Sydney Opera House 50 years on

The Roof

The SOH is full of misnomers, including its own name. The Sydney Opera House was intended primarily for symphony concerts, with opera coming second. These were then followed by ballet and dance, choral works, and pageants / mass meetings, in that order (Government of the State of New South Wales 1956). But the term Opera House was used early on and stuck: Sydney Concert Hall just didn’t have the same ring to it.

Similarly, the roofs are referred to as shells, but that only describes the initial scheme design. While it was hoped that membrane action would enable the forms to work, physical model tests demonstrated that the bending moments in the shells were far too large (Blanchard, Model tests for the SOH 1968) and another approach was needed.

While the roof schemes consistently had pairs of curved surfaces meeting at a ridge, the initial shapes were just freehand curves. Over the next six years, while the construction of the foundations and lower structure continued on site, the team of Arup and Utzon explored option after option: parabolic, elliptical, steel, concrete. Eventually they found the scheme that respected the original concept, was structurally sound, and could be built with the maximum repetition possible with the technology of the time. The final design had all the major roofs as segments of the same sphere (SOH n.d.).
 

Figure 2 History of the development of the roof design: 1957 - 1963 © Arup

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Apparently, a spherical scheme had been suggested by Arup engineers, rejected by Utzon, but accepted later when one of Utzon’s team came up with it…

Why was the spherical option so good? Early on, Arup recognised that a true shell would not work at these scales (the largest roof was 55 m high) so the construction would need to be precast concrete ribs that fan out from the springing point, post-tensioned in both directions to achieve shell-like behaviour. A spherical approach meant that the curve on every element was identical and that each cross-section, at the same distance from the springing point, was also identical. Starting at the springing point as solid T sections, gradually widening with height to an open Y, these ribs were built in maximum 4.6 m lengths to keep them within the tower cranes’ lifting limits. The result was that the two hundred-plus ribs were all built using just a dozen profiles.

Keeping the roofs spherical also allowed the tiled outer surface to be prefabricated. Each of these units had ceramic tiles fixed onto precast concrete shells, which were size matched to the ribs below and hung from them. This enabled both efficient fabrication and avoidance of differential thermal effects between the cladding and structure.
 

 

Analysis of the roof

While some use of computers had been made at Arup in the late 1950s, for solving large simultaneous equations and the like, this would be the first time that a digital approach would be the primary structural analysis (Ahm 1968).

"It was clear in these early days that to achieve a solution at all, to make it possible to build the structure, extensive use of electronic digital computers was necessary. It would otherwise been almost impossible to cope with the sheer quantity of geometric problems, let alone the complexity of the analytical work." (Arup and Zunz, SOH 1969).

Note the clarification of electronic digital computers: this was necessary retronym to differentiate the work from human and analogue computers.

 

The analysis of an early roof scheme had included a physical model; the then standard approach for complex structures. This was made in Denmark out of white Perspex at 1:60 scale, then shipped to Southampton University for testing under the supervision of Arup engineers, including then graduates Peter Rice and future Arup chair Bob Emmerson (Blanchard, Model tests for the SOH 1968). While subsequent schemes did not include physical structural test models, surface pressure loads were derived using models in wind tunnels.

As mentioned above, the shell roofs were a series of circular ribs, connected to their neighbours at discrete points and tied to a ridge member. This meant that despite the complexity of the roofs in 3D, each rib, with its curvature, varying cross section, and multiple load cases, could be analysed in 2D finite element analysis (Blanchard, The available programs 1968).

“It must be remembered that this was one of the first large-scale applications of electronic computers to a building structure and was made at a time when the capacity and speed of the machines, the number of available programs and the sophistication of the languages, were very much less than they are now.” (Arup and Zunz, SOH 1969)

At this time (the early 1960s) even the analytical methods were under development, so that the structure was analysed using both flexibility matrix and stiffness matrix approaches. The initial stiffness matrix analysis was limited to just eighteen joints (nodes), though was later expanded, allowing it to analyse models with thirty-five joints in fifty-five minutes.

The ribs were also analysed using a 3D flexibility matrix program (written by Peter Rice). The analysis assumed that they were statically determinate by adding redundant releases. Then the effect of each redundancy was analysed and added, giving the final major, minor, and torsional moments. This approach allowed the analysis of a small complete roof or half of a larger roof in three hours.

The largest model had 136 joints and five load cases. It took three weeks to create the model data and ran in four hours. In comparison I have an Oasys GSA model of a SOH roof, with 1304 nodes and 13 load cases, which runs in under two seconds.

The running costs of these early computers were not inconsequential. The 1968 computing special of the Arup Journal mentions a machine cost of £1 per minute, using the in-house machine that filled a large part of Arup’s Fitzroy Street office basement (Wymer 1968). Four hours of computer time then cost £240. Allowing for 56 years of inflation, an equivalent cost of the analysis run would be over £5,200 today. It is not surprising that while the engineers were encouraged to use the computer, they had to first justify the use to the Computer Group. They also had to demonstrate that they had done sufficient preliminary analysis of the problem.

Despite the costs, Arup felt that the computer analysis saved them time, money, and frustration, by automating the tedious and complex calculations required for the SOH roof geometry. The computerised approach to the analysis also led to an early incarnation of Building Information Modelling (BIM): the Arup design team were able to derive and issue about 90% of the setting out information to site in the form of computer printout (Beckmann 1968).

Similarly, the complex geometric constraints on the glass walls between the shells required a parametric approach, deriving their surface geometry of cones intersecting with the vertical line from a particular roof rib. This also automated the calculations of the moments on and reactions from each mullion, and output the six dimensions required to cut every laminated glass sheet (four edges and two diagonals) needed by the fabricator (Croft and Hooper 1973).

Conclusion

Though highly controversial at the time of its construction, the Sydney Opera House has since become a defining symbol of Australia and is celebrated as a UNESCO World Heritage site (UNESCO 2007).

Over the course of its 16 years of design and construction, the SOH pushed structural analysis into the digital age, pioneering techniques and technologies that are now commonplace. All this was achieved on computer hardware orders of magnitude larger and slower than modern smartphones; all done, not with mice and graphical user interfaces, but with paper tape and reams of numerical output. Without the electronic digital computer, we might not have the SOH, nor the engineering marvels that followed it. The SOH kickstarted the digital revolution in structural engineering.

And just three years after the SOH opened, the Arup Computing Group started to sell their programs to the world. This was not under the name of Arup, as consulting engineers were not allowed to advertise at that time, but under the brand Oasys - Ove Arup SYStems - which I am proud to be a part of. It’s still going strong, producing engineering programs that started with the SOH over sixty years ago (Oasys 2024).

Key Dates

Bibliography

Ahm, Povl. 1968. “Arups and the computer.” The Arup Journal 1: 3. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1968-issue-1 

Arup. n.d. Celebrating our enduring relationship with the Sydney Opera House. Accessed April 2024. https://www.arup.com/partnering-with-clients-celebrating-60-years-of-work-with-the-sydney-opera-house

. n.d. Designing the Sydney Opera House. Accessed April 2024. https://www.arup.com/projects/sydney-opera-house.

Arup, Ove, and Jack Zunz. 1969. “Sydney Opera House.” The Structural Engineer 47 (3): 99-132. https://www.istructe.org/journal/volumes/volume-47-(published-in-1969)/issue-3/sydney-opera-house/.

Arup, Ove, and Jack Zunz. 1973. “Sydney Opera House.” The Arup Journal 4-21. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1973-issue-3.

Beckmann, Poul. 1968. “The future of our computer.” The Arup Journal 19. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1968-issue-1.

Blanchard, John. 1968. “Model tests for the Sydney Opera House.” The Arup Journal 60. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1968-issue-3.

Blanchard, John. 1968. “The available programs.” The Arup Journal 9-13. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1968-issue-1.

Croft, David, and John Hooper. 1973. “The Sydney Opera House glass walls.” The Structural Engineer 51 (9): 30-39. https://www.istructe.org/journal/volumes/volume-51-(published-in-1973)/issue-9/the-sydney-opera-house-glass-walls/.

Government of the State of New South Wales. 1956. “Opera House Competition Guidelines.” Sydney Opera House. Accessed April 2024. https://www.sydneyoperahouse.com/our-story/jorn-utzon.

Oasys. 2024. History. Accessed April 2024. https://www.oasys-software.com/about-us/history/.

Rice, Peter. 1994. An Engineer Imagines. Ellipsis London Ltd.

Sydney Opera House. n.d. Our Story. Accessed April 2024. https://www.sydneyoperahouse.com/our-story.
—. n.d. The Spherical Solution. Accessed April 2024. https://www.sydneyoperahouse.com/our-story/the-spherical-solution.

UNESCO. 2007. Sydney Opera House. Accessed April 2024. https://whc.unesco.org/en/list/166/ 

Wymer, Charles. 1968. “Using the machine.” The Arup Journal 14-16. https://www.arup.com/perspectives/publications/the-arup-journal/section/the-arup-journal-1968-issue-1  

 

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