The Design and Analysis of "Quantum Cloud"

• Steel sculpture by internationally recognised sculptor Antony Gormley

• Custom fractal growth software written to develop the structural form

• Linear, nonlinear and wind assessment analysis

"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 O2 arena and the Emirates Air Line cable car in London, UK. It is the 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. At the time of its construction, in 1999, it was the tallest sculpture in the UK. The engineering design team of Elliott Wood Partnership and LUSAS consultancy services worked closely with the Gormley to develop the full scale realisation of his vision for the client, the New Millennium Experience Company. Fractal growth software written by LUSAS was used to develop the structural form, and modelling and analysis with LUSAS finite element analysis ensured the unique structure was fit for purpose.

Overview of the structure

The sculpture, 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 caissons.

Each of 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 this region.

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 prototyping. As Geoff Paice, Deputy Head of Engineering Services at LUSAS 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.

Structural analysis

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 times.

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.

Results

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 tetrahedral members.

Conclusions

The use of innovative engineering ideas from all members of the project team, LUSAS Engineering Consultancy Services' 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 tight timescale.

"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."

Antony Gormley