The Design and Analysis of "Quantum Cloud" - a sculpture
by Antony Gormley
"Quantum Cloud" is a 30 metre high x 16
metre wide x 10 metre deep elliptical cloud sculpture which stands on four cast iron
caissons in the River Thames adjacent to the Millennium Dome in London. It is the latest
work of "Angel of the North" sculptor, Antony Gormley, and is formed
from 1.5 metre long lengths of randomly oriented steel sections which diffuse at the edges
and condense into a 20 metre high human body form at the centre. It is currently the
tallest sculpture in the UK.
The engineering design team of Elliott Wood Partnership and FEA Ltd
worked closely with the sculptor to develop the full scale realisation of his vision for
the client, the New Millennium Experience Company. Fractal growth software written by FEA
was used to develop the structural form, and LUSAS finite element analysis modelled and
analysed the unique structure.
Overview of the structure
whilst visually random in nature, in fact consists of three distinct regions. A central
structural core of 1.65m sided, tetrahedral steel units provides support for an outer
steel tendril region that forms the cloud shape, and also provides the restraint for an
inner body form structure. The structural core rests on a lattice of 533x210x92 Universal
Beams via stools at every tetrahedral and lattice intersection. The steel lattice beams
are, in turn, bolted to 1016x305x272 Universal Beams that span between the four existing
the 325 tetrahedral units is formed from four, 1.5m long, steel hollow sections welded
together. Every unit is connected to its neighbours by a unique casting to which it is
initially connected via steel pins that are subsequently removed after the joints are
welded. Each tendril is fabricated in one piece for bolting to a spigot on the
main core. The body form members are threaded through the core and also held in place by
spigots. Galvanised, steel, 70x70x5 Square Hollow Sections are used throughout the core
and for the first member of the tendril that is welded to it. 70x70x3.6 Square Hollow
Sections are used elsewhere. Grade 50 steel with a yield strength of 420Mpa was used
throughout the structure with the exception of certain members at the base of the core
where steel with a certified 25% greater yield strength is used. In all, approximately
5.5km of steel section is used, weighing nearly 50 tonnes in total.
Generation of the structural forms
|Laser scans of the sculptor's body provided the raw data to define a 3D boundary
or 'domain' of the body form. The structural
core of the sculpture required as large a footprint as possible to help resist prevailing
wind forces. This, in conjunction with the estimated number of castings that could be
fabricated within the time available ultimately dictated the size of the structural core
into which the body was fitted.
To generate the
arrangement of members in the central structural core, FEA wrote custom software that,
from an initial starting point at the level of the supporting steel lattice, generated a
randomly oriented layer of tetrahedral units to occupy the width of the domain for a
particular level of the structure. Once one layer was complete, the software then used the
previously created nodal data to build the next layer, and so on, until the supporting
structural core of 17 layers was complete. An additional layer of tetrahedral units was
also generated beneath the supporting steel lattice to provide fixity for the tendrils in
- Chaos theory and fractal growth
techniques were used to create the outer tendrils representing the cloud structure.
- Using the same specially written software that generated the core, and
working from the stored nodal data for the edges of the core, tendrils were 'grown' from
the outermost tetrahedral units in a series of up to 5 organic growths or 'expansions'.
- A database of member locations was stored by the fractal software and
used to enable clash detection of new members with previously generated ones.
- Similar fractal techniques generated the arrangement of the body
form members using the specified body domain to limit the area of growth.
- The first complete set of tendril and body member generations gave an
indication of how much steel would be required to create the sculptor's desired visual
appearance and also provided an initial estimate of the total weight of the structure.
- The fractal software also generated LUSAS modelling and analysis data
files, a DXF file for use in creating detailed member design drawings and an input file
for SolidWorks which was used to create 3D casting models for subsequent rapid
As Geoff Paice, Deputy Head of Engineering Services at FEA explains:
"Our custom software converted the digital design directly into fabrication schedules
and erection drawings, thereby minimising the traditional paper-copy approach and
virtually eliminating manual drafting requirements. This potentially saved the project
months of CAD time and allowed the design to evolve while the fabrication proceeded."
Preliminary analysis and testing
A preliminary LUSAS analysis of the core at an early stage of its
development was carried out to find its Ultimate Limit State and to see if the proposed
method of design and analysis needed to be re-assessed. In modelling the structure, 2
engineering beam elements were used for each tetrahedral member and the castings were
modelled using a separate beam element for each leg joint. A single tetrahedral unit was
built and load tested to failure by the fabricators, Tubeworkers (Structures) Ltd. This
unit was also modelled, loaded and analysed in LUSAS. The results correlated extremely
well, showing the same failure mechanism, and verified the proposed modelling approach.
Prior to the full development of the structure, a trial assembly of 10 tetrahedra in a
pyramid of 3 layers was performed to prove both the construction sequence and the accuracy
of the fabricated components. This confirmed that the designer's methodology was suitable.
Structural development and the exchange of project data
In a series of iterative processes the final form gradually began to evolve. The
LUSAS web site was used as a live communication tool by the project partners to exchange data and view proposed
designs. Ray traced images and VRML models of potential structural forms, created by using
the LUSAS Programmable Interface (LPI), were put onto the web site to allow the sculptor
to examine the structure from every conceivable angle, and to make suggestions for
improvements. This totally eliminated the 'paper copy' approach and helped to speed-up the
development process enormously.
For each re-development of the tendril region, wind assessment with a 25
year return period was carried out to BS6399 : Part 2 : 1995, The Code of Practice for
Wind Loading, to see how dense the cloud could be built. The wind loading assessments
provided a set of equivalent loads which were applied to the core members in the LUSAS
model for each of the eigenvalue and nonlinear analyses of the structure. Applying
equivalent loads in this way reduced the model size and helped to speed-up the solution
At every project landmark, eigenvalue analyses of the whole structure
were carried out to assess likely wind induced oscillations. In addition, a detailed
analysis of one of the longest tendrils was done using full wind loading acting as a
dynamic pressure to evaluate the bending moments at the bolted connections. Once all
aspects of the structure had been approved a final, more rigorous, elasto-plastic analysis
was performed with the certified higher strength steel members in those regions where the
earlier analyses had indicated high stress concentrations.
In carrying out the wind assessment, two
shielding calculations were performed. The empirical method of Eden, Butler and Patient
was used initially to calculate the "total" solidity of the frame. This method
sums the projected areas of all members and divides by the total envelope area. A more
rigorous shielding analysis method for multiple plane frames was also used as described in
"The Designers Guide to Wind Loading of Building Structures, Part 2: Static
Structures". This method divides the space envelope of the sculpture into 1m3
zones. The layers normal to the wind were considered as "plane frames"
positioned at the centre of the layer, and the system was analysed as a series of 17
frames. Each 1m2 of cell on elevation was treated separately so that the
variation of solidity on elevation could be captured. The shielding effect of upstream
frames was computed using a summation method, leading to a build-up of shielding on the
downwind frames. In fact, the members at the back of the densified zone are almost totally
shielded. In both cases, a complete model of the sculpture was used for calculations, in
which, structural core, body form, and tendril expansion zones were included. It provided
a reasonable basis for the assessment of solidity through the structure for the most
onerous condition of a face-on wind.
Using the comprehensive results processing facilities in
LUSAS, maximum and minimum envelopes of factored dead and wind loading were defined and
the results were selected for viewing. The Groups facility was of particular use in this
analysis where the structure is so complex and plotted values cannot be easily seen. The
use of Groups allowed the results for a particular layer or region of the structure to be
looked at in isolation, as for example, for each layer of the structural core where a
force/moment diagram was plotted to show stresses and bending moments in each of the
The use of innovative engineering ideas from all members of the project
team, FEA's skill in producing complex custom software to grow and develop potential
structural forms, and the use of LUSAS Civil and Structural analysis software to
model and prove the structural integrity of the sculpture, ensured that the design and
analysis of a complex structure was completed to the sculptor's satisfaction in a very
Antony Gormley, in realising his vision, said, "Quantum Cloud
is a project that can only be realised with digital design systems and I am very fortunate
to have collaborated with energetic and ground-breaking engineers. The result, a
combination of art and technology, will be a monument to the future, expressing the
potential of the human being at the end of the twentieth century."