Suspension Bridges

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Suspension Bridges

• A study of the Brooklyn Bridge

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Background

• This activity would be appropriate for student at
  the 10th grade level
• The activity would proceed as follows
• 1. Find out background about the Brooklyn
  Bridge/Suspension bridges in general
• 2. Discuss the parabolic shape of the main cable
  of suspension bridges
• 3. Use dynamic technology to eyeball a parabola
  that resembles the main cable of the Brooklyn
  Bridge (TI-nSPIRE)
• 4. Research the dimensions of the Brooklyn Bridge
• 5. Determine the equation of the parabola for the
  main cable of the bridge using TI-nSPIRE
• 6. Determine the cost of the cable using the
  equation

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1. Facts about suspension bridges

• Suspension bridges are able to achieve longer
  spans than many other types of bridges
• They can be cheaper to build than other types of
  bridges
• In the NYC area, there are several suspension
  bridges, including the Brooklyn Bridge, Manhattan
  Bridge, Verrazano Bridge, George Washington
  Bridge, and others.
• Source http//en.wikipedia.org/wiki/Suspension_b
  ridge

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2. The main cable of a suspension bridge is in
the shape of a parabola.

• If a string (or cable) is suspended the shape
  formed is called a catenary.
• When the suspended cable is secured to the span
  of the bridge, it takes on a parabolic shape.
• Sourcehttp//www.carondelet.pvt.k12.ca.us/Family
  /Math/03210/page5.htm

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3. Use the dynamic grab move feature of the
TI-nSPIRE

• The basic parabola yx2 does not look like the
  center cable of a suspension bridge

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3. The grab move feature allows us to stretch
out the parabola

• This graph still does not visually resemble the
  center cable of a suspension bridge

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These graphs look more as we expect a suspension
bridge to appear.
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4. What are the dimensions of the Brooklyn Bridge?

• Span between towers 1596 feet
• Height of towers 276.5 feet
• Height of towers above roadway 117 feet
• Therefore, if we consider the lowest point to be
  the origin of a coordinate axis system, the
  parabola would intersect the points (-798,117),
  (0,0) and (798,117). 7981596/2
• Sourcehttp//www.endex.com/gf/buildings/bbridge/b
  bridgefacts.htm
• and http//www.endex.com/gf/buildings/bbridge/bb
  gallery/bbroyal1883.htm

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5. We can determine the equation for the
parabolic cable

• We can fit a curve to the points(-798,117), (0,0)
  and (798,117)

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5. Equation of the parabola

• The equation of the parabola according to the
  quadratic regression is y.0001837x2
• This can also be calculated by hand using algebra

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The graph must be scaled properly

• It is impossible to see using the standard scale
  of the
• TI-nSPIRE

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The zoom feature allows a better view
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The equation of the parabola can be used to

• Calculate the amount of cable necessary to build
  the bridge
• Calculate the cost of the cable
• Build a model of the bridge

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Difficulties

• Students must know proper scaling when dealing
  with real life situations and large numbers
• Although the new TI-nSPIRE has a wide variety of
  capabilities, it is not user friendly
• The regression feature would seem mysterious to
  students it would be ideal to do an algebraic
  derivation of this work and compare results to
  what the calculator found.

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Extensions

• Students could compare the equation of the
  parabolic cable of the Brooklyn Bridge to the
  equation of other local suspension bridges
• Students could do a historical study of the
  Brooklyn Bridge

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Assessment

• This type of project would require ongoing
  assessment.
• A rubric might include such categories as
• Uses a sensible coordinate axis system to
  represent graphs
• Is able to interpret results of the graph and
  apply to solving problems
• Is able to determine whether results make sense
  in the context of examination of the bridge