Jørn Utzon proposed the design of the Sydney Opera House. Its curved roof structures required extensive engineering research; construction involved much more than simply enlarging a sketch.

Opened in 1973, the building contains several performance spaces. The collaboration between design and engineering had a lasting influence, and the opera house became a major symbol of Sydney.

Stage II: Roof

The shells of the competition entry were originally of undefined geometry, but, early in the design process, the "shells" were perceived as a series of parabolas supported by precast concrete ribs. However, Ove Arup & Partners were unable to find an acceptable solution to constructing them. The formwork for using in-situ concrete would have been prohibitively expensive, and, because there was no repetition in any of the roof forms, the construction of precast concrete for each individual section would possibly have been even more expensive.

From 1957 to 1963, the design team went through at least 12 iterations of the form of the shells trying to find an economically acceptable form (including schemes with parabolas, circular ribs and ellipsoids) before a workable solution was completed.

The design work on the shells involved one of the earliest uses of computers in structural analysis, to understand the complex forces to which the shells would be subjected. The computer system was also used in the assembly of the arches. The pins in the arches were surveyed at the end of each day, and the information was entered into the computer so the next arch could be properly placed the following day.

He goes on to claim that "the existing evidence shows that Arup's canvassed several possibilities for the geometry of the shells, from parabolas to ellipsoids and spheres." Yuzo Mikami, a member of the design team, presents an opposite view in his book on the project, Utzon's Sphere. It is unlikely that the truth will ever be categorically known, but there is a clear consensus that the design team worked very well indeed for the first part of the project and that Utzon, Arup, and Ronald Jenkins (partner of Ove Arup and Partners responsible for the Opera House project) all played a very significant part in the design development.

... the two men—and their teams—enjoyed a collaboration that was remarkable in its fruitfulness and, despite many traumas, was seen by most of those involved in the project as a high point of architect/engineer collaboration.

The design of the roof was tested on scale models in wind tunnels at University of Southampton and later NPL to establish the wind-pressure distribution around the roof shape in very high winds, which helped in the design of the roof tiles and their fixtures.

The immensely complex design and construction of the shells was completed by Hornibrook, who were also responsible for construction in Stage III. Hornibrook manufactured the 2400 precast ribs and 4000 roof panels in an on-site factory and also developed the construction processes. The achievement of this solution avoided the need for expensive formwork construction by allowing the use of precast units and it also allowed the roof tiles to be prefabricated in sheets on the ground, instead of being stuck on individually at height.

The tiles themselves were manufactured by the Swedish company Höganäs Keramik. It took three years of development to produce the effect Utzon wanted in what became known as the Sydney Tile, 120mm square. It is made from clay with a small percentage of crushed stone.

Ove Arup and Partners' site engineer supervised the construction of the shells, which used an innovative adjustable steel-trussed "erection arch" (developed by Hornibrook's engineer Joe Bertony) to support the different roofs before completion. On 6 April 1962, it was estimated that the Opera House would be completed between August 1964 and March 1965.