A review of elastic grid shells, their erection methods and the potential use of pneumatic formwork

Abstract

The evolution of elastic grid shells has observed significant progress in the fields of computational form-finding, structural analysis and to some extent buildability since their inception in the 1960s. While the engineering precision of built elastic grid shells has increased on the whole (most notably Chiddingstone
Orangery & Savill Gardens), the size and span of modern elastic grid shells has decreased. Furthermore, building costs per square metre for such structures have also increased. Despite an increase in the frequency of elastic grid shells built in Europe over the last two decades, fuelled in part by academic curiosity, the low sample makes interpreting trends in their adoption rate difficult. Nonetheless the failure for more widespread adoption in the built environment of this low-tech, large-span building technology may be attributable to the increased serviceability demands of modernised building codes coupled with limitations or apprehension caused by health and safety legislation. While the idea has been considered before, it is argued in this paper that the use of air-inflated membrane cushions for the erection of elastic grid shells has
the potential to significantly reduce the demands on structural performance of the nodes and beams when compared with the crane and cable erection method and that when compared with the scaffolding erection method, the air-inflated cushion approach can offer paralleled safety but at a fraction of the time and cost. It is believed that this technique offers a way to once again facilitate largescale, low-cost elastic grid shell buildings in the modern built environment such as have not been since the likes of the Multihalle Mannheim.

Full text

A review of elastic grid shells, their erection
methods and the potential use of pneumatic
formwork
G. Quinn1, C. Gengnagel1
1Department for Structural Design and Technology (KET),
University of Arts Berlin, Germany
Abstract
The evolution of elastic grid shells has observed significant progress in the fields
of computational form-finding, structural analysis and to some extent
buildability since their inception in the 1960s. While the engineering precision of
built elastic grid shells has increased on the whole (most notably Chiddingstone
Orangery & Savill Gardens), the size and span of modern elastic grid shells has
decreased. Furthermore, building costs per square metre for such structures have
also increased. Despite an increase in the frequency of elastic grid shells built in
Europe over the last two decades, fuelled in part by academic curiosity, the low
sample makes interpreting trends in their adoption rate difficult. Nonetheless the
failure for more widespread adoption in the built environment of this low-tech,
large-span building technology may be attributable to the increased serviceability
demands of modernised building codes coupled with limitations or apprehension
caused by health and safety legislation.
While the idea has been considered before, it is argued in this paper that the
use of air-inflated membrane cushions for the erection of elastic grid shells has
the potential to significantly reduce the demands on structural performance of the
nodes and beams when compared with the crane and cable erection method and
that when compared with the scaffolding erection method, the air-inflated
cushion approach can offer paralleled safety but at a fraction of the time and
cost. It is believed that this technique offers a way to once again facilitate large-
scale, low-cost elastic grid shell buildings in the modern built environment such
as have not been since the likes of the Multihalle Mannheim.
Keywords: elastic grid shells, pneumatic formwork, active bending, erection

1 Introduction
Elastic grid shells are structures made from long continuous beams and employ
the principals of active bending [1] to achieve their target shape. Regular grid
shell structures on the other hand are made from elements of varied and finite
lengths. This paper is concerned with elastic grid shells only. The economic
advantages that arise from using elastic grid shells (low material quantities, cost
effective transportation, large spans and low-tech assembly of linear elements)
are undermined by the cost and complexity of the temporary formwork and
labour which are necessary for their erection.
This paper reviews in detail the most important western elastic grid shell
buildings since their inception in the 1960s. A literature review is also presented
of buildings and projects that have made use of pneumatic formwork. Until now,
the authors are unaware of pneumatic formwork having been used for the
erection of an elastic grid shell. The final sections of the paper make a case for
the use of pneumatic formwork for the erection of elastic grid shells, considering
both benefits and caveats. Finally, a simple prototype from a student workshop is
shown.
It is fair to say that the erection phase is usually a major, if not dominant, load
case for an elastic grid shell due to high bending stresses induced by tight
curvatures and point loads in the laths. This effect is dependent on the method of
erection as well as the shape and size of the shell. The main reasons for
minimizing bending-induced stresses are to prevent breakages of beams during
erection and to ensure that sufficient stress reserves are available in the beams
under external load cases. While every major grid shell project has experienced
breakages during erection, the number of breakages has progressively reduced.
For example: “...during the assembly of project Essen: due to inherent stresses,
several grid rods directly next to joints were broken” [2, p. 219]. At Manheim “...
quite a number of finger joints broke on site during handling and erection” [3, p.
126]. In the Downland grid shell “of the 10 000 joints in the structure, there were
approximately 145 breakages during forming. Almost all were failures of the
finger joints.” [4, p. 437]. Finally, in the Savill Garden grid shell, which had
extremely low curvatures and a fully scaffolding-supported erection there were
only “two fractures during the construction process” [5]. While this progressive
reduction of breakages is very positive, it comes at the cost of increasingly slow,
precisely measured and costly erection. It is supposed that pneumatic formwork
may facilitate a reduction of labour and cost during erection while
simultaneously further reducing the risk of localised bending-induced stresses
and breakages during erection.
Another main reason to limit bending stresses during the erection of elastic
grid shells is that for both GFRP and wood, creep can be accelerated by high
internal stresses. Various sources recommend limiting the internal stresses of
GFRP to between 30% and 60% in order to prevent worsening of this effect.

2 Review of pneumatic formwork for dome-like structures
Making use of pneumatic formwork for dome structures has intrigued engineers
and researchers for some time. As early as 1940, Californian architect Wallace
Neff developed a system of using inflated sailcloth cushions to support flexible
reinforcement which is then sprayed with shotcrete in increasing thicknesses to
create a strong and stable shell structure [6, p. 38].
Figure 1: Wallace Neff’s bubble houses
Developed in the 1960s, the Bini method [7] facilitates concrete shell erection
using un-stiffened formwork whereby wet concrete and sprung length-changing
reinforcement are all contained within an upper and lower membrane in which
concrete curing occurs in-situ after inflation. The Bini system enjoyed a strong
burst of adoption for small to mid-span structures during the ‘70s and ‘80s. More
than fifteen hundred Bini shells have been built in twenty-three countries with
spans from 7.5m to 90m [6, p. 38], proving without a doubt the potential for
success of pneumatic formwork. While the double membrane system coupled
with anchored foundations cleverly restrains the load-bearing wet concrete shell
during erection, the same system could not be applied to elastic grid shells since
when flat, they occupy a much larger footprint than when erect.
Figure 2: The Bini method for erecting concrete domes with pneumatic
formwork [7, p. 190]
In the 1980s Sobek [8] explored the use of pneumatic formwork for the
erection of concrete shells citing the same justification as the authors in this
paper i.e. the ever increasing expense of labour-intensive formwork. A focus of
Sobek’s work was on how to limit concrete strains during erection by stiffening
the formwork by partially filling the enclosed membrane with a fluid or by
strengthening the membrane with circumferential steel cables as previously
patented by Wallace Neff [9].

More recently Dallinger et al used pneumatic formwork to erect domes made
out of prefabricated concrete panels as well as ice sheets [10], fig. 3. Two
methods for stabilising the kinematic system during erection were developed:
firstly by combining pneumatic formwork with radial and circumferential
tendons which are shortened during erection (polyhedron method) and secondly
by combining pneumatic formwork with a rigid central mounting tower (cloister-
vault method). Kokawa et al [11] have also developed ice shells built on
temporary pneumatic formwork. Water is sprayed on in the same fashion as
shotcrete in Harrington / Neff shells, fig. 4.
Figure 3: Pneumatic formwork for the erection of prefabricated concrete panels
[10]
Figure 4: Ice shells created by pneumatic formwork and sprayed water [11]
The largest known project to have made use of pneumatic formwork for its
erection is the train car maintenance dome for the Union Tank Car Company in
Wood River, Illinois designed by engineer Richard Lehr working for
Buckminster Fuller’s company Synergetics with Chicago architects Battey &
Childs [12]. The steel dome with a span of 114.4m [13, p. 1137] was the world’s
largest clear span building at the time. Using a “huge pneumatic nylon bag” [14,
p. 216], the crown of the rigid (non-elastic) shell structure was raised to its target
height while the perimeter skirt was attached. This project demonstrates that
large and heavy dome-like can be lifted in a controlled and safe manner with
pneumatic formwork.
Figure 5: Left: Pneumatic formwork system for the large Union Tank Car Dome
in Wood River [15, p. 267], Right: The large nylon bag [12]

3 Review of relevant elastic grid shell projects
The following tables collate the most significant and relevant western elastic grid
shell buildings built since the 1960s. While many comparison tables on elastic
grid shells exist in published work, none have been as thorough or as the detailed
documentation provided by Otto et al in the 1974 IL13 publication from the
University of Stuttgart [2, pp. 268–309]. The following tables performs a similar
task but are populated by modern projects. It can be observed that since 1975,
the clear span of western elastic grid shells has never since achieved nor
exceeded the 60m clear span of the Multihalle Mannheim.
Figure 6: Clear span of grid shell buildings: a) Essen Pavilion, b) German
Pavilion, c) Seibu, d) Multihalle Mannheim, e) Japan Pavilion, f)
Weald & Downland, g) Savill Garden, h) Chiddingstone Orangery, i)
Soliday Pavilion, j) Flying Dome, k) Creteil Church
0
10
20
30
40
50
60
70
1950 1960 1970 1980 1990 2000 2010 2020
Span (m)
Year
Clear span of grid shell buildings
ab
c
d
e
f
g
h
i
j
k

Table 1: Comparison table part 1
[2], [16]
[2], [16]
[16, p. 246]
[16], [3]

Table 2: Comparison table part 2
[17][18]
[4]
[19]
[20][21]

Table 3: Comparison table part 3
[22]
[23]
[24]
4 Erection methods
The authors acknowledge four main viable means of elastic grid shell erection:
“pull up”, “push up”, “ease down” and “inflate”. All but one of these methods
have so far been employed for the erection of elastic grid shells. At the time of
writing, the authors are unaware of elastic grid shells that were erected by means
of pneumatic formwork.
Soliday Pavilion Flying Dome Creteil Church
Year 2011 2012 2013
Location Paris, France Berlin, Germany Creteil, France
Client Solidays' Fest ival UdK Berlin Eglise catholique du Val de Marne
Architect - - -
Engineer Olivier Baverel E. Lafuente, C. Gengnagel Esmery Caron / Olivier Baverel
Node de tail
Node
description
Standard s wivel scaffold connectors . "Doub le clamps" from sailing indust ry. Stand ard swivel scaffold connect ors.
Formfinding
method
Compass method Sphere + VaryLab mesh Compass method
Erection
method
"lift up"
crane & cable "push up"
by hand "lift up"
crane & cable
Material
GFRP from Topglass (polyes ter resin
from DSM & Owens Corning glass
fibre)
GFRP (Fibrolux GmbH)
GFRP from Topglass (polyes ter resin
from DSM & Owens Corning glass
fibre)
Round: 41,7 x 3mm Round: 20mm x 2mm Roun d: 41,7 x 3mm
1m 0.66 - 1.27m 1m
Cladding
Polyester fabric, doub le sided PVC
coated, 750 g/m2 + glass fibres
None.
Polyester fabric, doub le sided PVC
coated, 750 g/m2 + glass fibres
Shear stability "Third layer" GFRP tube. "Third layer" GFRP tube. "Third layer" GFRP tube.
Grid type Regular Irregular Regular
25m x 15m 10m 25m x 15m
Pitch 7m 5m 7m
pre-fab
Two scaffolding swivel conn ectors.
Limited bending s tiffness in joint.
80mm aluminium tube, diameter 30mm,
5mm wall thickness. M5 bolts clamp fit
against o uter wall of GFRP tube. No
penetration .
Threaded s teel bar into steel soc kets.
Steel sockets with three through-bo lts
to resist b i-directional bending and
torsion.
on site
None None None
Cross section
Grid size
Span
End-to-end
connection

Figure 7: Erection methods for elastic grid shells: 1) “pull up”, 2) “push up”, 3)
“ease down”, 4) “inflate”
4.1 “Pull up” (crane & cables)
The first known example of a timber elastic grid shell was the experimental
prototype by Frei Otto built in Essen in 1962. This 15m grid shell was erected by
means of a single mobile crane (fig. 8, left) but also wooden stilts were used to
support the perimeter. The German Pavilion at the 1967 Expo in Montreal was
also erected by cable hoists suspended not from a crane but instead from an
existing cable net structure (fig. 8, right). More recent examples of cable and
crane erection are the Soliday Festival and Creteil Church grid shells by Baverel,
fig. 9.
This erection method has the benefit of speed, however there are several
disadvantages. Cables, even when branched off into clusters of fixing points
introduce large point loads and subsequent stress concentrations into the
structure. While clusters of wires will better distribute the applied vertical loads
(out-of-plane), they introduce compressive membrane forces (in-plane) which
will increase buckling risk for the laths.
Furthermore the crane erection method can only apply force in the vertical
direction and is not restrained in the horizontal direction. The lack of horizontal
restraint from the cables is beneficial due to the necessary grid distortion during
erection. However global horizontal restraint of the grid shell itself or at least its
edge must be provided by separate means. Typically crane erection requires very
calm weather and is only practical for small shells.
Figure 8: Left: crane erection of the Essen Gridshell [3, p. 101], Right: cable
hoists from existing cable net lifting the German Pavilion [2, p. 247]
Figure 9: Crane erection of the Soliday Pavilion left [25, p. 10], and the Creteil
Church right [26]
1) 2) 3) 4)

4.2 “Push up” (static formwork / jacking towers)
Originally, the Multihalle Mannheim was planned to be erected using four 200
tonne cranes but eventually a system of jacking towers was devised by the
contractors and engineers in order to cut costs [3, p. 131]. 3.5m by 2.5m H-
shaped spreader beams were connected via ball joints to the 1m square
scaffolding towers which were up to 17m tall. These towers were jacked up
vertically using fork lift trucks which were able to accommodate the necessary
lateral translations of the lifting points.
A key feature of the erection process was that “the lattice was anchored with
cables at certain key points to prevent collapse”. The spacing between the towers
was 9m such that the laths themselves deflected by 200mm under bending from
self weight. This deflection had to be gradually reduced to around 50mm by
progressive stiffening of “strips” along the grid shell followed by height
adjustment of grid zones.
Figure 10: Horizontally unrestrained jacking towers as used for the erection of
the Multihalle Mannheim [2, p. 312]
4.3 “Ease down” (hydraulic/mechanical formwork)
The three most recent timber elastic grid shells built by Buro Happold (Japan
Pavilion, Weald & Downland Centre, Savill Garden) were erected by means of
scaffolding support underneath the entire grid shell area coupled with
incremental and controlled displacement of the laths. Under the UK’s 1994
Construction Regulations, the hazards of working at height under a temporarily
supported structure, as was the case at Mannheim, are no longer permitted [4, p.
440]. The erection of these three projects all made use of the modular scaffold
system PERI-UP, including the MULTIPROP jack. The unique aspects of this
method is the high layout level for the flat grid, from which gravity is harnessed
and the laths are gradually displaced downwards (allowing also for lateral
movements). Scaled physical models played a crucial role in planning, predicting
and checking the erection process [4, p. 443]. Detailed labelling and measuring
of the structures during deformation was carried out to monitor and control the
process. Additional straps and ratchets were required to initiate further
“scissoring” in order to successfully form the crowns and valleys of the Weald &
Downland Centre.

Figure 11: The Savill Garden grid shell was lowered into position gradually with
vertically adjustable formwork [27]
5 Pneumatic formwork for elastic grid shells
One of the most comprehensive and relevant works on pneumatic formwork for
dome-like structures is the chapter “Pneumatic Formwork for Irregular Curved
Thin Shells” by Hennik and Houtmann from the book “Textile Composites and
Inflatable Structures II” [28, pp. 99–116]. While the work focuses on the
application for concrete shells, many of the findings and references are relevant
and applicable to elastic grid shells. Guidelines on permissible sag for pneumatic
structures are available from Herzog [29] as well as various building codes. The
level of sag is dependent on the following factors: Internal static pressure,
external vertical load, membrane stiffness, curvature of the pneumatic formwork
and aspect ratio of the cushion (height/width). Flatter zones of a pneumatic
cushion are better able to resist vertical external loading with low static pressures
than “steep” surfaces and small horizontal contact areas, fig. 12. And yet, small
curvatures while beneficial for erection are undesirable for the final shell
geometry due to the resultant low shell stiffness. Therefore the shape of the
pneumatic formwork and the final grid shell must be developed in unison.
Figure 12: Free body diagram for static pressure and dead load for flat (A) and
steep (B) zones. [28, p. 108]
The self weight of wet concrete for a “thin” 100mm shell is 2.5kN/m2.
Comparatively, the self weight of a typical timber elastic grid shell will be in the
range of 0.1 to 1.0 kN/m2. As such the self weight applied by the grid shell and
subsequent sagging will be significantly less problematic than for concrete
shells. Furthermore, during curing concrete shells are extremely sensitive to
deformations and strains. By their nature, actively-bent grid shells on the other
hand can comfortably sustain large deflections (as long as stress concentrations
and utilisation are managed). However it is important to remember the role of air
moisture and speed of erection for certain timbers. The Chiddingstone Castle
Orangery grid shell experienced high ambient temperatures and low humidity
during erection such that the laths were regularly wetted to maintain moisture
levels [21]. Furthermore, over or undershooting the target shape due to air

temperature changes can lead to incorrect curvatures in the final shape which
could result in stability failure. While Neff and Sobek showed that rotationally
symmetric pneumatic structures can be stabilised by circumferential
reinforcement or by the addition of fluid, more recently in 2014, design group
“Numen” have shown through empiric prototypes that precise shape
manipulation and sagging control can be achieved by means of extensive internal
tensile bracing [30]. However, the concept of form stabilisation for inflatable
structures by means of internal cable bracing was patented as early as 1987 [31].
Figure 13: Precise shape and sag control via internal tensile bracing [30]
The most critical challenges for the erection of elastic grid shells by means of
pneumatic formwork are concerned with the following major issues: stability and
restraint of the grid shell mechanism during erection and ensuring that the target
surface geometry is achieved despite sagging of the cushion. It is proposed that
regardless of cushion type, the grid shell should be raised to a height higher than
its final destination such that the beam ends can be lowered to their supports via
deflation in a controlled manner.
6 Student workshop tests
To trial the proposal, a 2x3m grid shell made from 5cm strips of 7mm thick
flexible plywood was erected by means of a pneumatic cushion within the
context of a student workshop at the Department for Engineering Design and
Technology at the University of Arts Berlin. The grid shell geometry was form
found by means of the educational software tool “Push Me Pull Me 3D”[32].
The experimental erection of the model grid shell demonstrated a successful trial
highlighting the potential for the method as well as some of the difficulties such
as controlling the shape and sag of the cushion. Additional simulations have been
begun by the authors but were not ready for publishing at the time of writing.
Figure 14: Initial experimental trial of pneumatic formwork for the erection of
scaled model elastic grid shell.

Figure 15: Inflation sequence of scaled model.
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