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For Cable Stayed Bridges - Part Two - Click Here
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 against buckling 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.|
cable-stayed bridges 2 cable stayed bridges 2
|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 of the cable are joined directly to the ground at each side of the valley.||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.|
cable-stayed bridges 3 cable stayed bridges 3
|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 able to resist the possible effects of fatigue that might result from an alternating load.|| Great attention needs to be paid to aerodynamic stability in
suspension bridges. The effects of wind are much better understood than
they used to be, and the advent of the streamlined deck, used first in the Severn
bridge, has reduced the cost of suspension bridges.
Another advantage of the cable-stayed bridge is that the cables can be fabricated separately and brought to the site when required, rather than spun in place.
cable-stayed bridges 4 cable stayed bridges 4
The greater inherent rigidity of the triangulated cable-stayed bridges, compared with the suspension type, is a great advantage. 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, and 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.
cable-stayed bridges 5 cable stayed bridges 5
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.
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.
Statically Indeterminate Structures
A very important difference between cable-stayed bridges and suspension bridges is that the former are indeterminate and the latter are not. What does this mean?
Imagine lifting a heavy weight by a rope. You might use two ropes, one in each hand. You would automatically place your hands to equalise the tensions. You could still do that with the hands close together. But what if you tied the tops of the ropes together, and lifted with one hand? Unless the lengths were very close to equal, one rope would be slack. And what if they had almost equal length? How would we know how the load was being shared? If each rope could support only 0.6 of the load, and the sharing was 0.7 and 0.3, one would be overloaded. On the other hand, if both ropes were bungees, they would stretch, and the loads would be much nearer to equality. Here we have seen the ingredients of indeterminacy - more than one component doing the same job, and a large degree of stiffness. In an indeterminate structure, the simplest methods of calculation do not work.
That doesn't mean that indeterminate structures are not built: on the contrary, the redundancy can lead to greater safety, though as in the case of the overloaded rope, it can create problems.
Let's look at a small part of a suspension bridge. The deck normally possesses a measure of rigidity, if only to prevent it sagging between the hangers. In practice it is much stiffer than that, to spread the effects of live loads. So if we were to remove one hanger, the deck would survive, by increasing the tension in the neighbouring cables. If one hanger is a little too long, the main cable makes a smaller angle at the top of the hanger, and if it is too short, the angle is bigger. Since the angle of the main cable is simply related to the hanger tension, we can even calculate the change in tension. Note that we have four elements here - a very rigid deck section, a hanger that is very resistant to tension, and two main cable sections that are also resistant to change. The key here is the ability to change the angle.
Looking now at a cable-stayed bridge, we see that the situation is quite different - again a "rigid" deck and a "rigid" tower, and a set of cables that are hard to stretch. What is missing here is a variable that is compliant, as the angle was in the suspension bridge. If any cable is too long or too short, its tension will differ enormously from the desired value, because the change in strain of a steel cable for even the maximum safe load is very small. That section of the deck will experience forces that differ from the design values. Therefore, provision is made in a great many cable-stayed bridges for the tension in each wire to be adjustable during the building of the bridge. It is entirely possible to build a suspension bridge with no adjustments at all.
We wouldn't build a continuous beam bridge with piers as closely spaced as the cables of a stayed bridge. So why are the cables placed so closely? One difference between piers and cables is that cables are much narrower than piers, and therefore cheaper. Why are they narrower? Because they don't have to resist buckling. Physics books often mention symmetry and broken symmetry. Structural engineers experience asymmetry too. Gravity is the one asymmetry that is always present, because it distinguishes the directions up and down, by giving weight to every object, but if all the other forces are much greater, then gravity can be unimportant.
A graph of tension/compression versus deflection is often a virtually straight line through the origin, but on crossing from tension to compression, we enter a different world where buckling has to be reckoned with. Thus our compression members, or struts, are almost always thicker than our tension ones, or ties. That is the second broken symmetry of engineering. In a sense, these lead to a third, which is the fact that it is very often easier to destroy something than to build it.
Returning from this digression into physics, we see that once a bridge has been built, adjustments should not in principle be needed. In practice there may be creep of ground or concrete. More seriously, earth tremors may create significant changes in vital dimensions. So various means of jacking are sometimes provided. In fact, jacking is often adjusted during construction, as the forces gradually change. The feet of the Tour Eiffel incorporated large jacks for this purpose.
We will illustrate the point about indeterminacy by an exception - the Sabrina bridge in Worcester. Here the deck is in sections which are very narrow at the cable attachments, effectively forming hinges. Note that a joint may sometimes be regarded as a hinge if its flexibility is much greater than that of the surrounding material; a concrete hinge is of this kind. You can see that in the Sabrina bridge, the shape of each triangle is independent of the others, the hinges providing the compliance. For more about indeterminacy click here here.
|This picture of the superb Puente Tampico bridge was kindly donated by Gilberto Castañeda. The main span, across the Rio Panuco, is 360 m. Notice the unusual design of the towers below the span, with vertical piers resembling those of the side spans, and providing attachment for the deck. There is only one plane of cables; the deck must be stiff enough to transmit torsional forces to the nearest pier, a good reason for those central piers under the towers.|
=== cable-stayed bridges 6 cable stayed bridges 6
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.
Although the bridge was referred to during construction as the "Second Severn Crossing", there are about a hundred bridges over the Severn, and many more have been built and lost or destroyed. cable-stayed bridges 7 cable stayed bridges 7
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.
cable-stayed bridges 8 cable stayed bridges 8
|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 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. Building details|
cable-stayed bridges 9 cable stayed bridges 9
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. The manager gave kind permission for the map to be shown here. 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 at strategic points on the cables. The examples shown below are from the Severn suspension bridge, before and after refurbishment. cable-stayed bridges 10 cable stayed bridges 10
Dampers may also be added to stringed instruments such as violins, and to 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-west of the Severn cable-stayed bridge, just upstream of the confluence of the river Wye and the river Severn, a smaller cable-stayed bridge with a main span of 770 feet takes the M48 (ex M4) across the Wye, at the Welsh end of the Severn suspension bridge. Here are some pictures of the bridge in its original configuration.
The second picture has been squashed sideways by a factor of four, 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 provision of multiple cables in many cable-stayed bridges enables refurbishment and replacement, but in the bundled cables of the Wye bridge, ten of the twenty strands are inaccessible. The refurbishment, done between 1985 and 1991, replaced the bundles by groups of twelve well spaced strands.
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 outweighed by the cost of providing torsional stiffness. For box girders on piers, the potential untidiness of two rows of piers is avoided.
The towers are of steel box construction. Because of increased traffic, the single cable pair per span has been replaced by a harp like arrangement. The sag of the deck has been greatly reduced by this means. Wye bridge data Wye bridge changes
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.
=== cable-stayed bridges 1 cable stayed bridges 1
Modifying the Wye Cable-Stayed Bridge
One benefit of modifying something is that you don't have to build everything from scratch. One problem is that some of the original features of the design may not be what you would have wanted. Another is working out how to hold the structure up while you are making the changes. Yet another is the adverse reaction when users of the bridge are affected by closed traffic lanes.
The next set of pictures show the cables that were fitted as replacements for the original ones. In the bridge as designed, each tower carried cables made of close packed bundles of twenty cables each. Each tower now carries two cable sets made of twelve well spaced cables per set.
In these pictures you will have noticed the triangulated bracing between the cables which greatly reduces the amplitude of oscillations, the plates near the top where the towers were made higher, and the extra stiffening plates which cover the lower part pf the towers, from the deck to just above the lower cables. The towers and the cable anchorages are protected from the traffic by heavy steel fences.
You noticed also that the cables are not all attached in the same way. The outer sets of four are held by saddles bolted to the sides of the towers, while the middle sets are attached to the towers. The attachments are not simply bolted on the plates of the towers: we can be sure that they are connected within the towers to transfer the forces between the opposing cables, just as the wings of an airliner are attached to a beam that passes through the fuselage. Why didn't the engineers simply make two rows of six cables, hung on saddles? Perhaps the answer lies in movement of the bridge. If all the cables were at the same level, vertical movement of the bridge would make them expand and contract identically. The vertical displacement means that they will all behave slightly differently.
Why space out the cables? Spaced out cables offer the possibility of access and maintenance, impossible with the previous design. They also make possible the replacement of cables with new or refurbished ones. That is something that is not possible with the main cables of a suspension bridge.
The next set of pictures shows some of the details mentioned above. The long connectors on the ties between the cables are probably turn-buckles, which have left-handed and right-handed threads to allow the spacing to be adjusted. The cables have an outer layer comprising many helically wound wires. This bridge and its two larger neighbours live in a rather hostile environment - an estuary blown by salty winds which are predominantly straight up the estuary from the Bristol Channel, so the potential for erosion and corrosion is very real. The last picture shows the small inspection hatch giving access to the interior of the tower. It is surrounded by plating that reinforces the tower to reduce the effects of the hole.
The first picture shows that the sagging of the bridge has been very much reduced by the addition of the extra cables. The Severn suspension bridge is visible in the distance, as is the change in gradient at the start of the side span. The second picture, an earlier one rotated and compressed, reminds us that there are no sag free cables, though the sag is very small, because the tension is great.
There is something odd about the description of this Wye bridge: no mention has been made of what lies beneath the deck, and that is an important subject. The use of cables in a single plane means that the only defence the bridge possesses against torsion is its own stiffness, which must be able to transfer torsional forces to a place where they can be resisted. It is therefore imperative that the supports at the towers be designed to take these forces. A box section for the deck is a good means of providing stiffness. The next diagram shows a side view of one half of a cable-stayed bridge like the Wye example.
The next set of diagrams shows some of the possible ways of providing support at the towers. cable-stayed bridges 13 cable stayed bridges 13
In the first of these the pylon has to resist all transverse forces on its half of the span, and the cantilevers must take the torsion of the deck. In the second and third examples, the torsion of the deck is taken down to the ground, and in the third case, some extra stiffness is offered to the pylon. In the fourth example, the beam has to take the weight of a section of the deck. The supports of the Wye bridge look rather like the diagram below.
The potential problem with the single pylon is that matching the style of the upper and lower parts of the bridge may be difficult. Does this matter?
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