Many of the designs submitted during the competition phase proposed that the two halls be arranged back to back with a shared fly-tower in the centre,  Utzon regarded this concept as inappropriate since it would require two entrances at either end of the building which would be difficult to achieve on a peninsular site.  His design put the halls side by side which in itself posed challenges because the stages no longed had easy access from the sides and other systems needed to be developed for moving on and off the stage.

The site posed other problems.  It was composed of fill deposited within a sea wall. Water freely percolated through the silt.  Beneath is a bedrock of Hawkesbury sandstone that is heavily faulted and interlaced with clay seams.   The foundation for the building required 700 bored piers as well as reinforced concrete foundations on top of strip and pad concrete footings.

The politicians' nightmares referred to above, came in the form of a project that was expected to take 5 years and took 15 and in a cost overrun from the projected $3.5M to $102M.  The inevitable tensions led to a confrontation between representatives of the New South Wales Government and the architect and in March of 1966 Utzon went home to Denmark never to return.  He was replaced by a team made up of Peter Hall, Lionel Todd and David Littlemore. Over the next 10 years they along with Arup overcame what must have seemed like unfathomable problems to bring Utzun’s vision to fruition. 

The most visible of the challenges was the construction of the roof.  The Opera House website says that, "... “The design solution and construction of the shell structure took eight years to complete and the development of the special ceramic tiles for the shells took over three years. The project was not helped by the changes to the brief. Construction of the shells was one of the most difficult engineering tasks ever to be attempted. The revolutionary concept demanded equally revolutionary engineering and building techniques. Baulderstone Hornibrook (then Hornibrook Group) constructed the roof shells and the interior structure and fitout. “

Although the finished shells look like the billowing sails of ships, they disguise the fact that they are in fact made up of a series of concrete ribs arranged in a fan-like structure.  Arup explain that, "... The roof structure covers the two main halls and the restaurant. There are three main elements forming each roof structure  - main shells, side shells, and louvre shells.  ...  Each of these shells is made up of two half-shells, symmetrical about the central axis of the hall. Each half is a reflection of the other, mirrored about the vertical plane of the hall axis.   ..... Each half main shell consists of a series of concrete ribs. The centre-line of each rib is a great circle of the sphere. Centre-lines are equally spaced (3.65° apart) throughout each main shell, each centre-line passing through the pole of the sphere. In this way ribs radiate from the podium and they become wider up the shell, successive ribs becoming longer or shorter as the case may be.”