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Suspension Bridges

Suspension Bridges. A study of the Brooklyn Bridge. Background. This activity would be appropriate for student at the 10 th grade level The activity would proceed as follows: 1. Find out background about the Brooklyn Bridge/Suspension bridges in general

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Suspension Bridges

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  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_bridge

  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. Source:http://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 y=x2 does not look like the center cable of a suspension bridge

  6. This graph still does not visually resemble the center cable of a suspension bridge 3. The “grab & move” feature allows us to stretch out the parabola

  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). [798=1596/2] • Source:http://www.endex.com/gf/buildings/bbridge/bbridgefacts.htm and http://www.endex.com/gf/buildings/bbridge/bbgallery/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. It is impossible to see using the standard scale of the TI-nSPIRE The graph must be scaled properly

  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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