Early parabolic scheme, east elevation (1958/1961) by State Records of New South WalesSydney Opera House
When in 1958 the engineers at Arup and Partners requested that Utzon define the curves of the roof, he took a plastic ruler and, holding it perpendicular to a table, made it bend. Tracing the curves, he sent them to London explaining these were the shapes he wanted.
The outcome of the first exchanges between architect and engineer produced an initial sketch of the roof in which every curvature is different, a structurally unsound form with difficult bending moments near its footings.
However, this first geometrical approach to the shells was also visually beautiful in a distinctly different way to the drawings Utzon had submitted for the competition.
The ridge profiles were much higher and pointed now, and the end shell form of his competition drawings no longer cantilevered like a cliff cave over the sea.
These higher profiles also allowed far more volume for the stage towers, auditoriums and acoustics.
Red Book model, view from the Monumental Steps (1958) by State Library of New South WalesSydney Opera House
Page 13, South elevation (1958) by Jørn UtzonSydney Opera House
Utzon’s architects redrew all of the elevations of the Sydney Opera House to the new forms, and these are shown in the 1958 design documentation, known as the Red Book.
Clearly the profile of the roof had changed considerably, but it was received by the client and the public as a transformation for the better, for both logistical and aesthetic reasons.
Early parabolic scheme, southwest elevation, 1958-61 (1958/1961) by State Records of New South WalesSydney Opera House
Page 11, North elevation (1958) by Jørn UtzonSydney Opera House
Red Book model, east elevation (1958) by State Library of New South WalesSydney Opera House
Thin shell structures were the form of his original sketches and much favoured by leading architects and engineers at the time. Eero Saarinen, Felix Candela and Pier Luigi Nervi had already used concrete shell membranes in world-renowned structures.
Page 10, East elevation (1958) by Jørn UtzonSydney Opera House
Front Cover illustrating the Spherical Solution (1962) by Jørn UtzonSydney Opera House
The Yellow Book presented the "Spherical Solution" - a final design rationale for the roof of the Sydney Opera House.
The form of the shells had changed again and again, as architect and engineers struggled to find a buildable structure that captured the spirit of the design and could house the complexity of a working building.
After many failures, Utzon had a now famous epiphany that would solve what had apparently become an intractable problem.
Utzon's breakthrough was to derive each of the shells from the constant and universal form of the sphere. This one decision solved a multitude of problems. It captured the essence of the original sketch, while allowing the building blocks to be prefabricated with comparative ease.
It also raised the finished building out of a style identified with the times and gave it an ageless form.
The spherical solution underpins the roof form that we see today and is explored in more detail in "The Masterful Solution" exhibit.
Sydney Opera House: projection of the Spherical Solution (2015) by LatchkeySydney Opera House
From the beginning of their collaboration, engineer Ove Arup gently encouraged Utzon to pursue a geometry that would allow for repetition and therefore prefabrication. As early as 1958 he had suggested that the soffits of the shells (their interior surface) be ribbed to strengthen and articulate them.
By 1961, after many failures, Ove Arup and another senior engineer at Arup, Jack Zunz, resurrected the ribbed approach from 1958, pursuing the two options of a double-skinned shell structure and the ribbed form that would dramatically express the roof’s function through the exposed concrete of the shells’ interiors.
Spherical Solution, balsa and cardboard model, west elevation, 1962 (1962) by State Library of New South WalesSydney Opera House
In these models, we can see the fusion of the ribbed approach with the spherical geometry through which Utzon famously arrived at a final approach to the roof, informed by a three-year period in which Arup engineers struggled – and ultimately failed – to find a workable solution through parabolic geometry.
Page 5, West elevation (1962) by Jørn UtzonSydney Opera House
Page 27, Development of shells (1962) by Jørn UtzonSydney Opera House
Spherical Solution, bird's-eye view of the balsa and cardboard model (1962) by State Library of New South WalesSydney Opera House
Spherical Solution, bird's-eye view (1962) by State Library of New South WalesSydney Opera House
Various angles on an early model of the parabolic scheme (1960) by State Library of New South WalesSydney Opera House
Created by Sam Doust and the
Sydney Opera House GCI Team
State Library of New South Wales
State Records NSW