# Building Bridges

 Author: David Macmorine Unit Title: Building Bridges Grade Level: 11 Subject: Algebra II/PreCalculus Estimated Duration: 21 Days (50 Minutes) Date: July 2013
##### The Big Idea (including global relevance)

How is math used in the building of bridges?  For example, the Brent Spence Bridge between Cincinnati, OH and Covington, KY is classified as ‘Functionally Obsolete’.  This means, although the bridge is still serviceable, it carries 3 times the daily traffic as it was designed to handle.  This leads to economic waste in increased commuting time, increased gas consumption, and dangerous road conditions.

##### The Essential Question
1. What is the best type of bridge?
##### The Challenge

Students will construct a parabolic string consisting of 11 equally spaced vertical strings whos ends will lie on a straight line.

##### The Hook

Students will be presented with archived news stories about the status of the Brent Spence bridge. http://www.brentspencebridgecorridor.com/

A discussion will then begin as to what the replacement should look like. Should it be a truss bridge?  A suspension bridge?

##### Guiding Questions
1. Why are bridges necessary?
2. Are there alternatives to bridges?
3. What kind of bridges are there?
4. What types of materials are available?
5. What are some famous bridges from around the world?
6. What bridges around our area are there?
7. Are any of these bridges historically important?
8. Is Cincinnati special in the history of bridge building?
9. Do bridges fail?
##### ACS (Real world applications; career connections; societal impact)

The real world application of this bridge exercise is very relevant to our society and Cincinnati, Ohio in particular.  The Brent Spence Bridge connecting Cincinnati and Northern Kentucky has been classified as ‘functionally obsolete’ and is handling over 3 times the traffic is was designed to hold.  The applicable STEM careers which tie into this project are any of the engineering degrees needed in bridge construction – civil engineers, architects, geologists, material engineers, structural engineers, and the list goes on. The societal issues are also quite pertinent – there is a great deal of economic traffic which is handled by the I-75/71 corridor – it is, in fact, the most economically important north south highway in the United States.  The ‘bottleneck’ created by the Brent Spence adds to commuter times, slows down the economy, is dangerous, and has become frustrating for most people having to travel the route.  By upgrading the bridge the economic, societal, and stress levels of the commuters in this area, and the nation, will be improved.

##### Engineering Design Process (EDP)

Students will first identify and define how to construct the cables for a suspension bridge from the equation for a quadratic. They will then gather the information on how to calculate the vertical cables (strings) for their particular parabola.  They will then calculate the lengths, construct the vertical cables and will be tested by holding their ‘cable’ at the given horizontal distance, all the vertical cables should lie in a straight line. If not, they will have to go back and calculate and construct again.