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An Old Bridge and a New Bridge
Any means of reducing the span of a bridge is welcome, provided it still meets the specification for clearance over width below. Reducing the span reduces the self weight, the forces, and the cost. A simple means of reducing the span is to provide intermediate supports. Two possible ways of doing this for a bridge over a road are shown below.
This page uses some real examples to look at these two ideas.
An Old Bridge
The first example, at Whitney-on-Wye, shown in the three pictures below, is noteworthy, for it is a toll bridge and a grade II listed building. The income was decreed as tax free by a 1779 Act of Parliament. The original masonry bridge, built in 1779, was washed away by the river, as were two subsequent efforts. The current bridge dates from the 19th century. It is not obvious that wood is more durable than stone, but it is probably a lot cheaper to replace when the floods take their toll. Normally we associate tolls with massive modern undertakings, but there are several places in England were ancient toll rights are exercised. These can spoil your travel plans if you reach them unexpectedly in the middle of the peak traffic period. There is such a toll bridge at Eynsham, near Oxford, which creates very long queues, and another one near Bath.
The three wooden spans at Whitney are propped beams, as you can see from the top left corner of this photograph. (Or could they be considered as three-segment four-hinged arches with stabilisers?) The general views are looking upstream, and on the far side of the cutwaters you can see the sheets of metal which protect the timbers from flood water and debris.
In the diagrams above, the deck was assumed to be in segments which spanned the piers. But if the deck were continuous, the compression in the centre of the spans would induce tension above the piers, in order to maintain the same total length, as in the first diagram below. The assumption here is that the deck is fixed at the ends. Such a bridge is somewhat indeterminate in both type and forces. The deck could be post-tensioned or post-compressed to attain a situation with the same polarity of stress throughout.
It should be explained at this point that the diagrams are not strictly correct. The parts shown in red are probably not entirely in compression. Because they are not vertical, their weight is tending to bend them, and so they are acting as beams as well as struts. Whether any tension occurs in these members depends entirely on the weights of all the parts, and on the angles of the sloping struts. We can, in fact, regard a propped beam as a partially pre-stressed beam, stressed by the props rather than the usual steel wires, though wires are still necessary. Why? The variation in bending moment throughout is related to the distance from the funicular. The example shows a propped structure that is nearer to the funicular than most.
In the second diagram, we revert to a segmented deck, but with the joints near the props. Now the bridge is based on cantilevers.
We see that what looks like a simple structure allows of several different interpretations, depending on the exact mode of assembly. Unfortunately, it is not possible to get close enough to the bridge to examine the details.
Note the iron sheets which shield the wooden cutwaters against the ferocious flood waters and floating debris which sometimes hit the bridge. All along the Wye valley, you can see bridges with extra spans to accommodate flood water, and as we ascend the river, we see cutwaters, and platforms around the piers to combat scouring, a great enemy of bridges.
You will have noticed that the thrust of the two masonry arches is contained by the piers, Roman style, for they must have been placed before the timber was added, and they survive if the timber is washed away. The Romans were very conservative about the ratio of span to width of pier, reasoning that floods or enemy action, in destroying one span, would not take out the rest. With such a design, the arches could, if required, be built one at a time, using the same centring throughout. For arches in which the thrust propagates throughout the bridges, all the spans must be built together.
Building sturdy arches of small span with wide piers may seem like a good idea, but this type of construction reduces the area available for the flow of water. Compare the open construction at Bredwardine, downstream and up-page. Admittedly, there the river is rather wider, which helps greatly.
A New Bridge
The next example is a recently built footbridge in Swindon, Wilts, made entirely of metal, including very smart stainless steel guard rails. It is a very neat design. It looks at first rather similar to the Whitney bridge, but there is a subtle difference. Here are some pictures.
Note the very shallow deck structure, and the huge number of small holes in the surface of the deck, seen in the second and third pictures. These tend to equalize the air pressure above and below the deck. Does this help to reduce forces generated by the wind? Triangulating wires provide lateral stiffness. The holes in the I-beams are omitted where extra stiffness is needed.
Now let's look at one more picture. In spite of the vegetation we see that under each half of the bridge there two frames, not just one. One frame props the beam, while the other connects the foot of the prop to the end of the beam. That second frame lies parallel to the sloping bank, as in the diagram below. The bridge has been drawn as if it were floating in air with no support. In the second diagram it rests on two hinges, but a gap has been left at centre span. In that case, the force on each support must be vertical.
Imagine also that each half is designed to have the centre of gravity over the support. This means that when the gap is closed, there will be no change in any forces, because each half is balanced. The only horizontal forces at the supports will occur when live loads move across the bridge. These can be taken care of by making the piers a little wider. If each half does not have its centre of gravity over its pier, the forces at the supports will not be vertical. The piers should then be built on a slight angle, or be made to widen towards their bases.
Thus the strong outward thrust of a propped beam can be replaced by almost vertical forces, which are easier to counter. In the third picture, the ends of the beam are connected to the ground. The beam is now indeterminate, and the extra supports can be used to change the bending moments along the beam from the values they had in the free beam.
Another Beam Bridge
This footbridge crosses the A34 at Chilton. Since we have seen that a beam requires only two hinges as supports, the extra two here can be used to control bending moments. This bridges exhibits the use of completely unadorned grey concrete to create a simple and elegant structure.
The pictures below show some of the possibilities for bridges that look similar to this one, by making cuts in the beam. In each case, what are the advantages and the disadvantages of the design as compared with the actual one.
An aqueduct by Thomas Telford
Thomas Telford created many notable iron bridges. One of these is an aqueduct on the Shrewsbury canal. The sides were made by bolting iron plates along flanges. Telford would presumably have wanted the bolts to experience little or no shear stress, and the result is reminiscent of a jack arch. The diagram at left gives a rough idea of the design.
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