Question 7 Report Book

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Question 7

A bridge is used to connect two places separated by a river or stream. The Romans, the Chinese

and other civilizations have unique ways of designing their bridges.

Construct suspension bridges using different types of materials and investigate the maximum

weight it can withstand.

Discuss the outcomes of the experiment from an engineering point of view.

Aim/ Purpose

To investigate the relationship between the types of materials used to build a suspension bridge

and the maximum weight it can withstand.

Hypothesis

i) The higher the tensile strength of the cables, the more the load it can withstand.ii) The higher the diameter of the cables, the more the load it can withstand.

Variables:

Constant Variable: Wooden plank, Length of deck, size of hook, length of the

Suspenders (cables)

Manipulated Variable: Different type of materials (Guitar String, Tin wire, Stainless Steel,

Copper, Raffia string)

Responding variable: The maximum load the suspension bridge can withstand.

Conclusion: The higher the tensile strength of the cables, the more the load it can withstand.


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Introduction

A well-built suspension bridge is a most impressive sight to behold; it is a marvel of both

architecture and engineering and has been poetically described as a symphony in steel." The most

famous such bridge is undoubtedly the Golden Gate Bridge in San Francisco, USA. Built in 1937

and with a length of 1280 meters, it is widely regarded as one of the most beautiful bridges ever

built (see Figure 1). Another, nearly as famous, is the Brooklyn Bridge, in New York City, USA; it

was built in 1883 and has a span of 486 meters. The longest such bridge built to date (it was

opened only as recently as 1998) is the Akashi Kalikow Bridge in Japan; it has a Length of 1991

meters. In a suspension bridge the roadway is held by vertical cables or rods that are attached to

two curving cables that run along the length of the bridge. These cables pass over a pair of turrets

at opposite ends of the bridge and are securely anchored to deeply laid foundations. The basic

design of such a bridge has been known for a long time; one of the earliest suspension bridges was

built with bamboo in China (where else?) in the 3rd

Century BC.

Figure 1


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Figure 2

The vertical rods that hold a suspension bridge obviously need to be extremely strong, if they

are to support heavy vehicular trace. In this article we shall focus on the shape of the suspension

cable that holds the bridge via the rods. We shall show that the shape is a parabola and not

catenaries, as is sometimes supposed. The reason for the mix-up should be clear: the shape of a

uniform chain freely hanging under its own weight (e.g., a telephone cable) is a catenaries (catena

in Latin means `chain'), and a catenaries closely resembles a parabola in its lower portion. (See

Figures 2 and 3; the vertical scale has been shown exaggerated.)

Figure 3


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The Shape of a Suspension Bridge

We make a few simplifying assumptions about the various Cables used in the bridge, and the

turrets at the Of course, we may take the curve of the suspension cable to be symmetric in the

plane that bisects the bridge at right angles, perpendicular to its length. The well-known (and

highly readable) book by Simmons [1] uses these assumptions to formulate a deferential equationand then presents a solution. We give a different treatment here, based on one given by Petro [2].

Let the horizontal distance between any two adjacent rods be 2a, and let the points where the

rods are attached to the cable be P0, P1, P2, In Figure 3, the lowermost portion of the cable is

shown as segment P0P1. Let the height of P0P1 above the roadway be b. Let the angle made by

PkPk+1 to the horizontal be k, for k = 0, 1, 2, of course, 0 = 0. Impose a coordinate system in

which the roadway is the x-axis and the vertical line of symmetry of the bridge is the y-axis; then

the x-coordinate of Pike is (2k 1) a. Let the tension in segment PkPk+1 be to, and let the loadacting downwards along each vertical cable be W. Using Lames theorem1 on the relationship

between three forces in equilibrium.


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What is a suspension bridge?

A suspension bridge is a type of bridge where the deck is hung below suspension cables on

vertical suspenders. Suspension bridges are efficient at holding up a large amount of weight over a

long period of time. A suspension bridge has two towers that hold up the horizontal cables. From

these main horizontal cables hang vertical cables that are attached to the deck of the bridge. A

suspension bridge must with stand forces of tension on its cables and large amounts of

compression on its towers.

One of the several types of bridge designs

Used for the longest spans

Cables-suspend the roadway

Towers-stabilize wire cables (offer little support)

Anchorages-key to the structure, mass that keeps cables tight, gives the bridge structure


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WITH ANCHORAGES WITHOUT ANCHORAGES


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Due to the limitations of the truss bridge type, another bridge type is needed for long

spans. A suspension bridge can withstand long spans as well as a fairly decent load.

A suspension bridge uses the tension of cables to hold up a load. The cables are kept under

tension with the use of anchorages that are held firmly to the Earth.

The deck is suspended from the cables and the compression forces from the weight of the

deck are transferred the towers. Because the towers are firmly in the Earth, the force gets

dissipated into the ground.

The supporting cables that are connected to the anchorages experience tension forces. The

cables stretch due to the weight of the bridge as well as the load it carries. Each supporting cable

is actually many smaller cables bound together at the anchorage points, the main cable separates

into its smaller cables .The tension from the main cable gets dispersed to the smaller cables.

Finally the tensional forces are dissipated into the ground via the anchorage

Here is a cross section picture of what a main cable of a suspension bridge looks like this.

A cable stayed bridge is a variation of the suspension bridge. Like the suspension bridge, the cable

stayed bridge uses cables to hold the bridge and loads up.


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A cable stayed bridge uses the cable to hold up the deck. The tension forces in the cable

are transferred to the towers where the tension forces become compression forces. Letstake a

quick look at the forces at one of the cable points.

The Lifting forceholds up the bridge. The higher the angle that the cable is attached to the deck,

the more load it can withstand, but that would require a higher tower, so there has to be some

compromise.

With all cable type bridges, the cables must be kept from corrosion. If the bridge wants to

be longer, in most cases the towers must also be higher, this can be dangerous in construction as

well during windy conditions. The bridge is only as good as the cableIf the cables snap, the

bridge fails


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Roeblings Engineering Contributions:

Engineer famous for American suspension bridges

Use of steel

Development of wire cables

Spinning: assembling heavy cables in the air Advancement of stiffening trusses Truss: triangular structure that adds strength not weight


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The History

Early suspension bridges were simple and crude with a narrow walkway that was

suspended from chains or rope. Some of these early bridges are believed to have been used in the

7th

century by the Mayans, and later in China and Tibet. However these theories w erent proved,

the first suspension bridge design was drawn by Faust V rancid in his book Machine Nova in

1595.

Advantages and Disadvantages of Suspension Bridge

Advantages of Suspension Bridges

-They can span longer distances than any other type of bridge.

- They require less material to build, resulting in reduced construction cost.

- You dont have to shut down a waterway in order to build the bridge.

-They can withstand earthquakes better than stiff conventional bridges.

Disadvantages of Suspension Bridges

-Road deck can vibrate and even twist is high winds.

-The road deck lacks the stiffness required to carry heavy railroad traffic.

- Some areas of the bridge are difficult to install and maintain.

Under spanned Suspension Bridges

An under spanned suspension bridge is a lot like a normal suspension bridge except for the fact

that the main cables run underneath the deck. This design is functional but it makes the road deck

unstable and unable to hold up large amounts of wait.

The Road Deck

The road deck of a suspension bridge is very important. Most deck designs are made from open

trusses that allow wind to pass through. It is important to build the deck aerodynamically or else it

will twist and could snap. One of the more famous occasions of this happening was the Tacoma

Narrows Bridge. The truss work of the deck was too flexible and it snapped in strong winds.


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The Building Steps

1. First huge concrete caissons are sunk into the bedrock to provide a solid base for thetowers.

2. Next the towers are constructed on top of the caissons.3. Giant anchor points are created on both ends of the bridge to keep tension in the cables.4. Then the main cables are strung across the span of the bridge.5. A temporary walkway is constructed beneath the main cables so that construction can

begin on the road deck.

6. Suspender cables are put into place as the road deck is built to provide strength.7. When the road deck is finished, a layer of concrete is poured over the steel, followed by a

layer of asphalt.


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Construction of Deck

We decided to use wooden plank as our deck. Below is the measurement and diagram of the

deck. We use 23 wooden planks to build a deck. The size of a deck is = the length is 40cm and the

width is 4cm and the height is 2cm by the size. The total length of the deck is 125cm. Each wooden

plank consists of 1.5cm gap in between them.

40 cm

2cm

4cm

DECK

LOAD / WEIGHT

TENSION

Diagram 1

Diagram 2

CABLE


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We have changed the positions of the cable from vertical to horizontal to get better results.

Here we can feel that tension on the cable is delivered among the cables equally. So it takes longer

time to snap. Later we decided to change the positions of the cable has been fixed horizontally.

Now the tension applied to the cable directly and it snaps faster than the vertical style. We get abetter reading and cable snapping faster when fixes the cables horizontally. Below is the diagram

where the cable has been changed the positions.

CABLE

DECK

LOAD / WEIGHT

Diagram 3

TENSION


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The Principle Working Of Suspension Bridge

When we put the weight on the deck, the weight will exert pressure to the deck. The pressure on

the deck will be transferred to the cables. The force acting on the cables known as aTension.

The Tensile Strength

Tensile strength is defined as stress which is measured as force per unit area. Tensile strength of a

cable is the maximum stress that the cable can withstand before the failure or breaking. The

tensile strength of cables is measured in unit of Map (Megapascal).

The Snapping Of Cables

The cable will snap when tension inside the cable caused by weight is exceeded then the tensile

strength of the cables.

The Maximum Weight a cable can withstand before snapping:

Type of Materials (Cables) Maximum Weight it can Withstand

Raffia Cable (Suspenders) 4-6kg

Tin Wire 2-5 kg

Nylon Cable 5-7kg

Copper Cable 14-17kg


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Safety Precaution during Experiments

We have been advised to take safety precaution to avoid injuries during

the experiments. Teachers advice us to wear lab coat, goggles, safety boot,

woolen gloves when handle load more than 10kg. We are advised to be far

way except the person whom is putting the load. It is stated, every time the

snapping of the cable its known that the load used will fall down or the

snapping of cable cause the hook to fly over.

Every time we conduct experiments we need to make sure our safety and

the experiments will be carried out in our school study hut. We will make

sure that basic precautions are taken under considerations to prevent anyinjuries. We will make sure using different size of loads.


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"bridge." Encyclopadia Britannica. 2008. Encyclopadia Britannica Online. 9 Apr. 2008

.

Kwong, Norman. The Physics of Bridges. 7 Apr. 2008. .

Matsuo Bridge - Bridges. 6 Apr. 2008. .

Matthews, Theresa. The Physics of Bridges. 20 Mar. 2008. .

Morrissey, Michael. How Bridges Work. 6 Apr. 2008.

.

Vartabedian and Nicholas Riccardi. Minneapolis Bridge Disaster: The Physics Behind the Fall.Los Angeles Times 3 Aug. 2007: A20. ProQuest Newspapers. NC Live. Pettigrew

Regional Lib., Plymouth, NC. 6 Apr. 2008 .

http://en.wikipedia.org/wiki/Suspension_bridge http://www.visitingdc.com/images/golden-gate-bridge-picture.jpg http://www.sundialframingandphotography.com/images/smithsonian.jpg http://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+sol

utions&client=firefox-a
http://en.wikipedia.org/wiki/Suspension_bridgehttp://en.wikipedia.org/wiki/Suspension_bridgehttp://www.visitingdc.com/images/golden-gate-bridge-picture.jpghttp://www.visitingdc.com/images/golden-gate-bridge-picture.jpghttp://www.sundialframingandphotography.com/images/smithsonian.jpghttp://www.sundialframingandphotography.com/images/smithsonian.jpghttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://books.google.com/books?id=SU4FllCNFTEC&printsec=frontcover&dq=corrosion+solutions&client=firefox-ahttp://www.sundialframingandphotography.com/images/smithsonian.jpghttp://www.visitingdc.com/images/golden-gate-bridge-picture.jpghttp://en.wikipedia.org/wiki/Suspension_bridge


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