If you have any questions please write to dlocke@Brantacan.co.uk.
|The cable-stayed bridge is becoming very popular, being used where previously a suspension bridge might have been chosen. Very large spans have been built, for example - Tartara, Hiroshima, Japan, 2919 feet, Pont de Normandie, France, 2808 feet, Quingzhou Minjang, China,1984 feet.||What are the reasons for the popularity of the cable-stayed bridge? Let's look at an imaginary suspension bridge, and an imaginary cable-stayed bridge, shown in the diagrams below.|
We can list the main parts of each type of bridge -
|Suspension bridge||Cable-stayed bridge|
|Two towers||Two towers|
|Suspended structure||Suspended structure|
|Two main cables|
|Many hanger cables||Many inclined cables|
|Two terminal piers||Two terminal piers|
Both types of bridge have two towers and a suspended deck structure. Whether the towers are equivalent may become apparent. There is a difference in the deck structures. The deck of a suspension bridge merely hangs from the suspenders, and has only to resist bending and torsion caused by live loads and aerodynamic forces. The cable-stayed deck is in compression, pulled towards the towers, and has to be stiff at all stages of construction and use.
|A great advantage of the cable-stayed bridge is that it is essentially made of cantilevers, and can be constructed by building out from the towers. Not so a suspension bridge. Once the towers have been completed, steel cables have to be strung across the entire length of the bridge. These are used to support the spinning mechanism, used since the time of Roebling and the Brooklyn bridge, which takes thousands of strands of steel wire across the bridge.|
|Because the cable-stayed bridge is well-balanced, the terminal piers have little to do for the bridge except hold the ends in place and balance the live loads, which may be upward or downward, depending on the positions of the loads. A suspension bridge has terminal piers too, unless the ends are joined directly to the banks of the river.||The cables often pass over these piers and then down into the ground, where they are anchored, and so the piers have to redirect the tension. The four anchorages of a suspension bridge have to withstand the tension of the four cable-ends, and are often massive constructions. If the bridge is built on difficult ground, as in the case of the Humber bridge, the anchorage can present a fearsome problem.|
|The deck of a suspension bridge is usually suspended by vertical hangers, though, some bridges, following the example of the Severn bridge, use inclined ones to increase stability. But the structure is essentially flexible, and great effort must be made to withstand the effects of traffic and wind. If, for example, there is a daily flow of traffic across a bridge to a large city on one side, the live load can be asymmetrical, with more traffic on one side in the morning, and more traffic on the other side in the evening. This produces a periodic torsion, and the bridge needs to be strong enough to resist the possible effects of fatigue.||Great attention needs to be paid to aerodynamic stability in suspension bridges. The effects of wind are much better understood than they used to e, and the advent of the streamlined deck, used first in the Severn bridge, have reduced the cost of suspension bridges. The box-section of the Severn bridge contributes not only to aerodynamic stability, but to torsional stiffness. This and the inclined hangers owe much to the ingenuity and imagination of Fritz Leonhardt.|
The greater inherent rigidity of the triangulated cable-stayed bridges, compared with the suspension type, makes life easier for their designers and builders. On the other hand, if a cable-stayed bridge is built by the cantilever method, it is very vulnerable when the structure is very long but has not yet been joined together.
Although the popularity of the cable-stayed bridge is a fairly recent phenomenon, the principle is not new.
The great Brooklyn Bridge combines cable-stays with conventional suspension cables, while other bridges have used stays, even below the deck, to resist aerodynamic forces. To see a really beautiful picture of Brooklyn bridge by Anney Bonney, click here. The Albert Bridge, a small suspension bridge across the river Thames in London, also employs some stay-bars as well as a suspension chain.
The diagram below shows graphs of the bending moments along a cantilever caused by point loads at nine different distances from the point of attachment at the left. The free end of the cantilever is at the right. The moment at the attachment clearly increases as the load moves out. This principle is used in the steelyard.
|In fact, if we consider a cantilever of constant depth, we can
learn about the moments caused by its dead weight by adding together a lot
of these graphs.
Instead of building a rigid cantilever we can use a set of cables to support the deck.
|We could in fact consider a deck as being composed of a large
number of equal weights. What could
be more natural than to support them by series of parallel cables,
automatically giving the required increase in moment for the more distant
weights, while keeping all the tensions the same.
In fact, many cable-stayed bridges have other arrangements of the cables. Some smaller bridges even have only one or two cables per half-span. Some examples are shown below.
The penalty for the sloping cables is the compression induced in the deck. This very simple arrangement is, as usual, not the whole story: Very long cables oscillating in their fundamental mode can store a great deal of energy, so the larger bridges are equipped with light cables that run across the planes of main cables and connect them all together, and eventually to the deck.
Ail Groesfan Hafren - Second Severn Crossing
The most southerly bridge over the river Severn is the viaduct and cable-stayed bridge which carries the motorway M4 between Wales and England. It offers an alternative to the earlier suspension bridge, which carries the earlier motorway M4, now called M48. The designers made use of a large area of hard rocks on the western side of the channel, which are exposed at low tide, to enable a viaduct to be built. The main channel, called The Shoots, is spanned by the actual cable-stayed bridge.
The bridge is not far from the line of the Severn tunnel, which was a great feat of engineering, built from 1874 to 1886. Huge pumps were, and are, needed to remove water, and very large fans were installed to provide ventilation. The construction of the tunnel is described in "Track Topics - A Book of Railway Engineering for Boys of All Ages", by W G Chapman. This book also provides insights into some famous bridges of the Great Western Railway, and includes a drawing by W Heath Robinson depicting the assembly of Saltash bridge.
|This new Severn bridge is quite close to the ferry crossing that was used by the Romans in the days of the empire, illustrating, as many Severn bridges do, that the number of good crossing points is limited, and that people will use them during long periods of time. There is a visitor centre near the eastern end of the bridge. It offers video films, pictures, models, and descriptions of past and present crossings and local history.||
The bridge has high baffles on each side to deflect the wind. This greatly reduces the number of occasions on which any type of vehicle has to be banned from the bridge because of high winds.
Click for big JPEG.
|The large tidal range exerted a big influence on the construction work. Timing was crucial in operations such as floating out and raising sections of the bridge. Positioning of floating equipment was achieved using signals from navigational satellites||The picture at left was taken at a late stage in construction. On this occasion the tide was low, revealing the the English Stones, a large area of rocks on the eastern side of the channel. The cable-stayed bridge was complete, and the last few approach spans remained to be added.|
The approach spans are based on post-tensioned hollow beams, made from 3.5-metre match-cast sections which were floated out on a barge at high tide. The periods of high enough tides were very short, so timing was critical.
There is an interesting visitor centre at the end of Shaft Road, off Green Lane, Severn Beach, near the east end of the Second Severn Crossing. There are video films about the building of the new bridge. There are models of bridges. There are illustrations about the bridges and about the history of the area. A 24-page booklet is available, describing the construction of the new bridge. From the visitor centre it is a short walk to the Binn Wall, from which there are views of both bridges. You should telephone (01454 633511) before going, to make sure that it is open. There is also a good visitor centre near the Clifton Suspension bridge near Bristol.
Here are some facts and figures about the new bridge. The total length is just over 5000 metres, with a main span of 456 metres in a main bridge of 947 metres length. The number of approach spans is 45, divided between the Welsh end, 22, and the English end, 23. The bridge was built from 1992 to 1996.
It is so well integrated into the motorway that it is very easy to reach the cable-stayed section without realising that you have already crossed a long approach viaduct.
The next picture shows a small part of the Severn cable-stayed bridge. The picture has been tilted and compressed horizontally to show that, although the cables look straight, they sag. There are few perfectly straight lines in engineering, with the possible exception of verticals. Every part that is not vertical will sag a little, though of course "rigid" struts will not deflect visibly. The truth is that there are no rigid bodies. You can also see that two of the cables (the fifth on each side) are not evenly spaced with the others.
How can we measure the tension in a cable during construction? We could measure the curvature using surveying equipment. We could make the cable vibrate and measure the frequency. The frequency only varies as the square root of the tension, but it works. The method has also been used in setting up wire chambers for use in elementary particle physics. We could pull the cable sideways with a known force and see how much it deflects. Can you think of another method?
Here is a koto, one of the many musical instruments which comprise a sound-box, some strings, and one or more bridges to space them away from the box. The violin family, derived from the arabian rebec, is a well known example, along with derivatives like the hurdy-gurdy. They all use the principle that the string represents one half a wavelength of the oscillation (unless the player makes a harmonic by touching the string). The frequency depends on the tension and the mass per unit length of the string, as well as on the wave length. Many instruments have bridges that are not moved, but those of the koto are moved, even during a performance, to retune the instrument to a different scale. A note can be changed while sounding by pressing on the string in the non-vibrating part.
In the case of an amplified instrument such as an electric guitar, positive feedback can be used to prolong a sound, even to the point where it continues unaided by the performer. The converse, negative feedback, is used in amplifiers to reduce distortion of signals. In fact, negative feedback has been used in some very large structures in order to reduce the effect of wind. Some very tall buildings have massive pieces of metal at the top, which are moved in response to amplified signals from acceleration sensors. While the Pont de Normandie was being built, concern about the possible motions of the nearly completed spans was such that moving masses were seriously considered. But they were in fact never needed.
The differences between these stringed musical instruments and bridges are these -
Firstly, the strings of the instrument should oscillate: those of the bridge should not. In instruments like kotos and sitars, with long heavy strings, the oscillation may be long-lived, giving the possibility of subtle changes to the sound after the string has been plucked. In large cable-stayed bridges, the main cables are often provided with transverse wires that connect them all together. Given that the resonant frequencies of all the main cables are different (how do we know?) the effect will be to damp any resonances. In suspension bridges, small dampers may be provided a strategic points on the cables. The examples shown below are from the Severn suspension bridge, before and after refurbishment.
Dampers may be added to stringed instruments such as violins, and wind instruments such as trumpets. These are called mutes.
Secondly, the box of a musical instrument must be strong enough to support the tension in the strings. But the bridge deck is connected to the ground in several places, providing a significant contribution to its rigidity. Because of the modern tendency to play more loudly than in the past, many old violins have had to be modified to take the higher tension in the strings, rather as old bridges have to be strengthened to take modern heavy traffic. Chamber music is now often played in quite large halls, and in a concerto, the violin has to contend with modern orchestral playing, which is louder than of old. If the response of the hearing system were not logarithmic, violin concertos would probably never have evolved.
In a picture of two women and a koto by Suzuki Harunobu, the irregular line of bridges is likened by the artist to a skein of homing geese. The picture is called "Homing geese of the koto."
North of the Severn cable-stayed bridge, just upstream of the mouth of the River Wye, a smaller cable-stayed bridge with a main span of 770 feet takes the M48 (ex M4) across that river, at the Welsh end of the Severn suspension bridge. Here are some pictures.
The second picture has been squashed sideways by a factor of a quarter, to show the undulations in the steel deck, which sags between the supports. The high points are at the anchorages of the bundled cables into the deck, and at the towers, and are marked by horizontal black lines. Each cable contains twenty spiral strands, arranged in a triangular cross section with five layers, with 6, 5, 4, 3 and 2 strands per layer, respectively. The flat bottom of the section allows the cables to rest on the flat tops of the towers, held by simple clamps, avoiding the need for specially shaped saddles.
The stiffness of the box girder span is used to transmit torsional forces to the abutments, which are the only supports that are not on the centre line. This technique is used in many modern concrete spans and steel spans, supported either by piers or cables, because the simplicity provides a cost saving that is not overcome by the cost of the torsional stiffness. For box girders on piers, the potential untidiness of two rows of piers is avoided.
The towers are also of steel box construction.
Note the light traffic on this road, the motorway M4 which runs from London into Wales. These pictures were taken almost thirty years ago. As traffic built up, it became clear that a new crossing was needed. This has been described above. The road over the earlier crossing was renamed M48, and the M4 now follows the new route. It is much harder now to take pictures with no vehicles, and to avoid the vibration which persists after vehicles have passed.
Sabrina Foot-Bridge at Worcester
This beautiful and interesting little footbridge is found to the north of the railway bridge in Worcester, joining Le Vesinet Promenade to the west bank of the river. It is an asymmetrical cable-stayed bridge with one tower at the west end. An ingenious feature is the use of hinges where the cables join the deck.
This allows the use of rigid trusses without the necessity for extremely precise setting of the cable lengths. With a through truss, imprecise cable lengths would produce uneven tension in the cables, and unwanted bending stress in the deck.
The next picture shows that the cables are not perfectly straight. They cannot be straight, because of their weight. Each one follows a part of a catenary.
The use of long, highly stressed cables has the effect during construction that the shape of the bridge may vary significantly. All structures, of course, change during construction. Box girders being cantilevered may sag measurably until the span is joined in the middle. Suspension bridge decks may curve quite alarmingly.
The diagram below shows two stages in the construction of a cable-stayed bridge. In the first picture the last cable supports half the weight of the last deck section, but in the second it supports two halves, and so it must stretch and straighten. We are ignoring the stiffness of the deck, which will spread the load to other cables, but the general effect is similar.
If only bridge design were as simple as making a diagram like the ones below, for two tower designs and one tower designs. Do you think that any of these designs have advantages or disadvantages compared with the others?
Appearance of Cable-Stayed Bridges
|The cables can
be parallel or fanned from a point, or arranged in an intermediate
pattern. They can be reduced to only two in number, or even one, per
side. And instead of two planes of cables, a bridge can be furnished
with a single set along the centre line. There are even examples
where the plane of the wires is far from vertical.
If the cables fan from a point, as seen from the side, they must originate from a horizontal line. However short this is, it will affect the appearance from certain angles, because the cables are not coplanar. In fact, in most cable-stayed bridges, the multiplicity of sloping cables is liable to lead to a disordered appearance unless care is taken.
|In the left
picture above, the view from the road shows a somewhat disordered
appearance of the cables. This can be even worse if the cables are
fanned out from a horizontal row of holes in the pylon.
To achieve a vertical plane of cables, the second arrangement can be used, but now the tower is not elegant. Another solution is to abandon the idea of a vertical plane and make an A-frame, as in the right hand pair of diagrams. An A-frame is very rigid.
A third way is to use only a single plane of cables, relying on the deck to provide stiffness against torsion.
The picture below shows a part of the Sabrina bridge in Worcester. Although this is an elegant bridge, this view shows the difficulty of maintaining a tidy and ordered appearance from all directions. The suspension bridge, with its clear distinction between the dominant main cable and the thin hangers, does not suffer from this problem.
Oscillation of Cable-Stayed Bridges
Although the cable-stayed bridge is inherently stiffer than a suspension bridge, the relationship is reversed during construction. Construction of the deck of a suspension bridge does not begin until the cables are complete, and so all parts of the bridge are connected, however tenuously. But the cable-stayed span is built out in stages from each tower, and when the span is almost complete, the long cantilevers are at the mercy of the wind.
The diagrammatic plan view below, showing a part of a bridge, suggests what might happen. The amplitude is exaggerated. The deck could also oscillate in other modes with higher frequencies. In principle there could be horizontal oscillations allowed by torsion in the towers, and vertical ones allowed by bending of the towers.
The lower diagram suggests that when the two halves of the span have been joined, the resultant rigidity reduces the amplitude of any oscillations. It also increases the frequency. We can see this from the shorter wavelength, about equal to the span.
In principle an active damping system could be created using movable masses near the ends of the cantilevers during construction. Small signals from sensors on the deck would be amplified and used to control hydraulic or electric motors to move the masses. The system would require emergency power generators in case of a power supply failure. Such a system has been used in tall narrow buildings. Because the moving mass is much smaller than the effective mass of the structure it must move more quickly.
Upside Down Cable-Stayed Bridge
|In the paraglider the deck has become a wing, supported by the air,
with many threads converging below to carry the load, the pilot. The
high-winged monoplane with struts from wing to fuselage also recalls an
upside-down cable-stayed bridge in flight. But the wings of the
third aircraft resemble cable-stayed cantilevers when on the
The rotary clothes line is like a bridge which has three self-anchored spans. If the clothes are hung on the cords, which is the normal usage, the system is like a suspension bridge, but if heavy clothes were hung on the struts, it would be more like a cable-stayed bridge. The second picture shows numerous newly hatched caterpillars; a moth must have mistaken the line for a plant stem. Another kind of endless span is a childrens' roundabout which consists of a polygonal seat suspended from a pivot by a conical array of stays.
Invisible Cable-Stayed Bridges
Before the invention of steel-framed buildings, people sometimes wanted to build a library on an upper floor in a large building. To take the great weight of many shelves of books, cables or rods were used. The shelves were built back to back, at right angles to the walls.
The cables sloped down from the wall to the floor between the shelves, and were invisible. The inward pull of the cables at the top of the wall was taken by the beams in the ceiling. Thus the appearance of the room was not spoiled by the engineering.
During the 1980s and the 1990s, highly visible cable-stays and tie-bars were very popular with architects. These two examples are at Gloucester Docks and the Indoor Arena near Birmingham Airport, seen in the middle picture and at the far right of the third picture.
During those decades the classical ideal of hiding certain things was dropped by many designers. The Pompidou centre is a well-known example. This type of construction does not always create a restful feeling.
If you got this far, try a superb game about bridge building - http://firingsquad.gamers.com/games/pontifex/default.asp .
Links to Other Web-Sites About Cable-Stayed Bridges
Back to Home Page Back to Bridges
Arch Beam Box Girder Cantilever Pre-Stressed Suspension Truss