Suspension Bridge Construction (Parabolas in the Classroom)

"Is this reasonable?"

Only if you assume that the supporting cable is parabolic (guess this is what you're getting at from your thread title), and that it touches the bridge deck at the lowest point, and that the deck is straight & horizontal (and the towers are of equal height), and that you only want the cost of the vertical cables supporting the span between the towers, and that you specify the cost of cable per unit length.

If a student can come up with a "but I couldn't do it because I didn't have (insert anything you may have forgotten to specify)" - they will.

I'd suggest posing yourself the problem, then working through the solution, and carefully checking any assumptions you've made along the way.

Thank you for those thoughts...and YES, since this is a hypothetical bridge, ALL of those conditions are met. I did work through the problem, and I don't expect an honors student to have any trouble. I really just needed a reasonable cost per unit length and YES that would be only the cables supporting the span between the towers. In fact, I want it to work out that there is NOT enough money in the budget and now the student has to figure out how to redesign it to meet budget. HMMM thanks for the feedback!

'Fraid I don't know what level an "Algebra II class" is, it doesn't mean a lot to me (or probably to most folk in the UK) - sorry if I seemed condescending.

I'm also sorry to say I haven't got a clue how much these cables cost - but I'm pretty sure that you'd need to be able to give a fairly good estimate of the maximum load they are to be are subjected to, and the maximum acceptable extension at that load (maybe some more sums for your students?) before you could get a reasonable quote from a vendor. This also brings in the expected load of and on the bridge - 3' wide footbridge or multi-lane highway? I'm not trying to be difficult (honest !), but you've got an awful lot of variables in there.

Oh no you don't seem condescending at all....Algebra II (in the US in New Jersey) is taught typically to 11th grade students (third year of high school). They are about 17 years old.

I like your other suggestions regarding expected load and such. The problem is really hypothetical since my focus is on the study of parabolas. I'm just trying to make it "real" for the students who constantly want to know why we need to learn this! lol

If this is just for a question surely you could just put in a cost that seems reasonable to you. It doesnt really matter what the actual cost is!

Well, yes, I know that, but knowing around what numbers to start with would be helpful....is it thousands of dollars per ft., hundreds per ft.? I really have NO idea. Does anyone know what steel costs????

its just a question, just put any random price in there

and make it kinda hard

like 12.43 per 4 inches

or something along those lines

Maybe another parabola-related question could be framed around "my focus is on the study of parabolas" - how about a bit of design work on a parabolic reflector for solar energy? These can be 'cylindrical', with a pipe (carrying the water to collect the heat) running along the focal line, or a paraboloid with a heat-collector at the focal point.

Just a thought ... & sorry if I'm going off the edge of the bridge.

Thanks for the suggestions! This will surely be my next problem, especially with an energy conservation purpose......I love it! In fact I think I may spend lunch working on this next problem.

BTW- it's fun to "go off the edge of the bridge"

What I'm not getting is a study of parabolas in an algebra class. Do you mean that the class is studying geometric forms (as in, conic sections); or that a practical budgeting study based in part on a geometric form is what your "project" entails? That you wish to demonstrate how algebra can be applied to solve your "construction budget" calculations?

By the weigh, I've heard that a suspension bridge actually takes the form of a catenary curve...similar to parabola by not the same. A catenary curve would be that described by a string/rope/chain held at both ends and allowed to hang freely. The fine distinction is that bridge-span-suspending cables distributed at equal intervals along a parabola would not (each and every one) bear an equal share of the bridge span weight...thus could not be identical in strength properties/size/weight...cost.

UG

If I was estimating this job. I'd have a lot of questions. So I'll try to answer your question as directly as possible.

$50/LF - 2" Steel Wire Rope (installed), weight: 7.39lbs/LF, breaking strength: 198 tons

$65/LF - 2-1/2" Steel Wire Rope (installed), weight: 11.6lbs/LF, breaking strenght: 302 tons

$85/LF - 3" Steel Wire Rope (installed), weight: 16.6lbs/LF, breaking strenght: 425 tons

This is EXACTLY what I'm looking for! Thank you so much! I'm going to incorporate the breaking strength into the problem and pose additional questions about maximum weight allowances. I'm so excited.....now I really sound like a math geek!

Although this is not directly related to your question, you and/or your students may have fun experimenting with this software. I do not believe it will do suspension bridges but it still may have applications in your class when examining costs vs. requirements.

http://bridgecontest.usma.edu/download.htm

The exposure to computer simulations and design may inspire some future engineers.

Cheers!