Content uploaded by Emil Adiels

Author content

All content in this area was uploaded by Emil Adiels on Aug 13, 2018

Content may be subject to copyright.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

July 16-20, 2018, MIT, Boston, USA

Caitlin Mueller, Sigrid Adriaenssens (eds.)

Copyright © 2018 by Emil ADIELS, Nicolo BENCINI, Cecilie BRANDT-OLSEN, Al FISHER, Isak NÄSLUND,

Robert K OTANI, Emil POULSEN, Puria SAFARI, Chris J K WILLIAMS

Published by the International Association for Shell and Spatial Structures (IASS) with permission.

Design, fabrication and assembly of a geodesic gridshell in a

student workshop

Emil ADIELS*, Nicolo BENCINIb, Cecilie BRANDT-OLSENa, Al FISHERb, Isak NÄSLUNDb,

Robert K OTANIc, Emil POULSENc, Puria SAFARIb, Chris J K WILLIAMSd

*Department of Architecture and Civil Engineering, Chalmers University of Technology

Gothenburg, Sweden

emil.adiels@chalmers.se

a BIG Engineering

b Buro Happold Engineering

c CORE studio Thornton Tomasetti

d Department of Architecture and Civil Engineering, Chalmers University of Technology

Abstract

This paper describes the design, fabrication and assembly of an 11x11 m gridshell built of plywood laths

during a two and a half day workshop in a new undergraduate course about parametric design and digital

fabrication. The question was how to use full-scale prototyping to summarize and integrate the learning

outcomes in this course. A challenge was how to execute all production during two consecutive days

utilizing all 35 students. Exploiting a geodesic grid design, that is curves whose curvature vector is

parallel with the surface normal, the gridshell was made of straight predrilled laths that were bent and

locked into shape using a sequential erection method. The design was incorporated in a full parametric

model including automated design checks and the generation of all necessary production drawings.The

workshop and the preparatory work described in this paper was a collaboration between Chalmers, BIG

Engineering, Buro Happold and Thornton Tomasetti’s CORE studio.

Keywords: Timber gridshell, geodesics, differential geometry, parametric design, digital fabrication, architecture and

engineering, education and architecture, architecture workshop.

1. Introduction

A new course named Digital tools -Parametric design (3 ECTS) was planned and performed in 2017 by

authors Adiels and Näslund for 35 undergraduates at the double degree program Architecture and

Engineering (MArch and MSc in Engineering) at Chalmers (Adiels, [1]). The main goal of the course

was to give the students tools and knowledge necessary to sufficiently implement parametric design and

digital fabrication techniques in their future projects, but also inspire them to practice their unique

competence from both architecture and engineering. As an ending segment, a workshop of two and a

half days was planned to showcase the full potential of parametric and geometric modelling in

production. The scope was to build an indoor pavilion of a scale in which a group of people could stand

and move freely. Equally important was to embrace architectural and engineering creativity using

mathematics as a tool for efficient fabrication strategies. Industry specialists in the field of parametric

design were invited to create a dialogue about present and future applications of digital tools in both

academia and practice. The design, planning and execution of the workshop was a result of these

conversations between Chalmers, BIG Engineering, Buro Happold Engineering and Thornton

Tomasetti’s CORE studio. The workshop started with half a day of explaining the theoretical

background, the design process, and the parametric implementation, followed by two days for

production and erection. Pictures from the finished project, a symmetric geodesic gridshell built from

straight laths of plywood, can be seen in Figure 1.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

2

Figure 1, the result of the workshop was a geodesic gridshell built from predrilled planar straight laths.

2. Background

The students had prior to this course been trained in both architectural, mathematical and engineering

theory and methods through courses, workshops and architectural projects. This course is meant to

integrate these tools in a digitally driven design process linked to digital fabrication techniques. The first

part of this course had therefore focused on lectures and tutorials in the basics of parametric design and

digital fabrication. These aspects were examined through assignments and smaller projects (Adiels, [1]).

Since the earlier work covered and examined all course requirements it was possible test if the learning

outcomes could be summarized through a full-scale production in a workshop format.

This workshop builds on a workshop culture at Chalmers where engineering and artistic experiments

are exhibited through digital tools and mathematical modelling. For example, Figure 2a shows a

workshop where a brick vault is built on a falsework of plastic tubes that were actively bent into shape

(Adiels, [2]).

Figure 2, a) A vaulting workshop using falsework from straight plastic tubes(Adiels, [2]) , b) UWE Research

pavilion (Harding et al [9]) c) The geodesic dome by Buckminster fuller (Fuller, [3]).

Previous papers by authors have covered applications of geodesics in the design of textile (Williams [4])

and brick structures (Adiels et al [5]). Geodesics are curves on a surface that have zero geodesic

curvature. Since they follow the shortest path on the surface they become straight when unrolled onto a

plane (Struik [6]). Using the same notation as in Green and Zerna [7], a geodesic can be described as a

unit speed curve with parameter t, lying on the surface described by position vector r with surface

parameters 𝜃, 𝜃 (u and v in Struik).

𝐫 = 𝑥(𝜃, 𝜃)𝐢 + 𝑦(𝜃, 𝜃)𝐣 + 𝑧(𝜃, 𝜃)𝐤 (1)

The second derivative of r with respect to t, 𝐫

, is zero in the plane of the surface, giving the geodesic

equation for the curves1:

1 Equation 2 does not only describe the geodesics in Figure 1 but also the paths of planets moving in space time.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

3

+

Γ

= 0 (2)

Geodesics have been applied in architectural projects such as the geodesic dome by Buckminster Fuller

in Figure 2c, Ongreening Pavilion (Harding et al [8]), UWE Research Pavilion (Harding et al [9]) in

Figure 2b, and the Almond Pavilion (Soriano, [10]). The geodesics of the dome are rather the result of

the discretization of a sphere using the projection based on an icosahedron (Fuller, [3]). The other

projects have used a geodesic design in combination with a material that allows for constructing its

continuous laths from straight planar strips. The clear mathematical concept in combination with a low-

tech and economic production strategy for gridshells was of much influence for the design concept in

this project.

3. Limitations and preparations

For this project there were four restrictions that governed the design: (1) The design should use

mathematics as driver for geometry and production in a way that is comprehensible for the students

based on their previous knowledge and training. (2) Production of elements and erection must be done

in two days. (3) The structure cannot exceed a height for which scaffolding is needed due to safety

regulations. (4) The material cost should not exceed 1000 euro.

The workshop was to take place in our testing facility. The concrete floor which could not be penetrated,

but its 1x1 m grid of apertures with 24 mm radius could be used for anchorage, see figure 3a. The

production process was restricted mainly to manually operated machines and hand-power to produce

and erect all elements. Therefore, the design was chosen to utilize flat straight laths of plywood made

possible through a geodesic gridshell design. The design was to be incorporated in a full parametric

model that includes everything from the form to the generation of all production drawings necessary to

build the pavilion. These preparations were done in advance by the organizers of the workshop. The

preparations for the workshop was divided in the following steps: (1) Materialize geodesics into

structural elements. (2) Gridshell design (3) Link the design to automated generation of production

drawings. (4) Structural analysis. The content covered in this chapter was packaged into lectures

including theoretical background and a workplan used as an introduction to the workshop.

3.1 Material investigations

The mathematical concept of geodesics needed to be materialized into laths with a real material and

cross section. The laths must be sufficiently stiffer in one direction to avoid curvature in plane of the

surface and flexible enough in the weak direction to bend and twist using hand-power, but strong enough

not break during erection. Figure 3b-d shows the physical experiments performed to investigate these

parameters using 6 mm plywood of 50, 70 and 100 mm width, with and without connections. Laths were

connected by overlapping adjacent elements and connect with two M6 bolts with steel washers on each

side, similar to the Ongreening pavilion (Harding et al [8]). The cross section was chosen to be 50 mm

wide and 6 mm thick birch plywood with 5 layers. This was the most economic and slender option with

sufficient bending capacity. These experiments were important to get a feeling and understanding of the

capacity and geometrical constraints needed for the gridshell design in 3.2.

Figure 3a measurement of the aperture in the floor, b-d experiments investigating the capacity and user ability

for different plywood laths.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

4

3.2 Gridshell design

The form and pattern needed to integrate structural performance with a strict geometrical behaviour of

geodesics in a materialized spatial experience. To create a geodesic, one must satisfy two boundary

conditions either by fixing start and end points or starting point and direction. To control geodesic

patterns one must either use quite intelligent rules and, or, interactively adjust the patterns depending on

geometrical requirements (Pottmann et al. [11]). For this pavilion its geodesics could cross each other

and therefore be modelled independently for visual inspection of the geometrical requirements, such as

distance between connections and curvature of laths. Forms were examined using three approaches, see

Figure 4, a) free-form b) analytical (mathematical functions) and c) behaviour driven design.

A symmetrical shape and grid had many advantages from a production perspective. It meant fewer

unique building elements and simultaneous erection of similar sections. The gravity driven funicular

shape, in combination with laths mostly forming arches, was thought to avoid large deflections and be

stable during a sequential erection procedure. The final grid consisted of 8 different laths that were

repeated 8 times through rotation and mirroring, see figure 5, making 64 laths in total. Each bottom

curve was made using four points interpolated such that they aligned with the 1x1 m grid in the floor.

This meant four possible attachments for the base plate following the bottom curve.

Figure 4, Different surface designs that were evaluated, the design to the right proved most efficient in terms of

lath repeatability, lath adoption and structural efficiency.

Figure 5, The lath layout strategy seen in plan with 8 unique laths repeated 8 times to form the complete layout.

The orthogonal grid follows the 1x1 m grid of the aperture in the floor.

3.3 Parametric modelling and automation of production drawings

The parametric model was written in Grasshopper3d, a plugin to Rhinoceros3d, the development

platform familiar to the students. It allowed for changes to be incorporated, such as tweaks to the surface

and the lath layout, without any additional work needed for the visualization and the generation of

production drawings. It also served as an example for the students on how to structure code and solve

problems related to 1:1 prototyping. The code was divided into four sections: form finding, geodesic

patterns, production drawings and visualization. This section will focus on the production drawings for

the laths and base plates.

To generate geodesics on a surface, specific custom code was developed using the method described in

Adiels et al.[5]2. The geodesics on the gridshell became centerlines for developable surfaces with the

same width as the laths. Since geodesics are straight lines on the surface, measured lengths along them

maps directly to a straight line in a plane. If the geodesics are known, generating the production drawings

2 Currently there was no functionality in Grasshopper3d to generate geodesics using starting point and direction.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

5

becomes mainly a 1-dimensional exercise of measuring lengths. There were four steps in making

production drawings for the laths: (1) Unroll the laths from the gridshell to a plane (2) Make holes for

connecting laths crossing each other (3) Adjust the ends (4) Segment each lath into lengths fitting on a

plywood sheet. To check that this was correct, the straight planar segments were used to rebuild the

entire 3d model. This stage was essential to verify that all pieces fitted together correctly. These actions

have been summarized in Figure 6a. All drawings necessary for all laths generated by the code can be

seen in Figure6b. For the baseplates, made of two layers of plywood anchoring the laths to the ground,

only one drawing was needed. Due to symmetry and a minor adjustment of the seams the bottom plate

could be flipped over without any continuous joints between the two layers. All code for this project is

uploaded to a Github repository(Adiels et al. [12]).

Figure 6a) Showing the process making the drawings for the laths. This includes unrolling, marking connections,

adjusting edges and rebuilding the model using these drawings. 6b) shows all 30 elements needed to make all laths

3.4 Structural Analysis

Since the plywood strips used in the structure initially were straight, the elements had to be bent into

position by utilizing the material’s elasticity. To avoid material failure during erection and in final

position, a basic bending stress check was performed. From the parametric model the curvature along

each lath was evaluated at an equal distance from each other with sufficient frequency. The moment and

equivalent maximum bending stresses were calculated using equation 3 for the desired cross section

with material data from the supplier.

𝜎 = 𝑀𝐼

× 𝑧 , where 𝑀 = 𝜅 × 𝐸𝐼 (3)

The derived stressed stresses were checked against the materials bending capacity with the criterion

𝜎 < 𝑓

. The analysis showed a slight over utilization near the openings. However, in the material tests

in section 3.1 significantly higher curvature was observed, why the desired curvature was regarded

feasible. Note that the check above only applies for the prestress induced by formation process.

To verify the structure’s capacity to withstand the self-weight, a secondary analysis was conducted using

a structural analysis plugin for Grasshopper 3d named Emu (Poulsen [13]). By using its’ built-in time-

stepping based non-linear solver, it could be verified that the structure was stiff enough to avoid global

buckling failure from dead load.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

6

4. Workshop – Building a geodesic gridshell

Before the building the pavilion, day zero, two lectures were presented describing the design process

and the mathematical background behind the design. The entire parametric model was presented and

handed out to give the students an idea of the added complexity compared to their earlier projects and

assignments. The building of the pavilion was divided into one day for fabrication and one day for

erection. Workstations were prepared in advance for the first day and divided in two sections, one for

laths and the one for base plates and anchorage to the ground. Before fabrication started, all students

assigned themselves to different predefined tasks for the morning and the afternoon. This was used to

organize the fabrication and assembly of all elements such that the students were utilized as much as

possible. Day 1 and 2 of the workshop was filmed (Adiels [14]).

4.1 Day 1 – Fabrication and assembly of all building elements.

All building elements were made using equipment in an adjacent wood workshop and power tools

provided by our sponsor Cramo. The power tools consisted of 10 power drills with 6 mm bits, 2 chop

saws and 2 jigsaws. The laths were made from 6mm birch plywood boards while the baseplates were

made from two layers of 12 mm rough plywood. For attaching the laths to the baseplate, 112 steel angle

brackets were used. In total, 728 M6 bolts with nuts and 1456 steel washers were used for connections.

Figure 7a) taping paper drawings onto wooden strips b) predrilling marked wooden strips c) the base plates were

cut out using a CNC machine d) the base plates were made of two layers 12 mm plywood laminated using glue.

For the laths, 10 boards that were cut into 50 mm wide strips in the wood workshop. Meanwhile, other

students printed 1:1 paper drawings for all 30 elements forming the 8 different types of laths when

assembled. These drawings were cut and taped onto the wooden strips which were drilled and cut

accordingly, see Figures 7a - b. These wooden templates were used to mark up the rest of the strips

which were then processed in a similar fashion. After completing all 240 (8x30) strips, these were

connected using M6 bolts and nuts with a washer on each side, forming 64 (8x8) laths in total.

For the baseplates, 8 boards were cut using a CNC machine in the wood workshop running a single

drawing, see Figure 7c, which speeded up the cutting and reduced possibility for errors. The elements

were laminated using wood glue and screws forming 4 identical curved plates, see figure 7d. The CNC

machine also marked the placing of the steel angle brackets and cut holes that aligned with the apertures

in the floor. Wooden poles, 40 cm in length, were made to fit the holes such that the base plates stayed

in place due to friction between the poles and the concrete. The angle brackets were all at right angle

when delivered and needed to fit the angle of the model. The angles ranged between 90 and 70 degrees

and were therefore divided into 5 groups of 5-degree difference. Wooden blocks were cut at 85, 80, 75,

70 degrees and the angle brackets were hammered onto these to achieve sufficient angle. These were

then attached to the baseplates using wooden screws.

4.2 Day 2 – Erection and assembly of gridshell.

All elements had been made and assembled to full length on the first day and second day was all about

erecting and connecting all the predrilled laths into a gridshell. The assembly was done using a sequential

erection procedure, illustrated in Figure 8, connecting the laths with bolts, nuts and washers using

wrenches. Four teams would start, one in each opening, and work inwards. Before all laths could be

established in this manner the laths in the centre were erected to support the remaining. The tolerance

between the radius in the drilled holes and the bolts was very low, why the bolts often had to be screwed

through the holes, rather than just being pushed through. The overall process went smoothly with good

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

7

alignment of the holes in the different laths. There were some exceptions to this, especially in the centre

part of the grid were some force had to be applied to be able to connect the elements. One lath broke

during the erection, due to a knot in the middle layer of the plywood, but a new lath could be cut and

drilled from spares, which meant that the process could be resumed without much delay. Figure 9 show

various pictures from the erection and the finished pavilion.

Figure 8, The procedure of erection, starting from the outside going inwards in four teams. The laths in the centre

were needed to support the remaining laths.

Figure 9, Various pictures from the erection along with the finished pavilion with some details.

5. Discussion

The main goal was to use full scale prototyping to summarize and integrate the learning outcomes in a

course on digital tools and parametric design. Overall, we perceived the workshop as a success. In a

course evaluation done after the workshop where 60 % of the students participated, the course was rated

4.8 out of 5, top 10 placement at Chalmers. This included the entire course where the workshop was

roughly a third. Our biggest concern with the workshop, besides if everything would fit together, was if

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

8

the students would find it stimulating to build something that they had not designed themselves. We

quickly realized that the students took ownership of the pavilion by taking control of the different

workstations and fabrication processes. One area that could be improved was the drilling or marking on

the laths. When assembled to full length on the floor some became curved. The solution was to expand

the holes slightly and straighten them out. This could have been solved by having a larger tolerance

between the holes and the bolts. The result however, came out almost perfect which means that the

drawings and the work was well executed overall.

Two laths did break, one during erection and one when built. The first had a knot in the middle layer

and the second broke near a connection in the finger joints of the plywood. However, there was never

any danger. The material test did not consider possible defects in the plywood, and due to the small

width, the laths where extra sensitive. These unexpected events effectively showed the students why

design codes are necessary. However, a less stiff connection in combination with a curvature driven

segmentation could have avoided the second failure. A simple adjustment could have been to use rubber

or spring washers. Other improvements could have been to combine form finding with the generation of

geodesics. This could have integrated the structural and the geometrical behavior in a more natural way.

There were two main reasons for the successful workshop - good preparations and the placement in time

in relation to the student’s other courses. The workshop was scheduled after their other examination

period, meaning that the students could fully focus on the workshop resulting in a joyful atmosphere.

We believe the workshop will inspire students to learn more about geometry and applications in digital

tools. The material cost ended a bit over 1000 euros but compared to the learning outcome and the

positive reactions it was a very low investment.

References

[1] E. Adiels, “Digital tools – Parametric design course 2017.” [Online]. Available:

http://emiladiels.com/digital-tools-parametric-design-course-2017/. [Accessed: 15-Mar-2018].

[2] E. Adiels, “Brick Workshop in Mariestad – Emil Adiels.” [Online]. Available:

http://emiladiels.com/brick-workshop-in-mariestad/. [Accessed: 11-Apr-2018].

[3] R. B. Fuller, “Building Construction [U.S. Patent 2,682,235],” 1954.

[4] C. J. K. Williams, “Defining and designing curved flexible tensile surface structures,” in The

mathematics of surfaces, G. J.A, Ed. Oxford: Claredon Press, 1986.

[5] E. Adiels, M. Ander, and C. J. K. Williams, “Brick patterns on shells using geodesic

coordinates,” in IASS Annual Symposium 2017

[6] D. J. Struik, Lectures on classical differential geometry, 2nd ed. Dover, 1988.

[7] A. . Green and W. Zerna, Theoretical elasticity, 2nd ed. Oxford University Press, 1968.

[8] J. Harding, W. Pearson, H. Lewis, and S. Melville, “The Ongreening Pavilion,” Adv. Archit.

Geom. 2014, pp. 295–308, 2014.

[9] J. E. Harding, S. Hills, C. Brandt-Olsen, and S. Melville, “The UWE Research Pavilion 2016,”

in Proceedings of the IASS Annual Symposium 2017

[10] E. Soriano,“Low-Tech Geodesic Gridshell: Almond Pavilion” archi DOCT no 4., February,2017.

[11] H. Pottmann, Q. Huang, B. Deng, A. Schiftner, M. Kilian, L. Guibas , J. Wallner “Geodesic

patterns,” ACM Trans. Graph., vol. 29, no. 4, p. 1, 2010.

[12] E. Adiels, N. Bencini, C. Brandt-Olsen, I. Naslund, E. Poulsen, and P. Safari, “Github

repository,” 2018. [Online]. Available: github.com/archengtech/chalmersworkshop-dec2017.

[13] E. Poulsen, “Structural design and analysis of elastically bent gridshells - The development of a

numerical simulation tool,” Chalmers University of Technology, 2015.

[14] E. Adiels, “Geodesic gridshell workshop 2017.” [Online]. Available:

http://emiladiels.com/geodesic-gridshell-workshop-2017/ [Accessed: 15-Apr-2018]