print path, since it can only be printed after the formwork walls have finished and the steel reinforcement has been inserted (see Section 5.2).
Additionally, the layers of the cap follow the curvature of the formwork walls, since they are printed on top of the walls. The polyline defining the top of the formwork walls is used to generate the non-planar layers of the cap.
Lastly, the print paths of the column-slab transition are generated by taking the top polyline of the cap, copying it multiple times and scaling the resulting polylines (j). The print paths of the three formwork sections (formwork walls, cap, and column-slab transition) are then saved as JSON files, ready to be executed by the robotic arm.

Fabrication
The fabrication process of the floor slab is shown in Fig. 10 and consists of the following steps: The first fabrication step is 3D printing of the formwork walls. A layer height of 3.5 mm, layer width of 5 mm, and print speed of 100 mm/s were used. The first layer is printed directly on the MDF print bed. Circular fixing features with a height of 14 mm are integrated into the first four layers of the print. After the first four layers have been printed, these features are screwed into the MDF print bed, mechanically fastening the 3D print to the base without interrupting the 3D printing process. First, the formwork is printed to a height of 35 mm, which will serve as the distance for concrete cover of the reinforcing bars of the solid part of the slab (a).
After the first 35 mm of the print have completed, the printing process is paused and reinforcement bars with a diameter of 10 mm are inserted in one direction (b). Holes for the bars have been designed in the formwork walls, spaced at the required reinforcement grid spacing of 150 mm. Then, the printing process is continued until the process is paused again to insert the second layer of reinforcing bars. After placing the second layer, the print continues until the formwork walls are fully printed.
Then, the prefabricated reinforcement cages are placed into the ribs and the centre part of the floor slab (c). Concrete spacers are placed between reinforcement and formwork to ensure required concrete cover. After the reinforcement is placed, the cap of the ribs is printed (d).
The cap is printed directly on top of the curved formwork walls. The printing process of the cap utilizes the six axes of the robotic arm to align the extruder with the normal vector of the surface used to trim the formwork walls. In an attempt to improve layer adhesion between the top of the formwork walls and the first layer of the cap, the first layer was printed at a reduced speed of 20 mm/s while the top layer was heated with a hot air gun. Afterwards, the print speed was increased to 70 mm/s. A final step in the 3D printing process is printing of the column-slab transition (e). For this part, it was not necessary to orient the extruder according to the surface normal since the geometry of this part resembles a column-like vertical shape and can be printed while keeping the extruder vertical. Due to the short length of the layer paths (less than 1000 mm for the smallest section), the print speed had to be reduced to 30 mm/s to ensure sufficient cooling time between layers.
The completed formwork is then cast (f) with a conventional selfcompacting concrete with a maximum aggregate size of 8 mm (Holcim 3708CL). The concrete was cast into the central part of the slab in batches using a container with a maximum volume of 300 L. Due to the limited maximum volume of the container, four batches had to be cast to fill the formwork. As the concrete was only cast from the centre, the concrete had to flow over a distance of 1.3 m to the end of the ribs. This  proved difficult, as due to a slight delay between the different batches, the previous batch had stopped flowing when the next batch was cast. In an attempt to improve workability, manual vibration was used. After filling the formwork with around two-thirds of the total concrete volume, the cap of the formwork detached from the formwork walls in two of the ribs (Fig. 11d) due to the upwards pressure exerted by the concrete, as well as due to widening of the rib because of lateral pressure. Most likely, the detachment was caused by the weak bond between the step-like top layers of the formwork walls and the first layer of the cap. To avoid breakage of the formwork, clamps were added on the two ribs that showed delamination (Fig. 11d). Despite these issues, it was possible to fill the formwork completely.
After letting the concrete element cure for one day, the formwork was removed (g). This was done by using a hot air gun to slightly heat the thermoplastic formwork, which allows the formwork to be detached from the concrete. Due to the complex shape of the formwork, the stiffening ribs, the slab reinforcement going through the formwork walls, and the thicker (5 mm) formwork, this was a time-consuming task, taking a full day of work with five persons. Potential improvements to the demoulding process are discussed in Section 7.
After demoulding, timber formwork plates were added to the sides of the slab (h). Then, a low-carbon concrete with a maximum aggregate size of 16 mm (Holcim A151EVO) was cast around the ribs to form the 80 mm solid slab part (i). It was chosen to use a different concrete for slab and ribs as they had different requirements (as described in Section 3.3).

Structural testing
To investigate the structural capacity of the optimised column-slab prototype, the specimen was loaded until failure by applying a single point load in the centre, i.e., at the location of the column. The floor slab was supported by twelve radially distributed bearings at a distance of 1.2 m from the center (Fig. 12). An elaborate description of the testing setup and the results can be found in [32].
The smooth transition between the column and the ribs of the slab led to a very stiff behaviour compared to a solid reference slab with a thickness of 220 mm. The concentrated force from the column was distributed among the ribs, and a punching failure, which is typically observed at flat slabs supported on columns, could therefore be suppressed. The failure was characterised by the opening of a governing crack along the joint between one of the ribs and the solid part of the slab that was accompanied by rupture of the slab reinforcement. Huber et al. [32] have compared the structural performance of a solid flat slab to curved ribbed slabs by using FEA. Their results indicate that it is possible to reduce material use by 40% with respect to a solid flat slab, in pointsupported slabs with columns spaced 8 × 8 m.

Discussion and conclusion
This paper investigated the potential of using robotically 3D printed FDM formwork to produce full-scale, optimised reinforced concrete floor slab elements. The successful fabrication of a 2.7 × 2.7 m prototype (Fig. 13) shows that it is possible to use this fabrication approach to produce optimised slabs.
In this study, the design-to-fabrication workflow was developed for a rectangular grid of regularly spaced columns. This layout would result in a repetition of floor slab elements, making it advantageous if a formwork can be reused. Indeed, if many identical elements would need to be produced, it might be more cost-effective to produce sturdy moulds that can be reused for multiple castings. Therefore, the proposed fabrication process would either need to be adapted for the production of reusable 3D printed formworks (such as also discussed in Section 7), or be used within projects with little to no repetition of elements.
In this paper, we focused on the fabrication process of a section of the 8 × 8 m slab, a section above the column. However, to fully assess the feasibility of the proposed process, including the connection between elements, the entire 8 × 8 m slab would need to be fabricated, but this was deemed out of the scope of this study. However, several other parts of the slab (in particular, the ribs spanning between the columns) were also designed, fabricated, and structurally tested. The formwork of these parts can be seen in Fig. 7, additional information on these elements is provided by Huber et al. [32].

Design process
Using the design workflow described in this paper, it was possible to go from an initial linear-elastic structural analysis to a printable 3D model in a semi-automated process. The design was informed by structural design criteria and fabrication aspects such as the casting process. Some of the steps in the workflow still require manual input, such as the initial FEA that is performed as a first step (Fig. 2a), the design of the reinforcement (Fig. 2h) and the definition of some of the parameters describing the formwork detailling (Fig. 2k).

3D Printing of the formwork
This study combined 3D printing of planar layers with 3D printing of non-planar layers. As mentioned in Section 2, the reason for combining both approaches is that complex path planning is avoided for the largest part of the print. The disadvantage, however, is that the step-like wall does not offer an ideal printing base, as the first non-planar layer is not completely touching the step-like wall. This leads to a weak connection between wall and cap, which in turn lead to problems with the detachment of the cap during casting (Section 5.2, Fig. 11d).
Adding stiffener ribs to the formwork was necessary to counter the Fig. 12. Structural testing of the full-scale prototype. Fig. 13. The final prototype.
pressure exerted by the fresh concrete. However, the stiffeners had a substantial effect on the total 3D printing time of the formwork walls. Printing of the formwork walls with stiffeners took a total of 16 h and 6 min. In comparison, without stiffeners, the printing time could have been reduced to 9 h and 20 min (a reduction of more than 40%).

Reinforcement
Two reinforcement strategies were combined for the fabrication of the floor slab element: (1) straight bars for the solid part of the slab, embedded into the 3D printed formwork, and (2) prefabricated reinforcement cages inserted into the rib formwork. Both reinforcement strategies proved viable to be combined with the 3D printed formwork. However, some challenges were encountered.
Due to the reinforcing bars of the solid slab that were protruding through the formwork (Fig. 11b), formwork removal became challenging and time-consuming. It was considered to leave the formwork in place. However, this would have resulted in a plastic layer between the concrete of the ribs and the concrete of the solid part of the slab, which would have been detrimental to the shear transfer between the ribs and the solid part of the slab. Also, this would make it impossible to recycle the plastic formwork.
Reinforcing the formwork with prefabricated reinforcement cages proved an effective solution for the floor slab prototype. The reinforcement cages were assembled by hand, which, given the small number of cages, was not very time-consuming. Also, since the slab exhibited radial symmetry, all twelve reinforcing cages were the same. However, if this fabrication method were to be applied to an entire building, there would be many different reinforcement cages, which might make the manual assembly of these cages very time-consuming.

Casting
This research aimed to use conventional concrete for casting, as opposed to the set-on-demand concrete that has been used in previous projects involving thin, 3D printed formwork [19,23]. Conventional concrete is preferable, since it allows for a wide variety of concrete mixes with coarse aggregates, less cement, and fewer admixtures. Due to these aspects, the concrete can also be more sustainable and more economical. It proved feasible to use a commercially available selfcompacting concrete mix; however, this also resulted in several challenges.
The self-compacting concrete exerts pressure on the entire 3D printed formwork walls and cap, which exposes weak spots in the formwork where deformations might occur. A particular weak spot is the connection between formwork walls and cap, due to the step-like structure of the seam (Fig. 11c). Because of the formwork pressure, the rib formwork deformed, which caused delamination between the formwork walls and cap (Fig. 11d). The delamination did not lead to complete failure of the formwork (in accordance with the FE evaluations in Section 5.1). Still, it did result in inaccuracies of the final fabricated element. However, the observed inaccuracies were far less compared to the predictions of the FE model with a single rib delaminated. This could be explained by the facts (1) that only the lower ends of the rib caps uplifted, while the upper parts were still connected and (2) that the casting was done in four batches, causing the stiffening of the already cast batches resulting in a lower pressure from the concrete than the hydrostatic pressure assumed in the model. A more severe issue is that the stiffening ribs that had to be added to counter formwork pressure significantly increased printing time, as discussed in Section 6.2.

Outlook
The successful design, fabrication, and structural testing of the fullscale floor slab element showed that the described workflow was suitable for realizing material-optimised, ribbed reinforced concrete floor slabs. However, there are aspects that can be improved or have to be further studied in future work. A selection of suggestions for future work is provided in this section.
• As printing the formwork stiffeners had a significant influence on printing time, future work should investigate how to stiffen the formwork, without having an outsize effect on printing time. Different rib geometries, or stiffening patterns [24] might be investigated. Additionally, it could be possible to account for deformation during casting: designing the printed geometry so that the deformed formwork matches the desired final geometry. • To avoid having to stiffen the formwork, set-on-demand casting could potentially be used as it would reduce pressure on the formwork. To apply set-on-demand casting, three main challenges would need to be addressed: (1) scaling up the set-on-demand process to output higher volume and coarser aggregates [44], (2) improving sustainability of the set-on-demand concrete by reducing cement content [45], and (3) investigating the possibilities of using set-ondemand casting for horizontal structures (such as the floor slab ribs), instead of vertical structures (such as the columns that have been fabricated until now [20,46]). • The research presented in this paper aims to realize materialoptimised concrete floor slabs, which results in floor slabs with less mass. Inherently, this reduces the sound insulation properties of the floor slab. Therefore, optimised concrete floor systems might be wellsuited for buildings with an office function but would likely not meet the soundproofing requirements for residential buildings. Potential solutions to make lightweight concrete slabs suitable for residential applications could be: (1) adding additional insulation materials to the slab, (2) optimising the slab geometry for sound insulation [47], or (3) re-evaluating existing soundproofing requirements to allow for lightweight concrete structures. • Implementing our proposal of prefabricated floor slab elements on a construction site would require the development of joints between the slab elements. Although this was beyond the scope of this paper, it could be possible to develop keyed connections between the slab elements, such as proposed by Bischof et al. [48]. 3D Printing could enable novel connections with inherent surface roughness, although achieving high geometrical accuracy of the keyed joints would be instrumental to its success. • To scale up the proposed fabrication process, it would be necessary to rethink the reinforcement production process, as it would not be economically feasible to produce a high number of non-identical reinforcement cages manually. Here, automated methods for producing reinforcement cages could provide a solution [49][50][51]. • A critical issue that needs to be addressed in future work is the demoulding process, which currently is very time-consuming. Potentially, demoulding time could be reduced by implementing seams into the formwork. Additionally, a less complex shape or water-soluble formwork could ease the demoulding process. Another approach that needs to be studied is whether the formwork can be reused multiple times. Currently, this is impossible as the formwork cannot be removed without breaking it. However, by rethinking the fabrication process, it might be possible to create formworks that can be reused multiple times, which would significantly improve the sustainability and the efficiency of the fabrication process. • For this study, the PLA material used for printing the formwork was not recycled, as this was not the main objective of this paper. However, for the proposed fabrication process to be sustainable, it is essential that the printing material can be fully recycled. Studies conducted by the authors have shown that it is possible to fully recycle the used formworks by cleaning them, shredding, regranulating into pellets, and reprinting the recycled pellets. This will be described in more detail in future research. • A last aspect that has not been discussed in this paper but that will be relevant for the industrial application of the proposed floor system is the extra costs related to the fabrication process. Compared to conventional prefabrication of floor slabs, our material-optimised floor slabs require more manual labour (two casting steps, demoulding), more expensive machinery (robotic arm, extruder), as well as more high-skilled labour (robotic programmer). Quantification of the economic implications of these aspects is essential to evaluate the economic feasibility of the system, which will have to be studied in future work.

Funding
This project was funded by Siemens, Geberit and the ETH Zurich Foundation. This research was further supported by the The Swiss National Science Foundation (NCCR Digital Fabrication agreement number 51NF40-141853).

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.