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Suspension Bridges

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Suspension Bridges A study of the Brooklyn Bridge Background This activity would be appropriate for student at the 10th grade level The activity would proceed as ... – PowerPoint PPT presentation

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Title: Suspension Bridges


1
Suspension Bridges
  • A study of the Brooklyn Bridge

2
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

3
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

4
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

5
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

6
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

7
These graphs look more as we expect a suspension
bridge to appear.
8
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

9
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)

10
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

11
The graph must be scaled properly
  • It is impossible to see using the standard scale
    of the
  • TI-nSPIRE

12
The zoom feature allows a better view
13
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

14
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.

15
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

16
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
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