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DESIGN OF A TENSION FABRIC STRUCTURE WITH ANALOGY TO

NATURE

W. J. Lewis, S. Chen A. J. Corcoran, J. Connell, R. D. Flew, R. Hill, M. Kashef Alghata,

R. Rameez, A. S. Abi Sofian

School of Engineering, University of Warwick, UK

ABSTRACT

The aim of the project was to design a small-to-medium size tension fabric structure to rejuvenate a chosen area on University campus. The structure was to have an aesthetic appeal, with the fabric membrane having a minimum life-span of 15 years. The structure is an impressive culmination of a fourth year project which incorporates aspects of civil engineering and architecture. A considerable benefit realised from the project was the learning experience for the students, encouraging self-development in many different aspects: creativity, understanding of unconventional concepts, appreciation of the underlying theory and design methodologies.

INTRODUCTION

Presently, we observe growth in out-door living spaces and shelters from the elements, including solar radiation. Tension fabric structures have the potential to meet the demand in this area, but, to date, have been mostly utilised as large-size roofs over sports stadia and exhibition halls (Figure 1). Provision of attractive, small to medium size architectural enclosures has been relatively poor. This situation can be attributed to three main factors: (i) complexity of design, which still lies within the research domain rather than established practice, (ii) cost, and (iii) the need to incorporate both

architectural and engineering skills developed on a sound educational basis.

This article presents the story of the design of a tension fabric structure carried out by a group of Civil Engineering students at the University of Warwick, supervised by Professor Wanda Lewis and assisted by her PhD student, Stuart Gale, The project was carried out in collaboration with an industrial partner, Carter & Son (Thatcham) ltd. The design is a unique, previously unexplored shape, based on research into natural forms; it has aesthetic appeal and blends sympathetically with its surroundings (Figure 2). PROJECT AIM AND SCOPE

The aim of the project was to design a small-to-

medium size tension fabric structure to rejuvenate a chosen area on University campus. The structure was to have an aesthetic appeal, with the fabric membrane having a minimum life-span of 15 years.

The scope of the project included: (i) Conceptual designs involving sketches and

small-scale physical models (ii) Computational analysis and design of the full-

size structure, involving iterative refinement and interaction with physical models

(iii) Cost-benefit analysis

Fig. 1. Millennium Dome, London

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Fig. 2. Image of a proposed tension fabric structure

PRELIMINARY DESIGN

Fabric under tension develops a unique surface geometry, dependent on the chosen boundary conditions/configuration and the level of pre-stress. Therefore, it is not possible to define/impose the shape of a fabric structure using just architectural/engineering drawings; at the conceptual design stage, physical models are invaluable in producing first impressions of the structure, informing the designer about potential

problems with structural function, such as insufficient headroom, area coverage, or inadequate surface curvatures in the fabric membrane to drain water effectively. Conceptual design in this project involved research into the supporting structure as well as the fabric membrane. The Figure 3 below, charts the progression of the design concepts, which were inspired by nature. The final concept is shown in Figure 4.

Fig. 3. Initial sketches and design concepts realised by physical models

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The final concept, shown in Figure 4, consists of a supporting structure with three straight-line branches and three curved ones underneath a 6-panel fabric membrane.

Fig. 4. Final concept

DESIGN OF A FULL-SIZE STRUCTURE Supporting structure

The model shown in Figure 4 has been scaled up to a real-size structure. Figure 5(a) shows the overall dimensions of its supporting elements. The structure covers an area of ~20 m2.

Logarithmic spiral as an optimal branch form

Research carried out into an optimal shape of the curved branches resulted in adopting a part of a logarithmic spiral (Fig.6) as the final form. Logarithmic spiral is a naturally occurring form present within many natural structures that are tip loaded or subjected to uniformly distributed loads. One such example is a tiger’s claw whose contour produces a constant stress state under “service” conditions, where no point is more susceptible to failure than another, and no superfluous material is contained within the claw (Mattheck, C., Reuss, S., 1991). This shape had evolved to allow a fully grown tiger, weighing up to 306 kg, to support its entire body weight through its claws, as it hangs off the back of its prey, or climbs trees. The design rule of the logarithmic spiral is viewed as part of the more general constant stress hypothesis valid for all biological load carriers (Mattheck, C., 1990).

In this project, the supporting branches are tip loaded by the tension forces in the membrane and hence, the analogy seems appropriate. A tentative analysis of the branches using GSA software revealed the stresses in the logarithmic spiral branch to be lower than in a circular, or parabolic, profiles. Apart from the superior structural performance, the logarithmic spiral form also has an inherent aesthetic appeal.

Fig. 5. Supporting structure (a) overall dimensions of the supporting structure; (b) detail of a fabric–to-branch

connector

Fig. 6. Logarithmic spiral shape of curved branches

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Fabric membrane design

The fabric was chosen to be a PVC-polyester material, with an induced uniform pre-stress of 3.5KN/m in both the warp and weft directions of the weave (Fig. 7). The low level of pre-stress, ~5 % of the material breaking strength, was due to the anticipated high increase in stress under wind and snow loading, plus a high recommended factor of safety (5 or 6).

The membrane consists of six panel pieces, plus an additional central ‘cap’ to reinforce membrane in the region of high stress. Edges of the membrane contain inside pockets to allow the boundary cable to run through and be tensioned at the connection shown in Figure 5 (b).

Three stages to fabric membrane design had to be followed: (i) Form-finding, aimed at establishing a detailed surface configuration of the membrane under pre-stress (ii) Load /displacement analysis- aimed at finding stresses in the fabric under imposed loads, such as wind and snow, to ensure that the combined stresses do not exceed the design strength of the material. This was accompanied by displacement analysis to ensure that large displacements, expected of these highly flexible structures, do not interfere with the structure’s function. (iii) Patterning, aimed at shaping pieces of unstrained fabric from which the membrane is to be manufactured.

Form-finding. Concept of a minimal surface

As indicated earlier, the shape of a tensioned surface structure cannot be imposed, because of its highly non-linear response to loading; it has to be found through a computational form-finding process [Lewis, W. J., 2008, Lewis, W. J., 2003, Lewis, W.J. and Kowalinska, D., 2008). In this project, the shape of the fabric membrane is intended to resemble a stable minimal surface; a surface analogous to a soap-film (Fig. 8), which adopts its configuration by minimising potential energy of surface tension (Hildebrandt, S. and Tromba, A., 1984, Isenberg, C., 1978).

It has been acknowledged in the European design Guide for fabric structures (Barnes, M., Gründig, L., and Moncrieff, E., 2003) that minimal surface membranes are likely to have improved durability, as they suffer less from fatigue, compared to differentially stressed membranes, which are characterised by different levels of tensions in the warp and weft directions.

The process of computational form-finding consists of iterative calculations in which the shape of the membrane is gradually altered until the structure is in full static equilibrium under the prescribed initial tension. There are numerous numerical from-finding finding methods in existence; the one used in this project is based on the dynamic relaxation technique with kinetic damping [Lewis, W. J., 2008, Lewis, W. J., 2003, Lewis, W.J. and Kowalinska, D., 2008) offered by GSA software.

Load/displacement analysis

The computational load/displacement analysis can rely on a slightly modified numerical algorithm used for form-finding, except that, here, the shape of the structure has to be found not under pre-stress alone, but under pre-stress combined with imposed loading. The dynamic relaxation algorithm offered by the GSA software was again used to complete the analysis. It was found that the tension levels in the membrane under snow and wind loading increased to a value of ~ 9 kN/m.

It was also found that the initial pre-stress of 2 kN/m was insufficient to limit deflections, so it was increased to 3.5kN/m, as indicated earlier. The results for combined wind and snow actions are summarised in Figure 9.

As expected, the maximum deflections occurred in the areas of low curvature, in the vicinity of the corner supports.

Fig. 7. Weave directions

Patterning

The form found shape generated on GSA was exported into AutoCAD and converted into a mesh. The patterning procedure was then run on the mesh using MPanel software to generate six, two dimensional panels in unstrained fabric (Fig. 10). A seam allowance of 50 mm was applied to each panel to allow a lap joint suitable for fabric welding. Each panel can be cut from the fabric of 2.5 m - 3 m width.

It was possible to adopt time-saving measures through the use of the patterning software, the first of which was the ability to only focus on one third of the canopy due to the symmetrical shape. The second was the flattening, splitting, seam allowance and compensation steps could be combined.

Patterning is currently an area of intensive research aimed at reducing errors associated with flattening of 3D form-found surface membranes into unstrained pieces of fabric. As the 3D form-found surfaces are non-developable, errors associated with flattening (mapping onto a flat plane) are not negligible and techniques for their minimisation are being developed.

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Fig. 8. Model of a soap film surface formed between thread boundaries attached to the tops of posts

Fig. 9. Results of load/displacement analysis

Fig. 10. Final cutting pattern for the fabric membrane

COST BENEFIT ANALYSIS

There are several aspects to cost benefit analysis related to the project: social, economic, and environmental. These are discussed below.

Social benefit

The proposed site for construction of the fabric structure is at the rear entrance of the University House (Fig. 2), which hosts many administrative functions for the University and a working environment for students. The proposed fabric structure, or, preferably several of them, would revitalise and develop the site into a more

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sociable environment, providing an appealing area for work breaks, meetings, or enjoying food and drink. It would also serve as an extended workspace for students to read and revise outdoors.

Economic benefit

The University House holds a coffee bar and a restaurant. The proposed structure could be replicated to provide a number of shaded areas and this would increase footfall ensuring a longer dwell time for potential customers, leading to a greater revenue.

Images of the proposed iconic structure can be used on marketing material, aimed at attracting and inspiring future students. The structure itself can be used for education purposes, which would bring a broader economic benefit to society.

Environmental benefit

The structure aims to bring a new atmosphere through aesthetic design and hence increase the allure of the area. With the style of the design based on natural forms, it will visually integrate into the setting and stimulate more interest than a regular, more rigid canopy or shelter design.

Costs

Figure 11 gives a breakdown of costs, with an estimate totalling almost £14,000. There would be an economy of scale, if more than one fabric structure was commissioned.

CONCLUSIONS

The structure is an impressive culmination of a fourth year project which incorporates aspects of civil engineering and architecture. A considerable benefit realised from the project was the learning experience for the students, encouraging self-development in many different aspects: creativity, understanding of unconventional concepts, appreciation of the underlying theory and design methodologies. All of this, combined with pragmatism in a single circumstance, and working alongside an industrial partner was a feat that isn’t experienced in many undergraduate projects. The project’s ambitious outcome and short time scale provided a valuable management experience for the students, including: organisation of meetings, task allocations, progress monitoring/retention of effort levels throughout the project, conflict resolution, and compromise in decision making.

The proposed design is a natural structural form, an engineering art piece, which blends effortlessly with its surroundings - a reflection of an innovative design, achieved through research-led teaching.

Fig. 11. Cost estimate for the fabric structure

REFERENCES

Barnes, M., Gründig, L., and Moncrieff, E. (2003) Form-finding, load analysis, and patterning. European Design Guide for Tensile Surface Structures, M. Mollaert and B. Forster, eds., Vrije Universiteit Brussels, 206-210.

Hildebrandt, S. and Tromba, A. (1984) Mathematics

and optimal form. New York: Scientific American Library.

Isenberg, C. (1978) The Science of soap-films and soap

bubbles. Clevedon, Avon: Tieto Ltd

Lewis, W. J. (2008) Computational form-finding methods for fabric structures. Proceeding of the ICE, Engineering Computational Mechanics 161: 139-149.

Lewis, W.J. and Kowalinska, D. (2008) Konstrukcje

napięte: ich forma i praca”. Wydawnictwo Instytut Śląski, Opole, Poland.

Lewis, W. J. (2003) Tension Structures. Form and

behaviour. London: Thomas Telford.

Mattheck, C., Reuss, S. (1991) The tiger claw – anassessment of its shape optimization. Journal of Theoretical Biology. 150: 323-328.

Mattheck, C. (1990). Why they grow, how they grow--the mechanics of trees. Arboricultural Journal 14: 1- 1 7.