Tensile structure
This form of construction has only become more rigorously analyzed and widespread in large structures in the latter part of the twentieth century.
Russian engineer Vladimir Shukhov was one of the first to develop practical calculations of stresses and deformations of tensile structures, shells and membranes.
A more recent large-scale use of a membrane-covered tensile structure is the Sidney Myer Music Bowl, constructed in 1958.
Antonio Gaudi used the concept in reverse to create a compression-only structure for the Colonia Guell Church.
He created a hanging tensile model of the church to calculate the compression forces and to experimentally determine the column and vault geometries.
Since the 1960s, tensile structures have been promoted by designers and engineers such as Ove Arup, Buro Happold, Frei Otto, Mahmoud Bodo Rasch, Eero Saarinen, Horst Berger, Matthew Nowicki, Jörg Schlaich, and David Geiger.
The low weight of the materials makes construction easier and cheaper than standard designs, especially when vast open spaces have to be covered.
Common materials for doubly curved fabric structures are PTFE-coated fiberglass and PVC-coated polyester.
Other structures make use of ETFE film, either as single layer or in cushion form (which can be inflated, to provide good insulation properties or for aesthetic effect—as on the Allianz Arena in Munich).
In daylight, fabric membrane translucency offers soft diffused naturally lit spaces, while at night, artificial lighting can be used to create an ambient exterior luminescence.
Steel spiral strand cables have a Young's modulus, E of 150±10 kN/mm2 (or 150±10 GPa) and come in sizes from 3 to 90 mm diameter.
In order to induce an adequately doubly curved form it is most often necessary to pretension or prestress the fabric or its supporting structure.
The behaviour of structures which depend upon prestress to attain their strength is non-linear, so anything other than a very simple cable has, until the 1990s, been very difficult to design.
The most common way to design doubly curved fabric structures was to construct scale models of the final buildings in order to understand their behaviour and to conduct form-finding exercises.
Such scale models often employed stocking material or tights, or soap film, as they behave in a very similar way to structural fabrics (they cannot carry shear).
For example, this has in the past caused the (temporary) collapse of the Hubert H. Humphrey Metrodome, an air-inflated structure in Minneapolis, Minnesota.
Pretension is tension artificially induced in the structural elements in addition to any self-weight or imposed loads they may carry.
The alternative approximated approach to the form-finding problem solution is based on the total energy balance of a grid-nodal system.
is added to the cable, the extension becomes: Combining the above equations gives: By plotting the left hand side of this equation against T, and plotting the right hand side on the same axes, also against T, the intersection will give the actual equilibrium tension in the cable for a given loading w and a given pretension
