Extended Project

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THE FARNBOROUGH EXTENDED PROJECT 2010 ADVANCED LEVEL AUTHOR DECLARATION Title of the Extended Project: What are the differences and similarities between Cable Stayed and Suspension Bridges and where are they best suited? Word count: 4,514 Submission date: 28.10.2010 I affirm that this Project is offered for assessment as my original and unaided work, except in so far as any advice/and or assistance from any other named person in preparing it, and any quotation used from written sources are duly and appropriately acknowledged. I agree that my submission may be referred to the JISC Plagiarism Service in order to fully authenticate my work. Name: David Bedford The Sixth Form College Farnborough, Prospect Avenue, Farnborough, Hampshire, GU14 8JX Tel: 01252 688200

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What are the differences and similarities between Cable Stayed and Suspension Bridges and where are they best suited?

Transcript of Extended Project

Page 1: Extended Project

THE FARNBOROUGH EXTENDED PROJECT 2010

ADVANCED LEVEL

AUTHOR DECLARATION

Title of the Extended Project:

What are the differences and similarities between Cable Stayed and

Suspension Bridges and where are they best suited?

Word count: 4,514

Submission date: 28.10.2010

I affirm that this Project is offered for assessment as my original and unaided work, except in so far as any advice/and or assistance from any other named person in preparing it, and any quotation used from written sources are duly and appropriately acknowledged. I agree that my submission may be referred to the JISC Plagiarism Service in order to fully authenticate my work.

Name: David Bedford

Candidate number: 91113

Supervisor: Jane Gostling

Project Leader: Simon Reigh, Faculty Director (Business, Information & Global Studies)

The Sixth Form College Farnborough, Prospect Avenue, Farnborough, Hampshire, GU14 8JX Tel: 01252 688200

Page 2: Extended Project

What are the differences and similarities between

Cable Stayed and Suspension Bridges and where

are they best suited?

Acknowledgments

I would like to extend my thanks to Neale Lawson and to his extensive

library. I also would especially like to thank Jane, my supervisor. But most

of all: the internet and its many search engines.

Abstract

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This is a study of cable stayed and suspension bridges and where they are

best suited. I find that suspension bridges initially have the role of

spanning gaps, but prove to be inefficient in cost and build time but prove

to be affective of spanning huge gaps as they are the only type of bridge

that can do that.

I find that cable stayed bridges are more cost effective and a lot faster to

build than suspension bridges and are now taking the place of suspension

bridges where 50 years ago a cable stayed bridge would not have even

been an option.

I conclude that suspension bridges will not be as popular as they were and

that cable stayed bridges will be built more often but the suspension may

still be the only option when huge spans are necessary.

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What are the differences and similarities between Cable Stayed

and Suspension Bridges and where are they best suited?

When a bridge is commissioned many different bridge types and designs

can be submitted, this can lead to a difficult decision as to which is the

best suited for the place and budget. When it comes to bridging long

spans or wide rivers there is no competition for suspension or cable

stayed bridges. However these are relatively new bridges and in the past

these same gaps were

spanned with many piers

examples of the old a new

is visible in many places

such as the fourth estuary,

where you have the Fourth

Railway Bridge, a

cantilever bridge, and also

the Fourth Road Bridge, a suspension bridge.

Suspension bridges were first used thousands of years ago in Asia, South

America and Africa. They consisted of vines tied to trees across a valley;

they held strong twigs or wooden planks which were used as a walkway.

They were very important as they enabled people to cross rivers and

valleys much faster than would have otherwise been possible. However

these are not the type of suspension bridges we imagine today, bridges

made of steel and concrete, with supporting towers and huge lengths of

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cable. The first modern suspension bridge was built in 1801 by James

Findly, it was an iron chain bridge, however there is no more information

on this bridge as it served near as much no purpose other than as an

experiment. He built one after in 1808, this has more documentation. It

consisted of two spans; the longest of them was just over 60m or 200

feet. Part of it broke when a herd of cattle were driven over it and it fell

down later in heavy snow fall in 1816. It was not a great start but it drove

a rapid development in suspension bridges.

The first success came in 1810 with the Essex-Merrimac Bridge, built by

Finley and a carpenter called Carr, this had a span of 240 feet, the chains

broke in 1827 but were replaced and this bridge had a service of 99 years

before it was dismantled and replaced by a wire suspension bridge much

along the same lines. The first suspension bridge in the UK was the Union

Bridge, it spans the river tweed connecting England and Scotland. It was a

record breaker at the time with a span of 137 meters. It is still standing

today and serving its purpose of as a single lane road, it is the oldest

bridge in the world that

is still being used; it

dramatically cut journeys

by 11 miles. It is supported by 6 iron chains, 3 on each side, in 1902 wires

were added to support the roadway even further.

Wire suspended bridges started later than its chain counterparts, they

quickly overtook the chain bridges as they were more reliable and less

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likely to suddenly break as it is more apparent when wires break as it is a

slow process and is easily observable. When James Findly's bridge

collapsed in 1808 it was temporarily replaced by a wire bridge. The first

permanent wire suspended bridge came in 1823 and had two spans of

40m, but they have really come of age since. The first suspension bridge

to use steel cables was constructed in New York by John Roebling who

died before its construction so his son, Washington Roebling and his wife

saw it through, it connected Brooklyn and Manhattan, the Brooklyn Bridge.

It was 50% bigger than anything that had been done before. It is one of

the few bridges of this time to still be standing as none of them were

tested against the wind before being built. Roebling built a truss system

that was 6 times stronger than he thought it needed to be and that's why

it is still standing today. It was thought that the bridge would not be

strong enough as nothing on this scale had ever been attempted before

so an extra 250 cables were added diagonally – much like a cable stayed

bridge, these were later found to be unnecessary, rather than be used

elsewhere they left them because of their distinctive beauty.

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The Akashi-Kaikyō

Bridge, also called

Pearl Bridge, is

longest suspension

bridge with a span

just shy of 2km (1,991

metres), it was

finished in 1998 and

overtook the Humber Bridge which has a span of 1,410 meters, it took 12

years to build and was built after a series of deaths from the ferry crossing

which happened in quick succession. During construction an earthquake

hit when only the towers had been built. They had moved as a result, this

meant that an extra 1 meter had to be constructed, harder than it sounds!

It has been built to withstand winds of 286 km/h (178mph) and

earthquakes measuring 8.5 on the Richter scale. The steel cables contain

300,000 km of wire and are 1.12 meters thick. It is a truly amazing feet

and a real testimony to modern engineering.

Cable stayed bridges can be traced back to 1784 when a German, Carl

Emanuel Löscher designed a timber bridge. They were not used or

developed as the French engineer Navier inducted a study in the 19th

century which showed that suspension bridges should be used rather than

cable stayed bridges as the process of balancing the load could not have

been done as easily as modern technology now allows. German engineers

headed up the design of cable stayed bridges after the Second World War

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when they were challenged to find new and different ways of crossing the

Rhine to replace many of the old existent bridges and the ones that had

been destroyed during the war. Dischinger proposed a type of suspension

bridge that incorporated cable

stayed bridges. He conducted a

study into this, it lead to no bridges

but proved to be a major step

forward to creating the first ones. It

was not until the late 1950's when

Dischinger designed the first truly

cable stayed bridge. The Strömsund Bridge built in 1955 had a main span

of 183m and two side spans of 75m. Spans of this size really only became

possible after improvements were made through structural analysis. Cable

stayed bridges had been attempted before this but this is considered the

first by many. A further three bridges were built over the Rhine.

The first cable stayed bridges used very little cable but this created

substantial erection costs as supports would been needed to hold the

deck as wires were put in place. More cables were added generally as this

proved more economically viable. They were really only given their break

when suspension bridges started failing due to wind causing oscillations

and eventually failure. The most famous of which is the Tacoma Narrows

Bridge, nicknamed Galloping Gertie, which collapsed only 4 months after

it was completed in 1940.

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The Sutong Bridge in

China has the longest

span of any cable stayed

bridge. At 1,088 meters

it is not as vast as the

longest suspension

bridges but is certainly

catching up. It was awarded the 2010 outstanding civil engineering

achievement award by the American Society of Civil Engineers. As well as

being the longest suspension bridge in the world it also has records for

the largest foundation ever attempted and the 577 meter long cable stays

were the longest ever manufactured. The total length of the bridge is

8,206 meters; it took 4 years to built and cost £1.1 billion. It reduces the

time to get from Shanghai to Nantong form a four hour ferry crossing to a

1 hour drive.

There are two main types of

cable stayed bridges – radial

(fan) and parallel (harp). This

represents the arrangement of

the cables. In a radial cable

stayed bridge all the cables

come from a single point on the

tower to several points on the road, the advantage to this is that it can

create a near vertical force on the tower due to the smaller angles

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between the cables and the tower. A parallel cable stayed bridge the

cables come from different points on the tower and the deck, and all the

cables are parallel to each other. This can mean that large horizontal

forces from the deck are transferred on to the towers which can cause a

lot of stress. This is overcome by having a split in the concrete or

structure allowing for movement.

Bridges have to be able to support two loads: its own weight which is

called a dead weight and also the weight of the things crossing it, the live

load. Bridges do this through tension and compression. Tension is where a

material is stretched, in metals it causes atoms to slip over each other

stretching the metal. In other materials it causes them to snap and sheer.

Compression occurs when a material is squished causing a metal to

buckle and deform and non-metals to crush. All bridges manage these

forces in different ways. Hanging bridges, suspension and cable stayed,

deal with these in the same way. The tension is in the wires, as they are

being pulled by the road deck to where they are attached either to an

anchorage point, in the case of suspension bridges, or onto the

tower/opposite road deck, in the case of cable stayed bridges. The tension

in the wires in turn exerts compression on the towers which they are

attached to or resting on, this compression is the dissipated into the

foundations bellow the bridge. There is also compression and tension on

the road deck, the road deck wants to bend, the wires are required to

reduce and support the bending preventing disaster. As the deck bends

with the ends pointing towards the ground there is tension at the top and

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compression on the underside. A successful bridge manages these forces

well enabling it to both carry the dead weight and the live weight.

Suspension bridges can be anchored in two ways, the cables need

anchoring so as to keep tension in the cables, keeping the bridge from

falling down. They can either be self-anchoring or use like most have

separate anchorage points. Self anchoring bridges have their cables

attached to the end of the road deck this limits the length of the span as it

would put large amounts of stress on the road deck, the longest of this

type has a span of 300m. The proven method is creating a separate

anchorage point. This usually consists of the cables embedded in large

amounts of concrete, the wires are spread in the concrete foundations so

the there is not too much force at any point acting on the foundations.

This can be costly due to the vast amount of materials needed, take the

Humber Bridge for example: it uses 490,000 tonnes of concrete. This all

has to be laid in one sitting so cracks do not form. During the construction

of the anchorage points for the Humber Bridge 1000m ³ of concrete was

laid per day.

This is an advantage of cable stayed bridges in that they do not need

anchorage points as the weight is balanced out on each side meaning that

one side is supporting other and that same side is supporting the other

side -which is supporting it. This is also a technique used in buildings;

Wembley stadium wanted an uninterrupted viewing area this meant there

could no pillars supporting the roof. They decided to build a huge arch

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that would not only be a landmark but also support the roof. The roof was

tied to the arch using the same cables that would be used on a cable

stayed bridge. The brilliant thing is that the arch needed no supports

either as it was held in place by the weight of the roof. This is a great cost

cutter as fewer materials are needed.

A suspension bridge deck is held by the suspending cable, its distinctive

curve is called a cantenary. This usually refers to a curve of an object

under its own weight such as in a chain held at two points. But in a

suspension bridge the weight of the cable is usually negligible, the curve

is created by the uniform distribution of the weight against the length of

the cable. The curve can be represented by an equation. If you call the

length between the towers L and the weight is uniform then the total load

can be expressed by wL w being mg(mass x gravity). The “sag” of the

curve is s and the cable pulls on the tower with a total force or tension T.

The vertical component can be represented by V

and the horizontal by H. If we consider the total

forces in the x axis then T=H at the lowest point as

H is a tangent to the curve at that point. If V

equals the weight of the cable as weight acts in vertical component, then

the dy/dx (gradient) of the cantenary is WV/H. When integrated this then

gives y=(w/2H)x² which is a parabola x² with parameter w/2H. We can find

out the value of H by using the tension at certain points on the curve and

using trigonometry to work out the horizontal component. The total forces

of the horizontal component must equal 0 otherwise the bridge would

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collapse. This gives the remainder Hs=(wL/2)(L/4). At the bottom of the

curve there are no vertical components so (wL/2)(L/2) =Hs+(wL/2)(L/4).

To work out the tension we can substitute x=L/2 back into y=(w/2H)x²

then s=wL²/8H and the equation is x²=(L²/4s)y. Knowing that L and s give

the shape of the curve and then the tension of any point of the curve can

be expressed as T=(wL/2)[(L/4s)² + (2x/L)²]^½.

In a cable stayed bridge the tension can be worked out as if it were a

triangle. It would be a right angled triangle therefore the simple laws of

trigonometry can be applied. To work out the tension you could express

the total load again as wL, this is held by two towers but they do support

the span load together so it is wL/2 for each tower. The weight only acts in

the vertical direction so the cables have to support this weight this means

the smaller the angle of the cable against the tower then the lower the

tension. By expressing this angle as θ then Tension=w/cosθ, as θ

increases cosθ decreases. In a cable stayed bridge, as in a suspension

bridge, the horizontal forces cancel out however in a suspension bridge

they are only acting on the towers, in a cable stayed bridge they are

acting on the towers and deck. This means that the deck is under

compression in the horizontal direction and has to be strengthened to

withstand Tsinθ. This is usually done by using steel box girders or

concrete. This is one of the main reasons why cable stayed bridges will

not be as long as suspension bridges as the towers would have to increase

considerably or the deck would have to be able to resist higher

compressive forces without gaining to much weight, where as in a

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suspension bridge they just have to make the anchorage points larger to

withstand the higher tension forces.

Another factor that engineers have to take into account with cable stayed

bridges is that the tension is going to change as the day goes on due to

expansion and contraction. This could lead to disaster as the towers could

shear as could the deck as it is lifted or dropped. They have allowed for

this by using an inverted Y which allows for bending even in concrete

structures. This means that taller towers could be built as expansion and

contraction be accounted for.

Britain still had one more Estuary to cross in the 1970's, the last big span

was needed over the Humber river, a bridge had be thought of for over

100 years and in 1935 after the completion of the Golden Gate bridge a

proposition was put forward Sir Ralf Freeman. It needed to be a single

span due to fierce opposition from the people who used it, Freeman

realised that a bridge would only be built if it was a single span. The

government only made feasibility study for the bridge in 1969. They

proposed due to the maximum traffic at the time that it was only feasible

to create a two lane highway across the river. In 1971, Freeman Fox &

Partners who had been waiting for the contract since 1927 finely got given

75% of the money to build the bridge. It was to be the longest single

spanned suspension in the world, yet it was produced very economically

using the latest bridge technology. The road deck was made using steel

box girders which Freeman Fox had used on the Severn Bridge and

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concrete towers which were less expensive than steel and could be built

faster and easier keeping costs low. It was built using the latest methods

such a wind testing, it had to withstand base winds of just under 100mph

and the top of the towers had to stand up to over 150mph. Various

models were crated and tested and they showed that it was feasible. It

was unknown territory for many as never had a bridge been built on this

scale with a low budget.

They met problems when looking at how they were going to make strong

foundations, the geology was different on the opposite sides of the river.

On the north side foundations would be relatively easy to build as the

chalk created a solid base. However on the south side the chalk had be

eroded from the glacial river before, all that was left was a clay that when

it contacted water it created a slurry, not ideal. As well as poor

foundations it was also being built 500m from the shore which adds extra

problems. The solutions was to build a hollow caisson to go 16m below

the surface, which is about 4 giraffes, 8m of which is bellow the

Kimmarage clay. As it was sunk it hit some high pressured water which

burst into the structure washing some lubricant away, this meant that an

extra 3,000 tonnes had to be

added to sink the tower, this

also caused costly time wise,

however on the north tower

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they regained that time from the experience that they had gained from

the south tower.

The steel box girders had proved very successful; they were part of the

longest bridge in the world outside the USA and on the Severn Bridge.

They wanted to stretch what they had done before by almost 50%. It is a

hollow box which has been built from a stiffened plate. The sections are

22m by 4.5m they are a trapezium shape giving them their extra strength.

They are shaped to also use the wind to relieve the deck of weight which

also adds to saving costs as they are shaped much like an aeroplane wing

providing lift. The structure also allows access from the inside which

makes it allot easier to build and fabricate and ensures a strong weld. It

took 124 box’s to complete the road deck each box weighs 120 tonnes,

which means the total weight is 14,880 tonnes. The total length of the

cable that supports this could go two times round the world! It was

completed in 1981 and was the longest single spanned suspension bridge

for 16 years, testament to its engineering.

The Tarn Valley in Southern France became a huge stepping stone when

the A75 was being built in 1975 and it was not until 1994 that they

decided a bridge a few miles down from Millau was the solution to the

huge valley. Then in 1996 the bridge was chosen, it was drawn up by Lord

Foster and headed by the French construction company Ponts et

Chaussées. It was chosen because of its aesthetic integration and just

pure beauty. In 1998 the government granted a 75 year period for the

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construction and management of the viaduct. On the 14 December 2001

the fist brick was laid and construction started making headway. The

Millau Viaduct was such a huge task that is called in the most advanced

technology and wide range of specialists ever on one building site.

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In was done in six stages which were: Raising the piers; launching the

deck; the junction; installing the pylons; the cable stays and laying the

road surface. The piers needed to have huge foundations which would

keep them upright. They are known as Moroccan Wells and are 5 metres

wide and 15 metres deep. There is also a foundation slab above this which

is 5 metres tall and required 2,100m³ concrete to be continually poured.

After this the piers began to rise at 4 metres every 3 days, work had

started on March 2002 and ended in December 2003. The deck is made of

173 central box beams and weighs 36,000 tonnes. As the bridge has a

slight curve each section is unique making production even harder. 96%

of the work on the deck was done at ground level which reduced risk and

cost. 150 people worked for 20 months to complete this section. Rather

than raising the deck to

the tallest bridge in the

world they slid each

section out. Giant

supports were used

between each pier to

help carry the load.

Hydraulic rams were

used to do this, they lifted the deck up each time and slid it forward

before repeating the process again 60cm at a time. At a speed of 9m per

hour they eventually meet on the 28th May 2004. As the launching

operation took place the piers were being put in place, they were

transported over the bridge, where they were partially stayed so the deck

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did not take a nose dive. Each pylon is 700 tonnes and 90 metres high.

Each pylon then carries and is supported by 11 pairs of cable stays in total

weighing 1,500 tonnes. The longest cables have a tension of 1,200 tonnes

and were installed in the protective sheathe cable by cable by a shuttle

were they would be pulled to the right tension. The deck was then

surfaced using a special formula that could cope with the contractions of

the bridge but meet motorway standards. It is 6cm to 7cm thick and is

without blemish to maximise longevity and the need for re-surfacing. It

added 9,500 tones to the bridge and was laid continually so minimise

imperfections, this meant there was a constant stream of 25 Lorries to

supply the two finishers. It was then heat sealed at 400ºC so the steel

deck bellow would not corrode. The bridge has been a great success and

is a modern marvel.

In terms of making an economically viable bridge then large spans are

more costly than multi-span counterparts. This is because of the increase

of expensive materials needed, hard and time consuming construction

techniques and engineering ability as well as other things. By breaking

records you have either found a really effective technique or more likely it

is a demonstration of a countries wealth. In some cases is it necessary like

at the Golden Gate Bridge when a single span was needed as the military

required it. This is why we are currently seeing more cable stayed bridges

as they are cheaper to build and take less time. Suspension bridges are

the most expensive because of the technicality of the, build, construction

and materials needed. Studies into how long it is possible to build the

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different types of bridges have been made. The American Society of Civil

Engineers suggests a suspension bridge could reach a single span of

7,000m; the limiting factor would be the stress in the main cable. This is

double the amount a single span of a cable stayed bridge could stretch to,

3,500m. The limiting factor of a cable stayed bridge would be girder as

compression forces would be too high. This really stresses how much it

would cost to build bridges with such large spans, as the longest

suspension bridge is 1,991m, 5,009m away from what is possible with

steel and concrete. And the longest span for a cable stayed so far is

1,088m; 2,412m away from what is possible. But these bridges are far

ahead of other types, arch bridges have a maximum span of 1,600m, and

truss bridges have no perceivable limit as long as the girder is deep

enough, however the financial limit would be a small 550m.

So why would you build a suspension bridge a not a cable stayed bridge or

the other way round, where are engineers today placing these bridges

and why did they use that type? Suspension bridges can span much

longer distance than that of a cable stayed; this would be used when a

busy shipping channel cannot be interrupted. Even if a multi-span cable

stayed bridge could give the height and spans for all large ships to pass

under, if one were to cash in to the towers foundations the result would be

disastrous; loss of lives, money and the connection that the bridge

provided in the first place. The amount of material is less than any other

bridge over long distances; this could leave to cost reduction and is more

environmentally friendly. During construction access is only needed to

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place the temporary cables so the waterway can remain open, reducing

financial strain on other companies also using the water way. They can

withstand large earthquakes due to less materials and their flexibility.

However they fair terribly in wind due to their flexibility and aerodynamic

properties, to stop this decks need stiffening and aerodynamic profiling.

Also thanks to its low deck stiffness it makes the suspension bridge

unsuitable for rail use and other high concentrated live loads.

Cable stayed bridges excel in places when the suspension bridge fails, it

has a much higher deck stiffness so can handle rail traffic as well as other

concentrated live loads. It can be constructed by pushing out the decks

using the cables as both the temporary and permanent supports. This

technique was used during the construction of the Millau as no materials

could be raised as the bridge was so high up, the largest tower was taller

that the Eiffel Tower a near impossible task that could not have been

feasibly spanned by a suspension bridge. The horizontal forces balance so

no large anchorage system is needed. They can also cover a larger

distance than suspension bridges as they can have multi-span structures,

where as a suspension bridge has a limit of two spans, however this itself

is incredibly hard to construct and anchor down. There is only one

suspension bridge which has three spans and that is technically two

suspension bridges joined together as there is a central anchorage point,

the San Francisco Oakland Bay Bridge. In all they both have there

advantages and disadvantages. I believe that cable stayed bridges will

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replace many of the original suspension bridges, like the Second Severn

Crossing or the proposed replacement for the Forth Road bridge.

Evaluation

When I decided to do an Extended Project I did not know what I wanted to

do it on. I knew it would be something to do with engineering, In the end I

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choose to do something with bridges so I started my research. I had

previously watched a program on the building of the Millau bridge, this

lead me to many other interesting articles on cable stayed bridges, so I

knew I was going to include that. It also highlighted that the general

public did not know the difference between cable stayed bridges and

suspension bridges. I decided that I would highlight the differences

between the two and also the similarities.

I knew my Granddad was also interested in engineering, I gave him a call

and he sent down a couple of books which I found interesting and also so

articles which help build my background knowledge, which I have found

very useful. I also took out a few books from the library some were not so

useful but one was particularly useful and gave the general gist of how

they worked and were built. Often when I was writing I did not quite have

a grasp of the topic so I would have to do some more research, so I knew

what I was writing was correct and could be justified. This took time and I

lost the fluidity that I was writing with so I had to leave it for a bit and then

come back. If I were to do it again I would have a more thorough plan and

therefore greater background knowledge. This would improve the fluidity

of the essay and make it easier to read.

Bibliography

BBR. (2005). Cable Stayed Structures and Stay Cable Technology. Retrieved from BBRNetwork.com: http://www.bbrnetwork.com/inside/cable-stayed.htmlBeckett, D. (1980). Brunel's Brittain. David and Charles.

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Belard, A. (2005). the a75 autoroute (clermont-ferrand to béziers). Retrieved from ABelard.org: http://www.abelard.org/france//motorway-aires10.phpBenckett, D. (1984). Stephensons' Brittain. David and Charles Ltd.Bernado, S. D. (1990). Motion Based Design Of Cable Stayed Bridges. Rome: University of Rome.Blockley, D. (2010). Bridges. Bristol: OUP.Bridge Pros. (n.d.). Cable Stayed Bridge. Retrieved from BridgePros.com: http://bridgepros.com/learning_center/cable-stayed.htmBrown, D. J. (1998). Bridges: Three Thousand Years of Defying Nature [Paperback]. London: Mitchell Beazley; New edition edition (1 Sep 1998).Calvert, J. B. (2002). Parabola. Retrieved from MySite.du.eu: http://mysite.du.edu/~jcalvert/math/parabola.htmHumber Bridge Board. (2008). Engineering the Humber Bridge. Retrieved from HumberBridge.org: http://www.humberbridge.co.uk/media/Engineering_The_Humber_Bridge_e-book.pdfHumber Bridge Board. (2005). Technical Information. Retrieved from HumberBridge.co.uk: http://www.humberbridge.co.uk/explore_the_bridge/engineering/technical_information.phpLe Viaduc de Millau. (2007). History. Retrieved from LeViaducdeMillau.com: http://www.leviaducdemillau.com/english/divers/construction-histoire.htmlLocke, D. (2001). Cable Stayed Bridges. Retrieved from Brantacan.co.uk: http://www.brantacan.co.uk/cable_stayed.htmParabolas in Suspension Bridges! Oh, my! (n.d.). Retrieved from Carondelete.ca.us: http://www.carondelet.pvt.k12.ca.us/Family/Math/03210/page4.htmQingzhong, Y. (2007). Challenges of the Sutong Bridge. Retrieved from transportation.org: http://downloads.transportation.org/InternationalDay/You.pdfRyan, V. (2005). The Millau Bridge. Retrieved from TechonlogyStudent.com: http://www.technologystudent.com/struct1/millau1.htmRyan, V. (2002). The Normandy Bridge (Cable Stayed). Retrieved from TechnologyStudent.com: http://www.technologystudent.com/struct1/norman1.htmSayenga, D. (2008). James Finley. Retrieved from StructureMag.org: http://www.structuremag.org/article.aspx?articleID=804Tang, D. M.-C. (2010). The Story of World-Record Spans. Civil Engineering , 56-63.WGBH Science Unit. (1999). Super Bridge. Retrieved from PBS: http://www.pbs.org/wgbh/nova/bridge/Wikipedia. (2010). Millau Viaduct. Retrieved from Wikipedia.org: http://en.wikipedia.org/wiki/Millau_bridgeWikipedia. (2010). Suspension Bridge. Retrieved from Wikipedia.org: http://en.wikipedia.org/wiki/Suspension_bridge

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Wikipedia. (2010). Sutong Bridge. Retrieved from Wikipedia.org: http://en.wikipedia.org/wiki/Sutong_BridgeWikipedia. (2010). Union Bridge. Retrieved from Wikipedia.org: http://en.wikipedia.org/wiki/Union_Bridge_(Tweed)

(Qingzhong, 2007) (Ryan, The Millau Bridge, 2005) (Ryan, The NormandyBridge (Cable Stayed), 2002) (Wikipedia, 2010) (Wikipedia, 2010) (Bernado,1990; Benckett, 1984; Beckett, 1980) (Locke, 2001) (BBR, 2005) (Belard,2005) (Le Viaduc de Millau, 2007) (Humber Bridge Board, 2005) (Humber

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Bridge Board, 2008) (Parabolas in Suspension Bridges! Oh, my!) (Sayenga,2008) (Wikipedia, 2010) (Wikipedia, 2010) (Bridge Pros) (Calvert, 2002)(Blockley, 2010) (WGBH Science Unit, 1999; Brown, 1998) (Tang, 2010)

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