How Do Bridges Stay Up? Beams, Arches, Suspension and the Forces Between

The simplest bridge is a beam resting on two supports, and it works by bending. A load in the middle pushes the beam down, which stretches the bottom fibres and squeezes the top ones, so that the beam is in tension below and compression above, with a neutral line between where nothing happens. The further apart the supports, the greater the bending for a given load, rising with the square of the span, so a beam that is doubled in length must be four times as strong, which is why beam bridges are short, a few tens of metres, or made of steel or prestressed concrete girders shaped as an I, with the material concentrated at the top and bottom where the stress is and little in the middle. A truss is a beam with the middle cut away into triangles, which puts each member in pure tension or compression and spans further for the same weight; the railway bridges of the nineteenth century were nearly all trusses.

An arch carries its load by compression alone, which is what stone and brick are good at, and it does so by turning the downward push of the load into a sideways thrust along its curve into the abutments at each end. Every stone in a Roman arch is squeezed by its neighbours and squeezes them back, and the structure gets stronger under load until the foundations give; the Romans built arches that have carried traffic for two thousand years, and the Pont du Gard still stands three tiers high. The limit is the thrust, which the ground must resist, and the span, which for stone rarely exceeded fifty metres. Steel and concrete arches reach 500 metres, as at the Sydney Harbour Bridge and the Chinese arches of the 2000s, and an arch can be built above the deck, with the road hung from it, or below, with the road on top.

For the longest spans the load is carried in tension, by cables, which steel handles better than anything, since a steel wire can hold a load equal to its own weight over a length of more than twenty kilometres. The kinds:

• •Suspension bridge: two towers, main cables draped between them and anchored in the ground at each end, and the deck hung from the cables by vertical hangers; the cables pull the towers down and the anchorages inward, and the deck is a stiffening beam to stop the whole thing waving; the Akashi Kaikyo in Japan spans 1,991 metres and the Canakkale in Turkey 2,023
• •Cable-stayed bridge: cables running straight from tower to deck in a fan, so that the deck is held at many points and the tower takes the load in compression; simpler and cheaper than suspension for spans up to about 1,100 metres, and the form of most large bridges built since 1990
• •Cantilever: arms projecting from piers, each balanced about its support and meeting in the middle, as at the Forth Bridge, whose engineers demonstrated the principle with two men on chairs holding up a third

Bridges fail in a few known ways, and each failure changed the rules. The Tay Bridge in Scotland blew down in 1879 with a train on it because the wind load had not been calculated; the Quebec Bridge collapsed twice during construction, in 1907 from underestimated weight and in 1916 when a lifting casting broke; and the Tacoma Narrows suspension bridge in 1940 twisted itself to pieces in a 65-kilometre-an-hour wind because its slender deck acted as an aerofoil and the oscillations fed on themselves, a failure caught on film that made aerodynamics part of every bridge design since. The commonest cause now is neglect: the Morandi Bridge in Genoa fell in 2018 when corroded cable stays that had not been replaced gave way, and the Minneapolis interstate bridge in 2007 when an undersized plate finally cracked. Fatigue, the growth of cracks under millions of load cycles, and the rusting of steel inside concrete are what inspectors look for.

The longest single spans are suspension bridges because the cable is the only element that can carry its own weight over two kilometres, and the limit is that a longer cable spends more of its strength holding itself up; the theoretical maximum for steel is somewhere around five kilometres and for carbon fibre much more. The longest bridges overall are chains of ordinary spans, the Danyang-Kunshan viaduct in China running 164 kilometres on thousands of concrete beams. Proposals for the Strait of Messina and the Strait of Gibraltar have sat on drawing boards for decades, defeated by depth, earthquakes and cost. A bridge remains the structure in which the forces are most visible: the arch that pushes, the cable that pulls and the beam that bends are the same three ideas that a child with blocks, string and a ruler discovers on the floor.

A bridge is not rigid, and it is designed not to be. Steel expands by about twelve millionths of its length for every degree of warming, which sounds tiny until you apply it to a long deck. A one-kilometre steel span experiencing a forty degree swing between winter night and summer afternoon changes length by roughly half a metre. If that movement were blocked, the stresses would crack the structure, so bridges sit on bearings that let the deck slide or rock, and the joints in the road surface, often visible as metal teeth you drive across, give it room to grow and shrink.

Movement can also cause trouble. When London's Millennium Bridge opened in June 2000, it began to sway sideways as crowds crossed. Each small sway made walkers shift their steps slightly to keep their balance, and as more of them fell into step with the motion, their footsteps pushed the bridge further, a feedback loop the designers had not anticipated. The bridge closed after two days and reopened in 2002 with dampers fitted to absorb the energy. Engineers now check footbridges for this effect, and the episode shows that the loads on a bridge include the behaviour of the people on it.

Every bridge ends at the ground, and the hardest part to build is often the part nobody ever sees. A pier standing in a river must reach soil or rock that will not shift or wash away, and the water is in the way. Engineers deal with it in two main ways. A cofferdam is a ring of interlocking steel sheets driven into the riverbed and pumped dry, so builders can work in the open on the bed. A caisson is a huge open-bottomed box sunk onto the bed, with air pumped in to hold the water back while workers dig away beneath its edges and it settles deeper.

The pressurised caisson carried a hidden danger. Under extra pressure more nitrogen dissolves into the blood, and if workers return to normal air too quickly it forms bubbles in the joints and nerves. Builders called it caisson disease; divers later called it the bends. During the building of the Brooklyn Bridge in the 1870s many men were struck down, and the chief engineer, Washington Roebling, was left so ill that his wife, Emily Warren Roebling, carried his instructions to the site for years. The remedy, slow and staged decompression, was worked out properly only decades later.

In 1779 the world's first major bridge made of cast iron was completed across the River Severn in Shropshire, at a place now called Ironbridge. Iron was a new material for such a structure, and the builders used techniques borrowed from carpentry, joining the cast iron sections with dovetails and wedges, as if they were timber.

The bridge's semicircular arch spans about thirty metres, and it showed that iron could carry heavy loads across a river, encouraging iron and later steel bridges around the world. The surrounding Ironbridge Gorge, with its furnaces, mines and factories, is often called a birthplace of the industrial revolution and was added to the UNESCO World Heritage list in 1986.

Bridges carry load to the ground in three ways: beams and trusses by bending, with tension below and compression above, which limits them to short spans; arches by compression, turning the load into sideways thrust that stone resists well; and cables by tension, which steel handles best and which lets suspension and cable-stayed bridges span up to two kilometres. Failures from wind, underestimated load, aerodynamic flutter and corrosion have each rewritten the rules, and the longest spans hang because only a cable can carry its own weight that far.