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Next to Holborn Tube station in central London stands one of those 1960s strip-window office buildings that are so banal they often get overlooked. But a second glance at Procter House reveals an unusual feature: its middle section, all six storeys of it, straddles a four-lane highway.

Four decades after construction, the bridge building has undergone a major refurbishment.

It was acquired by a property developer who wanted to upgrade the specification and add more rentable floor space. The developer's architect, on the other hand, was keen to lighten its appearance so that it would appear to float over the street. But it was the structural engineer who held the trump card. The bridge structure, it insisted, could not carry any more weight.

In the end, developer, architect and engineer all achieved their objectives. Their solution involved a fusion of architectural and engineering devices – and old-fashioned arithmetic.

The original intention of Bee Bee Developments was to smarten up the tired old building, strip out internal partitions, insert modern services and add floors on the roof. The stumbling block was that any extra load on the bridge block would have to be supported on the original pair of hefty post-tensioned concrete beams running through its base.

"Determining the load the post-tensioned beams could carry was uncomfortable territory," says Ron Packman, director of structural engineer Packman Lucas. By pure coincidence, Packman had investigated the building's innovative structural system as a student in the 1960s. "The grouted steel tendons would have stretched a little over the years, with the effect that the prestressing would have diminished a little. The only thing we could say about the building structure was that it was holding up very well, and had another 50 years' life in it. So we took the existing building load as the design load for any alterations." In other words, says Packman, "if we wanted to add floors, we would have to shed [the equivalent] weight somewhere".

This is where the desire of architect Ttsp to lighten the building's appearance externally and internally offered a way out of the structural impasse. "The bridge building was more of a barrier across the road than a gateway," explains Ian Miller, associate director at Ttsp. "So we tried to lighten it up as much as we could by deconstructing the facades and putting them back together again." Accordingly, the stone spandrel panel and strip windows were removed. More daringly, three out of four of the bulky structural concrete columns set at 1.5 m centres directly behind the facade were cut out. The strip windows and stone panels were replaced by lightweight curtain walls, and the eliminated structural columns were replaced by hefty steel beams that spanned between E E every remaining fourth column.

As viewed from the outside, these replacements have transformed the plodding external wall into a taught, transparent skin that makes the bridge link appear fittingly weightless. As viewed from the inside, they have had the effect of funnelling daylight deep into the open-plan office floors, while opening up oblique views out of the building.

The facelift to the facades was much more than cosmetic surgery. Packman Lucas calculated the total quantity and weight of all the building material to be removed, and then subtracted the load of the replacement curtain walls. "It came to many tens of tonnes," recalls Ron Packman. "By taking out all that kit, we had enough spare loading capacity to add another storey and a bit. And this also gave us the opportunity to downsize plant in the existing roof space and, at the same time, increase the air-handling capacity." Increasing the building's height by more than one extra storey was in any case frowned on by the local authority planners.

The next problem was that the floor-to-ceiling heights of 2.65 m were too low to accommodate the current standard office fit-out of raised access floors for cabling and suspended ceilings concealing air-conditioning gear. "So we hacked out the 70 mm deep floor screeds and put in raised floors 125 mm deep," says Miller. "And we suspended integrated 'multiservice beams', supplying fresh air, heating, cooling and lighting from the concrete floor slabs above." Here again, Packman Lucas calculated that removing the load of the floor screeds offered the opportunity to add more fabric to the building. Together with the increased daylight penetration into the building through the transparent facades, this suggested that more floor space could be gained by extending the floorplates out by 2 m on either side.

However, extending the floor plates at the perimeter presented a tricky problem of its own. The floor extensions would have to house another multiservice beam recessed into the perimeter, together with all the ducts, pipes and casing supplying it. These could all be neatly concealed in a narrow ceiling void beneath a slimline floor slab – but only provided there were no structural downstand beams in the way. The solution this time was to suspend the floor extensions and the perimeter curtain walls from just one set of beams that cantilevered out from the second and top floor on either side.

When it came to physical construction, yet another loading problem presented itself. According to the structural engineer, just as the primary post-tensioned beams could not safely support any extra loading, neither could the loadings be reduced. "The post-tensioning exerts a very large upward force," explains Packman. "This meant that when the contractor came to take away all the redundant columns and floor screeds, it had to maintain the same overall load throughout the process," he continues. "So the removal was phased. After the columns and screeds were cut out, they were laid on the floor slabs. And whenever there was a delivery of new concrete, there was a removal of the same amount of demolition waste. And a man with a clipboard kept a tally of all materials in and out to make sure they balanced." The completed bridge building, renamed The Eye and currently on the market, offers prospective tenants office space as stylish as anything in central London, as well as the distinction of being based in a highly conspicuous gateway building straddling a bustling city road. From the developer's point of view, it delivers a 30% increase in net lettable space. And as the structural engineer confirms, the building now weighs slightly less than 5% more than it did before refurbishment. By anyone's reckoning, it's a weighty achievement.