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Mathematical formula A new home for University of Cambridge mathematicians is under construction - in a giant hole in the ground. Dave Parker reports.

Log on to the Internet over the next few weeks, call up http://www.cms.cam.ac. uk/camcol.html, and a picture of a crucial stage in the construction of the new buildings for the University of Cambridge Centre for Mathematical Sciences should eventually appear. A video camera on a nearby building, currently transmitting regularly updated images of the 14.9M project, will show the first critical operation in the construction of the central 'green roof' structure - the placing of a slender curved steel beam on to two triangular steel structures perched on top of a group of concrete columns.

Structural engineer Buro Happold project engineer James Rowe has been known to predict that the beam will 'just click into position'.

And given the precision of fabrication specified for both the connecting nodes and the structural steelwork, the odds would seem to be very high that his prediction will be totally accurate. But if main contractor John Laing Construction does find the roof structure straightforward to erect, it will be the result of more than good workmanship by steelwork fabricator Hawk Structural Steelwork and node founder BAS Castings, as Buro Happold senior associate Richard Harris explains.

'In fact the roof is curved in section, tapering in plan and sloping in elevation, with every one of the six arches a different span. Developing a structural system which enabled the nodes to be positioned within a millimetre or two was the biggest design challenge we had to face.'

The basic concept of the central grass-covered roof, Harris adds, came from the pressure on architect Edward Cullinan to reduce the visual impact of the project, designed ultimately to house up to 900 of the world's top mathematicians. One of these will be Professor Stephen Hawkings and 'the Centre will have particularly good disabled access,' Harris comments.

With the site surrounded on three sides by residential property, Cullinan's response was to sink the whole development one storey into the ground. And rather than construct 'a series of bunkers', Harris goes on, the architect opted for a central sunken area topped by the grass roof, surrounded by three storey pavilions.

This central core will be open to natural daylight but will not block sightlines through the complex from its boundaries. Under the clear span roof will be a large meeting/assembly/circulation area, designed to encourage the serendipitous academic encounters that sometimes trigger major mathematical revelations.

'We never considered anything but concrete for the roof itself,' says Harris. 'The high thermal mass would moderate thermal movements and make it possible to build it without movement joints.

'And a concrete roof would be easy to waterproof with a straightforward sheet membrane under the soil. But the supporting structure went through several manifestations.'

A series of tubular steel balanced cantilevers supported on stub columns was the first option developed. 'We rejected a steel arch because we considered it would generate too much side thrust,' Rowe reports.

'Tubular steel would also allow us to deal with the complicated geometry fairly easily. There was at least one major drawback, however; the relatively large reactions to load variations if the structure was designed to be economical.'

This could put the integrity of the waterproof membrane at risk. There was also a visual drawback. The row of vertical tie downs at the perimeter would detract from the architect's 'ribbon of glass' concept for the external glazing.

Precast concrete had been chosen for the faceted roof initially, but for the next major analysis Buro Happold turned to a much stiffer, all insitu concrete roof and portal frame solution. No additional fire protection would be needed and the tie-downs would be eliminated.

'Unfortunately. there were severe construction problems,' says Rowe. 'Each arch is a different radius, with spans ranging from 21m down to 10.5m. It proved impossible to develop a common geometry, so there would be no repetition on the formwork. We were also worried about the problem of accurately centring the formwork.'

Finally, Buro Happold opted for a steel/concrete composite solution for the five widest arches, with slender 254 by 254 by 107 steel universal columns enclosed in C35 concrete . 'Steel beams can be bent to shape very accurately,' Rowe points out. 'The idea is to erect the steel element first, then hang the formwork and falsework for the concrete off it. This gives us geometrical accuracy and takes care of the fire protection as well.'

Main arches are at 7.8m centres, with the sixth arch a simple concrete portal frame. Secondary beams are also composite, but will be 'pre-coated' with concrete up to the level of the top flange of the 254 by 254 by 89 steel section on site before erection. In its first manifestation, the design went back to vertical tie downs at the end of the backspans, but a more detailed analysis showed there was no need, as there was no significant uplift when the main span was loaded.

'Although we specify a lightweight compost for the 300mm of 'soil' on the slab, we have to allow for a long term natural increase in density due to the composting of grass cuttings,' Harris explains. 'And for saturation as well. We've also designed for a 5kN.m2 live load.'

At first the triangular buttresses which support the arches were normal reinforced concrete linked together with prestressing tendons buried in the first floor slab. But as design progressed, the team became increasingly concerned about the need for locating the nodes accurately.

'All the arch loads from the roof are concentrated on the node pins,' says Harris. 'So the buttresses have to locate the nodes within +/-1mm, and be capable of transmitting the loads down to the horizontal ties in the slab.'

For architectural reasons a 'very clean concrete element' was desirable but so was constructability. Eventually, a composite solution was chosen again. At the heart of each buttress a triangular steel frame carries a machined steel shear key at its apex. After the concrete surround is cast, the nodes are fitted and aligned in preparation for the erection of the steel arch element. The essential horizontal tie is now provided by closely-spaced T50 bars cast into the floor slab and picking up loads through bond with the concrete. There is no mechanical connection.

Rowe reports that developing the final design for the node casting involved more than computer analysis. 'CAD didn't allow us to fully resolve all details of the casting. In the end I constructed a half-size clay model and the architect and I worked on it until we were both satisfied.'

Each casting weighs around 1,000kg and Laing is still developing its method statement for the exact arch erection sequence. The same goes for the roof construction technique, although Harris expects a proprietary formwork system to be used for the soffit shuttering. At the moment the triangular buttress frames are being erected on top of the columns supporting the first floor slab, preparatory to slab construction.

He adds: 'By comparison, design and construction of the pavilions will be relatively straightforward. Basic frames are an insitu concrete flat slab design, with the main problem being the integration of the structure and a highly developed naturally controlled environmental system.'

The eight pavilions, and the circular library, will be built in phases as funds are raised. Currently, the linked Pavilions 1 and 2 and Pavilion 5 are under construction alongside the central core, with completion due in January 2000. Phase two, the library, is now at scheme design stage, thanks to a 7.5M donation from Intel chairman Dr Gordon Moore.

Even when all 900 mathematicians have taken up residence, their impact on traffic patterns in the neighbourhood will be minimal. Less than 90 car parking spaces will be provided, Harris reports. He adds: 'When we did our initial traffic impact assessment, this being Cambridge, we also had to consider the impact of pedestrians and cyclists.'

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