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The newly completed Hall 3 at the world famous Frankfurt Trade Fair sports the latest example of the spectacular Grimshaw wide-span roof – in this case designed with Arup as concept structural engineer. In form and construction technique, this is totally original – and radically different from the practice's earlier coverings.

Externally, the roof of Hall 3 resembles a row of five giant silvery horns spanning the length of a rectangular building, and these are scalloped on the cross axis into a series of rounded peaks and valleys. Inside, the huge undulating metallic vault leaps up and over the column-free upper hall one jaw-dropping bound.

As a feat of structural engineering, Hall 3 is full of superlatives.

With its 40,000 m2 of exhibition space, the two-storey hall is by far the largest at the Frankfurt Trade Fair, itself one of the three largest exhibition centres in the world. The upper hall is claimed to be the largest column-free space in Europe. More extraordinary still, the roof spans 165 m lengthwise between supports.

All this inhabits a different universe from the crinkly-tin boxes that make up the out-of-town business park known as the National Exhibition Centre in Birmingham. Frankfurt's internationally famous trade fair takes pride of place in the city – close to the centre and the River Rhine. The key to the trade fair's marketing strategy is the civic pride that the whole complex radiates – most conspicuously in Murphy/Jahn's pencil-shaped Messeturm skyscraper, which pipped Canary Wharf tower to become Europe's tallest building (pictured left).

As well as being the largest exhibition hall building in the trade fair, Hall 3 occupies a key site overlooking the central square, or agora. The requirement was that the upper hall should be free of columns to be fully flexible in internal layout and glamorous enough to attract the most prestigious clients – most notably the yearly international automobile exhibition.

Determined to develop "the flagship of a new generation of exhibition buildings", the trade fair organisation Messe Frankfurt invited 12 international architects to enter a design competition in October 1999. Just as in the simplest caricature of the design process, Grimshaw's concept fell into place during a single day's brainstorming by eight architects and engineers. "By 6pm, we had cracked the problem with a brilliant idea," says Grimshaw's associate director Ingrid Bille.

The brilliant idea that won Grimshaw and Arup the competition was to take what is basically a large-span aircraft hangar structure and morph it into something far more original, sculptural and efficient. By spanning the building lengthwise, the wide front wall has been liberated from any load-bearing function so that it could be fully glazed to form a single vast shop window facing the agora. The moulding of the roof into complex double-curves has added stiffening, so that it could be form a shallower arch than is usual in hangars, and this in turn reduces the internal volume requiring air-conditioning. "We wanted a low, gentle, elegant arch instead of a big, bulky arch," explains Bille.

The single weakness in this ingenious idea is that the full sculptural geometry of the roof can only be appreciated from the sides, rather than the agora at the front. The competition design concept was further weakened during detailed design, when large skylights were replaced by air exhaust vents. Fortunately, clerestory windows below each perimeter arch allow a background level of daylight to enter the upper hall. Electric lighting for that floor radiates from vast curving booms slung from the main roof arches. Powerful spotlights on the booms bounce light off circular mirrors fixed to the sides of the arches. Large air-conditioning fan-coil units are also housed in the booms.

Four floors of foyers are arranged on either side of the cathedral-like space of the main upper hall, and these have their own architectural drama. The overall building design is made up of two distinct elements: the curving tubular steel roof structure and the concrete post-and-beam structure of the first floor. These are kept apart in most of the building, but come together in these side foyers, creating rich opportunities for dramatic interplay.

The roof vaults are supported at their ends by A-frames, in which large raking struts of tubular steel have been exposed to view. For its part, the concrete first-floor structure terminates in 10 large hollow concrete cores containing toilets, escape stairs and services plant. The walls of the concrete cores facing the foyers have been raked to match the tubular steel A-frames alongside them, and large voids have been left beside and in front of them. The combined effect is to open up diagonal views through all four floors of the foyers and into the main halls, and at the same time to display the complex rhythmic counterpoint of the raking steel and concrete structures.

The vast open floors of a top-grade exhibition hall cannot function without a dense hinterland of back-up services – air-conditioning, lighting, water, power and IT cabling. But as Bille says, "We don't like to spread services all over our buildings." Accordingly, they have been concentrated into confined zones and, wherever possible, hidden from view. As well as in the roof booms and concrete cores, services have been packed into the rear wall and inside the first-floor structure, which is a walk-through zone for services and escape corridors.

In Grimshaw's design, even this services floor has been exploited for its architectural potential. The main high-level covered walkway linking the entire campus of buildings has been threaded through the side foyer spaces and along through this service floor, where it passes directly behind the window wall facing the agora. In this way, the building can be enjoyed while it is closed down between exhibitions, and by non-delegates during exhibitions.

Hall 3 of Frankfurt Trade Fair is Grimshaw at his finest. The onerous technical demands of a world-class exhibition hall have been resolved and moulded into a highly original work of architecture. The only problem is that this glamorous, curvaceous piece of metal engineering promises to steal the thunder of the new car models exhibited inside.