Cabled Stayed Bridges - Part Two

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Jackfield  Bridge  in  Coalbrookdale

Not far downstream from the famous Ironbridge, the Severn is crossed by a much newer structure - a cable stayed bridge. Here are some pictures. As the plaque states, an earlier bridge, known as the free bridge, because the other bridges were tolled, was built in 1909, in the early days of reinforced concrete. The famous name of Hennebique, the great pioneer of reinforced concrete, appears on the plaque. In 1994, an asymmetrical cable stayed bridge was built as a replacement. The second picture shows a small segment from the old bridge.

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Cable stayed bridges are apt to look somewhat angular and highly stressed. This design makes no attempt at disguising anything: all the parts are so clearly visible that the bridge could be used as a textbook example. In the last picture we see the cable anchorages, the terminal deck pin, and the foot of one strut, which is tapered to the point where it is more or less a pivot. The last picture but one shows that the tower, except for the upper segments, is not in a vertical plane.

The tower is essentially an A-frame or shearlegs, but instead of continuing to an apex, it is truncated, rigidity being provided by the ring, which also supports the two vertical cable supports. These supports continue above the cable attachments, tapering to provide a neat finish to the tower, which otherwise might have looked somewhat stubby. If you approach Ironbridge from the east, intending to park in the Ironbridge car park, you will cross this bridge. You can walk easily from the Ironbridge to the Jackfield bridge along the south bank of the river Severn. On the way, you may see this exhibit -

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The thick orange deposit in the bed of the stream shows the presence in the rocks and soil of the iron that was the basis of industry in Coalbrookdale.

Across the river you will see the ruins of some furnaces.

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Sabrina  Foot-Bridge  at  Worcester

This beautiful and interesting little footbridge is found to the north of the railway bridge in Worcester, joining Le VĂ©sinet 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 accurate setting of the cable lengths. With a through truss, inaccurate cable lengths would produce uneven tension in the cables, and unwanted bending stress in the deck.

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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?

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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.

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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.

GlasBells85.jpg (97262 bytes)GlasBells86.jpg (67245 bytes)These pictures, of Bell's bridge in Glasgow, show a similar construction, but with symmetrical spans, needed because the bridge is a swing bridge, pivoting around the central pier.

CliftonArch.jpg (44490 bytes)On entering upon a suspension bridge, you will generally be confronted with an orderly view, comprising the graceful sweep of the thick main cables, and the parallel lines of the thin hangers. Like an arch, a suspension bridge is readily understood, and is sometimes preferred to a cable-stayed bridge by non-engineers.

WeiirdCSBridge.jpg (96004 bytes)What is this?

It is one thing to draw a lot of shapes for a bridge. It is another to make something sensible. Engineering is not geometry.

If we look at the places where cables are attached to the deck and the tower, we can write down some conditions that must be met. Look at the diagram below, and work out the conditions for equilibrium.

We should note that A1 is not equal to A2 because the cable sags. We should also note that T2 is greater than T1 because T2 has to hold up the weight of the cable as well as a part of the bridge.  Is this a correct statement? And we should note that the cables will stretch, while the deck will be very slightly compressed.

We also require the condition that no bending moment be introduced into the deck or the tower because of the cables: in other words, we should build as if the tower and the deck were not very rigid, and try to keep them straight. The resultant forces are therefore required to be parallel to the deck and the tower.

We can write the following four equations, which will be repeated for every cable in the bridge. Then we have to solve the entire set of equations, remembering that any change in any force changes the length of the member, producing yet more equations.

T1 sin (A1) = M1g

T4 sin (A4) = M4g

T2 sin (A2) = T3 sin (A3)

Solving sets of such equations is often difficult. Rather than do it directly, it may be better to start with some approximate values. We then create a list of discrepancies which will guide us to better values, which we insert into the equations. This process is repeated until the values change very little. The process is called iteration.  Naturally, we try to make the changes in such a way as to minimise the number of iterations.

In order to satisfy all these conditions, we might find that the cable attachments are not uniformly spaced along the deck or up the tower. We have, however, another variable at our disposal, namely, the angle of the tower from the vertical. Yes - it does not have to be vertical, and in some cable-stayed bridges the tower is very far from vertical.

In practice, each cable is tensioned using a device which includes a measuring instrument which enables the tension to be adjusted to the calculated value. This is better than simply building the bridge to an absolute set of sizes, because the adjustments can reduce the effects of dimensional tolerances in all the parts.

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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. Click here to run or download a program showing the exchange of stored energy and kinetic energy in an oscillating cantilever. Because the stored energy is a combination of compression energy and tension energy, which are portrayed as red and blue respectively in this web-site, the stored energy is shown as magenta, a combination of red and blue.

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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.

FrogCantApril.jpg (68616 bytes)These pictures show a cantilever with and without vertical oscillation, caused by a gust of wind.

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.

CSFarmA.jpg (48862 bytes)A small cable-stayed span. This beam is actually hollow. It carries material between two farm buildings, blown by a current of air. To save weight, the span is supported by cable-stays. On the right side, the support is self-anchored by a tie below the span.

 

Upside Down Cable-Stayed Bridge

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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 ground.

 

 

Two of these pictures show how elegantly the lines spread the weight of the man over the canopy, also maintaining the correct aerofoil shape. The third one shows a man making meticulous preparation for a flight. The canopy and the lines on the ground are reminiscent of a tree that has been cut down and chopped up, or perhaps a shot bird - bearing no resemblance to the thing in its element.

 

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.

 

Visible Cable-Stays

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 in a building at the NEC near Birmingham Airport, seen in three of the pictures.

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Here is a cross section, not to scale, through such a building, before the roof has been added. Apart from the effects of self weight, all these parts are free of bending moment.

Many stadia have roofs that are cantilevered, using all a great variety of designs, some using cables.

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.

CraneZ.jpg (53798 bytes)Here is a type of crane which can be seen on almost any large building site. The truss provides lightness. The stays allow a longer reach than the truss alone could support. The roof supports shown above are like very solid versions of this crane.

CableGate.jpg (41368 bytes)CableGate2.jpg (141228 bytes)To make a gate, you can go for a rigid and rather heavy construction, which imposes great stress on the gate-post and its foundation, or you can go for lightness, and use cable-stays to hold up the gate.

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

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