In Your Classroom: "Stressed Out"

by Brian McCombs     Department: In Your Classroom

Bridges.  We see them everywhere and everyday.  They are engineering wonders with loads of mathematics and science behind their structure.  From amazingly beautiful and aesthetically pleasing, to ones that are cumbersome looking yet very effective, bridges can be found in many different shapes and sizes.  Yet no matter what they look like, they all must serve the same basic purpose.  To get something or someone from point A to point B, by going over something that would otherwise make the 'journey' impossible/impractical. 

In my precalculus/physics course I teach, each spring we conduct our annual Balsa Bridge Building Contest.  Students are required to use a specified amount of Balsa wood (used because of its brittle nature when twisted, but its amazing strength when the ends are pushed on.  Bridge supplies can be purchased at AC Supply), some wood glue, and a lot of thought to build a bridge that will hold the most weight, when compared to its own mass.  This ratio of weight held to mass of the bridge decides our course champions.  The students love this project, especially watching the bridges explode under the pressure.   I would believe however that this project, or ones similar to it, is fairly familiar to many educators.  As I watched this segment, and thought about what I wanted to write about it, I tried to think of other mathematical applications/projects I could use in a classroom relating to bridges and their structures.

One idea is the following:  A teacher can give his students the dimensions of the roadway of a particular bridge.  Or better yet, have the kids research several on the internet.  Based upon the area of the roadway, or just the length of it, students can then estimate how many automobiles could fit on the roadway.  Based upon this information, and a little more research on the weights of various cars, trucks, or busses, students could then get a range of weights that could be on the bridge at any one time.  What if the bridge could hold 16 busses, how much would that weigh?  How about 10 SUV's and 14 cars?  What if we did, 3 semis, 8 SUV's, 6 cars, 3 motorcycles, and one 10-speed bike?  The amount of variables a teacher could use is endless.  What a great introduction into the use of variables in a prealgebra or algebra 1 course.  We could even extend this more by plotting out the various weights, based upon every student's example, and maybe find an equation for the line of best fit, or quadratic, or whatever equation it may form.  Maybe we find there is no correlation between the number of vehicles, the type of vehicles, and the weight.  Now we are getting into statistics terms and maybe some algebra 2 or precalculus.  What fun!!

What if the students researched photos of unique bridges on the internet.  They could study the geometry or trigonometry behind each photo.  Sometimes bridges have a "half-eliptical" opening for cars to pass through.  Sometimes, it's more rectangular.  Why the difference?   Which is better?  Students could take a photo from the internet, or a digital photo of a bridge in their neighborhood, and insert it into a program such as Geometer's Sketchpad.  Upon doing so, they could plot/name the coordinates making up the bridges opening.  They could then find the trigonometric equation fitting those points, or perhaps a ratio of length to width of the openings.  Is there a limit to that particular ratio?  What do they find is the range of the length to width ratio for the openings?   What conjectures can they make?  And what further research might that lead to? 

A teacher could work further with the idea of the "half-eliptical" opening by having students find the curvature required, so that cars would not hit the side of the bridge.  If a student were to have two cars passing side by side under a bridge, he would have to make sure there was enough clearance on the side for both of them.  With rectangles this is fairly simple.  But with an elliptical form, there is a lot of mathematics behind these calculations.  What if it was two semi-trailers going under?  Have the students find the optimum size ellipse to create for the vehicles to pass safely.  What if the teacher required the class to create a bridge that was not only strong, but had this elliptical underpass, just the right size for two semis to pass under?  What a cool project that could be?

On an a more basic scale, just identifying all the basic geometric shapes and concepts within a bridge's structure could be another means of incorporating mathematics.  Within any bridge a student could see a ray, an angle, a triangle, a rectangle, a cylinder, etc.  One photograph could be a summary of an entire chapter from a geometry text.  Ok, maybe two or three photos.

As I wondered about other ideas to use with bridges, I looked to the web for more ideas.  I found the some wonderful sites that have very thorough and extensive projects relating to the building of bridges, and their uses in a mathematics classroom. 

If your school district has access to the Zome System there is a wonderful Bridge Building Project site with a 20-step project layout already written for you.  I suppose a teacher could use Tinker Toys or Knex systems to build the bridges as well.  Check out the Zome Bridge Building Project.  It is very extensive and thorough in the explanation of the project.  Students attempting this would need a basic understanding of geometric shapes, concepts, as well as good writing skills, and the understanding/exposure to the concepts of stress and gravity.

Another wonderful site detailing a project on bridge building can be found here.  It demonstrates a 15-day project, detailing the vocabulary learned/needed each day, materials needed, photos of existing bridges, links to standards information, as well as any prerequisites required of the students.  Teachers wishing to use this project could certainly use photos of bridges in their immediate neighborhood to substitute for the ones used by the project's author. 

A very famous mathematics problem is Euler's "7 Bridges of Konigsberg" problem.  This website has a detailed explanation of Euler's question and "solution."  I say "solution" in quotes because this is actually unsolvable.  There are great follow-up questions as to why it's unsolvable, but it is a wonderful example of Topology.  It also is a great example to show the students on a day you just feel like challenging them, or if you are interested in a Math History aspect of a course.

PBS lists several great resources on their Teacher Resource page.   Check out the Nova program "Super Bridges" with the accompanying lesson plan.  Also, "Secrets of Lost Empires" shows the construction of a rope bridge.

Finally, what bridge project intro would be complete without the video from the Tacoma Narrows Bridge collapse in 1940.  There are several sites on the internet with this video.  YouTube's video clip is wonderful as it links the class to the actual newsreel with reporter's comments regarding the bridge.  Just like the old movie theaters.

YouTube:  Tacoma Narrows Newsreel

If you use anything in your classrooms relating to bridges and the mathematics behind them, I would love to hear about it.

Additional WIRED Science Video Segments
Don't forget to check out our Video Section for other segments from WIRED Science that you can use in your classroom.

Tags:

+ Add Comment

Post your comment

Name
Email Address
URL

Remember personal info?

Captcha:

Type the characters you see in the picture above.