The development of the beam bridge
What are the disadvantages of a beam bridge?
All beams tend to 'sag' between the piers and 'hog' over the piers themselves. This results from the downward forces of the load and the upward forces at the pier supports. The greater the span or the load, the greater the tendency towards sagging and hogging.
The longer a beam is, the weaker it becomes. The greater length gives more weight and more leverage for that weight - increasing the 'bending moment' (see the module on beam calculations for more detail on this).
This is why the bridge tends to sag more in the centre. It is rather as if you were holding a piece of A4 paper out towards someone else. The paper is much more likely to bend if you place a weight on it or hold it by its corner rather than at its centre. Both the weight and the unsupported length of an object make it more likely to sag.
© structurae.de (Klaus Föhl)
As the width of the span is increased, any beam bridge will eventually crumple on the top and snap on the underside. This is why beam bridges rarely span more than 80 metres.
Tackling the problem of sag
© Simon Dakeyne
To make a beam bridge as strong as possible, it is often necessary to reinforce it with 'girders'. The strength of a girder depends on its depth, not its width. Then more material is added where it's needed – at the top and bottom, where the tension and compression act.
So the most common girders used to support beam bridges have a cross-section in the shape of a capital H on its side.
To create beams that have the effect of being very deep but don't weigh much, ingenious nineteenth-century bridge designers in the United States added supporting latticework, or a 'truss' to the bridge's beam. There are many subtle variations on the truss, with the name of each variation immortalising its inventor.
Each design dissipates the main load through different combinations of 'struts' in compression and 'ties' in tension. As a vehicle passes over the bridge, a particular member of the lattice may go from being in compression to being in tension, so the material chosen for a truss must be able to take both kinds of force. Typically, of course, large truss rail bridges were made from iron (and more recently steel), but rural America is also home to thousands of small, wooden truss bridges.
Another approach to strengthening a beam bridge is to make the shape of the bridge itself thick and strong where it needs to be, and light and delicate where it doesn't matter.
© National Railway Museum/Science & Society Picture Library
This is the idea behind the 'cantilever' bridge design. The part of the beam near to the pier support is so strong that it can support the slender parts in the middle of the span.
The effect is rather as if, between them, two very long diving boards actually spanned the width of a swimming pool. It would then be possible to cross the pool, stepping (in the centre) from the end of one 'cantilevered' board onto the end of the other, with no pier support at the point of contact.
A particularly nice illustration of the principle behind the cantilever was produced at the time of the building of the Firth of Forth rail bridge in 1882. Two 'big strong men' play the parts of the main towers, and between them they support the weight of a smaller, lighter person suspended in the middle. It is one of those icons of Victorian persuasion: 'See it and believe it!'
© Imperial College, London
But, in the end, for all the tricks you might try, a beam bridge can't escape the fact that it will sag in the middle. There is simply nowhere else for the loads to dissipate.
The human mind had to think of a way to get those sagging forces away from the middle of the span. And it did so – by inventing the arch.
© Science Museum/Science & Society Picture Library
Redheugh Bridge, Newcastle. Beam bridges rarely span more than 80 metres.
Underside of a modern concrete road bridge.
View of the Forth Bridge, January 1997.
A historical demonstration in 1887 showing the weight of the central span of a bridge being transmitted to the banks through diamond shaped supports. The central "weight" is Kaichi Watanabe, one of the first Japanese engineers who came to study in the UK. Sir John Fowler and Benjamin Baker of Imperial College, who designed the Firth of Forth bridge, provide the supports.
'The Fife cantilever', c.1880s