Geometry Meets Music: The Philips Pavilion

The pavilion structure supposed to be a self-supporting, column-free, and hollow structure with acoustic qualities. 

Xenakis found a brilliant solution for the shape of the building in a series of conjoined curved planes that formed an enclosure that looked like a tent. The chosen design consisted of nine hyperbolic paraboloids joined at their edges. These hypar shells (short for hyperbolic paraboloid) served both as roof and walls. The structure had the floor plan shaped similar to the stomach of a cow (as shown on the model below). 

Visitors entered in groups of 500 at intervals of 10 minutes. After curved hallway people slowly entered into a room in darkness for an eight-minute audio-visual spectacle called Poème électronique. They were sitting and lying on the floor, witnessing full-body sensations while listened to the cut-out abstract sounds and watched visual effects projected on the walls of the pavilion. It was an immersive experience. 

At the end of the projection, spectators were "digested" through the stomach exits while another group entering.
 

Poème électronique is considered the very first multimedia work. The music was composed by Edgard Varèse, the father of electronic music. Le Corbusier himself was responsible for the whole visual show.  Here is how it sounds.  
 

This self-standing "tent" structure had never been seen or done before. What Le Corbusier did with the design, Varèse did with the sound. Hundreds of thousands of people queuing to get in to see and hear. The pavilion hosted 2 million visitors!
 

The final structure was 22 meters high and certainly pushed the limits of engineering of that time. The pavilion was built by the Belgian company Strabed. 
 

To build such a complex form, Xenakis proposed a structural system of prefabricated concrete panels hung in tension on the 7 mm wire cables, laid on both sides of the shell. Despite being a curved surface,  a hyperbolic paraboloid can be generated by straight lines, and thus the method of using prefabricated panels was easy to implement. 

An ingenious Xenakis' solution included about 2000 precast 5 cm thick panels, made in the hangar shed on simple open sand moulds that matched the curvature of the pavilion. The sandhills were divided into quadrangles by a grid of planks. The size of the precast slabs was about 1 square meter with a light reinforcement mesh to prevent breakage during transportation to the site. 
 

At the edges of each hyperbolic paraboloid shell (lines of intersection), were cylindrical concrete ribs, 40 cm in diameter, as the structural elements cast in-situ. The scaffolding wooden beams followed the ruling lines of the hyperbolic paraboloid shells. 
 

The steel cables were positioned inside and outside of the shell, following the ruling lines of hyperbolic paraboloid geometry, and anchored to the concrete ribs and foundation beam that formed the base of the pavilion.  The "Strabed " system used for mounting prestressing cables introduced the special feature of fitting the anchors for the wires to the structure in advance, which had greatly accelerated the erection. Once the panels were erected, the entire structure had been post-tensioned, making a monolithic structure. The outside of the shells including the prestressing wires had been covered with aluminium paint and the interior plastered with a sound-absorbent layer of asbestos material which created a cavernous acoustic.

Image Left:  Interior during construction. 

Image Right: One of the pinnacles from inside with speakers. More than 400 speakers, grouped in the clusters, were fixed to the interior walls of the pavilion coated in asbestos. 

The image below shows the numerous prestressing wires of high-tensile steel, which were applied on both surfaces of the shell and left visible.  Some concrete ribs were also given torsional prestressing which is thought to be the first application of torsional prestressing to concrete.