Keywords: tensegrity, spline, form-finding, large span, torsion free, membrane.

Although based on structural principles that have been known for many centuries (e.g. Apurimac Bridge in Peru 1350 AD [1]), it is only in the second half of the 20th century that the potential of tensile roof structures began to be realised as a direct result of the arrival of new analysis techniques and new engineered materials. Early tensile structures, though elegant in shape, were crude in detail as a result of technology that was still under development, and also due to a lack of awareness of the importance of the shaping and supporting elements in the new architecture that was being generated. Systems that shape the fabric must be expressive of their function and of the materials of which they are made. The aesthetics created by the slenderness and by the delicate equilibrium between compression, tension and bending elements in systems such as Frei Otto's model for a crane [2], the initial proposal for the Eden project and the original design for the Oleada (Expo 1992, Seville [3]) have been precedents and points of reference for this research.

This study presents an arch tensegrity system with continuous tubular compression boom forming a curved spline, which may be deployed from straight by pre-stressing a cable bracing system. This tensegrity arch supports a pre-stressed membrane of 57 m span and 29.5m total width. A spline is here defined as a spatial curve bent from an initially straight member with a uniform second moment of area about any axis perpendicular to its centroidal axis. This spline system relies on the proven fact [4] that the torsional stiffness of any continuous spline is uniquely a function of its geometric stiffness provided that the detailing does not introduce any concentrated torsional moments. For large spans above 50m, the pre-stress in the membrane alone is not sufficient to stabilise the spline under loading. The shaping system presented offers a particular approach to stiffening the spline - a tensegrity type of bracing system imbues the spline with additional bending (but no torsional stiffness). It was found that this 'torsion free' feature is adavantageous as it allows membrane stresses on either side of the arch plane to balance each other under assymetric loading conditions.

This paper reviews the feasibility of this innovative large span tensegrity spline structure for the support of pre-stressed membranes with respect to material considerations and concepts, form-finding and load analysis and makes design suggestions to extend the potential of this new type of system .

1

P. Drew, "Tensile Architecture", Crosby Lockwood Staples, Granada Publishing Ltd, 1979.

2

F. Otto, "Spannweiten", Verlag Ullstein, West Berlin, Germany, 1965.

3

M.R. Barnes, W. Renner, M. Kiefer, "Case studies in the design of wide-span Expo structures", In "International Symposium on Conceptual Design of Structures", 1, 814-824, 1996.

4

S.M.L. Adriaenssens, M.R. Barnes, "Tensegrity spline beams and grid shell structures", Engineering Structures, 23, 29-36, 2001. doi:10.1016/S0141-0296(00)00019-5

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