Building a bridge...sorta.

[byosys]

First off, I want say that this is for a school project. However, we were instructed to do outside research, and this is the best starting point I can think of for my project.

2nd off: I'm not sure this qualifies for the highly technical fourm as it is not about computers. However, it is about science and engineering, and that has to count for something.


Our assignment is as follows: we are to design and manufacture a "bridge" that will span a 40cm gap between 2 cinder blocks. I say "bridge" because it is more of a beam sitting between 2 cincer blocks. The beam has to be the following:
-65cm length, minimum.
-either 1" square or 1.1" in diameter at the ends (don't ask me why it is in inches and not metric)

The winner will be determined by who has the lowest rating according to the forumla:
rating = bend * weight^2.

Forgetting the technical word, I'm defining bend as the flex of the beam when a 10kg weight is placed in the middle of the "bridge".

We are given 2x4s to cut down to the proper size, sheet metal to cut as needed, heavy 1" diameter PVC pipeing, and glass fiber tape if we want it. We can use any materials that we can procure, but keep in mind this is a high school project and I don't want to spend more than 10$ on materials.

My 2 design philosophy's are:
1. Make it as strong as possible, weight be damned. If my teach can't measure any bend, our rating will be 0 (0*x*x = 0) and our team will win.

2. Make it as light as possible, bend be damned. Weight gets factored in twice, making it a more important factor than bend.

Here are my ideas so far:

1. cut the sheet metal in to 4- 1" wide strips and sodder them together. This will be very light, but will bend alot as well. This is philosophy #2.

2. Cut a 2x4 into a 1" square and attach a stip of sheet metal to either side of the beam. The sheet metal will add minimal weight, but will help resist flex. Philosophy #1.

3. Go for a compromise. Cut a 2x4 into a 1" square and then start to shave some of the wood off of it. I'm not quite sure how to shave down the 2x4 to get the best strength/weight ratio. Anyone have a diagram that provides the best strength/weight ratio? Or a table of materials that we could use instead of the given materials?

Any insight would be helpful.

 

[ZeroNine8]

You said your constraint is a 1" square or 1.1" diameter circle on either end...what about the middle?

The closer you make this to a triangle, the better off you are.

If there is no limit to your dimensions mid-span, make a 1" wide sheet metal strip to be the base from one side to the other.

Use rigid elements (1"x1/2" or so wood ought to do well) to form a triangle rising from each end to a point over the center of yoru span. Run a support from your peak of the triangle to the mid point of the span (soldered sheet metal might work here.

If you have to be less than a 1" square over the entire span...well good luck

 

[HermDogg]

The correct way to go about this would be to just make yours large (if you indeed gave the proper language) and then if the teacher complains, point out the technicality. If you ask first, there's always that chance that the teach will say no.

 

[Mday]

you're not designing a bridge, you're designing a truss system. if it was really a bridge, that weight would be distributed equally across it, but you have a weight in the middle.

the best design is an arc

 

[bobsmith1492]

Try the West Point Bridge Designer. It is a neat simulation program that you can use to check out different designs of bridges, and it's fairly easy to use.

 

[Lynx516]

The moment of inertia is king in this situation. For a given mass the one with the largest moment of inertia in the axis it lies in will perform the best. So basically largest moment of inertia possible and the stuff with the largest youngs modulous you can find that will take the load.

Carbon fibre sheet would be good. Get a peice of wook and by wrapping it in carbon fibre cloth and using epoxy to bond the sheets together you should get a very light structure whihc is strong and has a huge youngs modulous

 

[magomago]

maybe do a quick moment balance and draw a moment diagram also to see which parts of the bridge need to be the strongest? Though considering it is just a single 10kg block in the middle of a bridge...IIRC it will be in the middle as ML/4 where M is mass L and length. Work from there

 

[mryellow2]

How will the weight be placed on the "bridge"?

In any case I'd do a simple arc like Mday recommended.

Cut the arc in the plywood and then cut it into strips. Cut a few strips of the sheet metal into the same shape as the plywood and then glue+screw as many as you can fit together within your dimension constraints. Done correctly I don't think there'll be any discernible "bend" in your bridge.

edit: What I'm seeing in my head ~>Yes, I'm bored at work =p

 

[byosys]

Thanks for all the help guys. I don't have time to whip up a diagram right now, but I will once I get back from my math course at a local university.

So far, just about every group has decided to go with the same general design as mryellow2 suggested, but all of their designs are flat. Further, we are using epoxy instead of screws (lighter, and epoxy will hold it). Instead of cutting an arc out like mday suggested and mryellow nicely drew up in a diagram, were going to use the same basic wood shapes (albit flat) and prestress them on a mold my teacher has. I don't know all the physics behind it, but I'm assuming if they prestress concrete to use in skyscrapers, then prestressing has to be a good thing.

The weight will be placed on the truss via a paint bucked hung from a string in the middle of the truss. The bucked will be filled with water so it weighs 10kg (it will be filled from the start, not hung empty the water added slowly.)

Sorry for the breif post and run. I'll whip up some diagrams and go into more detail once I get home.

Thanks guys.

 

[rocadelpunk]

Originally posted by: bobsmith1492
Try the West Point Bridge Designer. It is a neat simulation program that you can use to check out different designs of bridges, and it's fairly easy to use.

yah.

there's a competition for this, i forget the website or who hosts it...i think mit?

i had to do this for intro engineering course...with balsa wood and what not.

was fun : )

yah, find the simulation program.

 

[Mday]

the arc was a hint. If he builds what mryellow2 drew, it'd be over designed imo. dont forget, you have to support the bucket some how. it does not really matter if the bucket is placed on top or hangs from the bottom. but in terms of supporting the bucket and load distribution, it sure as hell does affect your design. it is in your best interest to make use of the fiber glass tape... high tensile strength!

pre-stressing wood is not really a good thing. Consider how pre-stressed concrete works... you have the re-bar pulled to close to their failure, then concrete is cast and set. the ends are "capped" so when the re-bar is released from their anchor, the concrete is in compression due to the contraction of the re-bar. pre stressing wood is essentially compressing it in all directions, thus compressing the cellulose structure, eg you smush the cellulose structure closer. think of it as burnishing wood.

anyway, the analysis of the stresses on the "bridge" is statics. you have compression top and tension on the bottom, this is the direction of the forces. Why? cuz the tendency is for the bridge to bend downward.

YOUR solution is something like this:
metalplate wood metalplate wood metalplate wood metalplate
FIBERGLASS FIBERGLASS FIBERGLASS

are you designing a stick, or something that looks like a bridge? cuz hell, it's freaking 1"

PS, i have an even better design in my mind =)
try bending a piece of corrugated cardboard, and tell me what you discover =)
if i remember, i'll come back and help you more

you dont need CMEtruss. you're not really designing a truss tructure.

 

[byosys]

Sorry for the delay, but I think I've got a few good ideas down.

First is the prestressed idea described above. I came up with this because it's different from the same wood-sheetmetal-wood-sheetmetal-wood design everyone else is using. I can't win if I do the same thing everyone else is doing....
More specifically, with this design I'm betting that the pre stressed wood will resist any downward flex more so than flat wood would. I don't know for sure, but I'll find out on friday.

2nd. Instead of going for the 2 metal sheets and 3 wood peices, I'm gonna see how metal - wood - metal works out. Given our system for determining points (pts = weight^2 * flex, lower is better), I'm highly doubtful that the 2 extra peices of wood will be worth it.

3. A 1" square of sheet metal soddered together and possibly covered in carbon fiber (we will have an extremely limited amount to work with) or glass fiber tape. The high tensil strength (which is the type of strength I'm looking for, right?) should minimize flex to some extent, while the minimal design will minimize wight. Thinking about it, this design sounds better than all my other ones...

If you guys recomend, I may just end up wrapping all the the designs in glass/carbon fiber tape. It should help minimize bend while addling very little weight. However, I am skeptical as to how strong it will end up being. I know everyone says that the said tapes are strong, but I just can't visiulize how such a tape could be as strong as everyone says.

Other stuff:

The bridge designer looks cool, but it's totally overkill. I'm trying to design a "light but stiff stick" more than a bridge.

I'll see if I can get some digital pics of the structures in the process of being built to give u guys a better idea of what is actually going on. Theoritical design is great, but useless if I can't build it...

Thanks alot guys.

 

[Mday]

the tape is strong in tension. no one here said to wrap everything in tape.

a hollow tube of SHEET metal will not provide much torsion control. it'll twist and bend then collapse.

I suggest reflecting on my comment about the corrugated cardboard. SHAPE is important.

 

[byosys]

I'm trying to understand what you are trying to get at by using the cardboard example. I know that I want a triangle shape if possible. Since I'm limited to a square or a circle, that isn't possible.

I'm gonna go with the assumption that you are trying to make a point about how an object bends in different planes. The prestressed wood arch that I'm making is made using seveal wood "strips" bend in their flat direction. Think of the wood stips in the picture above. Instead of having them cut in a way so the short end of the rectangle is on the top, the short end is on side. It wasn't possible to pre stress the wood in the other plane. It was too stiff. I'm gonna try to make the design in the picture above by cutting it out of plywood. The only difference is that instead of wood-metal-wood-metal-wood, im gonna keep it to metal-wood-metal. Virtually no strentght is added (as far as I can tell) buy adding the extra wood and doubling or trippling the weight by adding more wood. This way we have an arch supported by sheet metal oriented so that the stress is in the way that it dosn't like to bend (I love my complete lack of technical terms here, but oh well.)

Is this the point you were trying to make?

 

[DrPizza]

It's a little late for me to chime in with my 2 cents worth:
But, as far as weight^2 * bend

It was stated, and assumed that because the weight is squared, you want to minimize that the most.
I think it should be pointed out that it depends on the units used!!
i.e. if the weight is measured in kilograms and the bend in nanometers, then, bend is going to be more important.

However, here's my suggestion: Mathematically cheat!
If the weight is measured in grams,
use a strand of web from a spider.
.002 grams, squared, is even closer to 0

So the 20kg bucket falls to the floor. 2 meters times .002 squared is pretty close to zero.

 

[byosys]

Our truss needs to be able to support the weight which is only 10kg, not 20 (sorry if I confused you guys). I'm not sure about the units, but it won't such a wide difference as nm to kg.

As far as breaking it goes....My teacher would probably claim that since it failed to hold the weight, the bend would be infinity. Which would give us 0*0*infinity, giving the engineering teacher a headache.

 

[Mday]

Originally posted by: byosys
I'm trying to understand what you are trying to get at by using the cardboard example. I know that I want a triangle shape if possible. Since I'm limited to a square or a circle, that isn't possible.

I'm gonna go with the assumption that you are trying to make a point about how an object bends in different planes. The prestressed wood arch that I'm making is made using seveal wood "strips" bend in their flat direction. Think of the wood stips in the picture above. Instead of having them cut in a way so the short end of the rectangle is on the top, the short end is on side. It wasn't possible to pre stress the wood in the other plane. It was too stiff. I'm gonna try to make the design in the picture above by cutting it out of plywood. The only difference is that instead of wood-metal-wood-metal-wood, im gonna keep it to metal-wood-metal. Virtually no strentght is added (as far as I can tell) buy adding the extra wood and doubling or trippling the weight by adding more wood. This way we have an arch supported by sheet metal oriented so that the stress is in the way that it dosn't like to bend (I love my complete lack of technical terms here, but oh well.)

Is this the point you were trying to make?

meh, close enough...


use a drill or something to drill out the middle of the beam. then fold the sheet metal so it makes a series of triangles. The sheet metal will try to break the wooden enclosure, so wrap it in the fiberglass tape to limit the expansion of the "WWW" shape, then shove it into the wood, and then wrap that with the fiber glass tape. ask if the thickness of the tape is considered in the 1" dimension. of course this is moot if you cant bend the sheet metal =p

This is THE strongest design if you can get the metal configured and bent correctly.

 

[pm]

There's a computer game available, formerly known as Pontifex but apparently now going by the less original name of "BridgeBuilder Game". Pretty fun to play and good for learning the basics about how to make a bridge that can bear a load.

Not especially applicable to the original poster's question, but a fun game to play.

 

[byosys]

I've actually played bridgebuilder, but not for the purpose of learning. It was pretty much the only game allowed on the computers in our libary, so I was more or less stuck with it. The bent sheet metal is REALLY strong. For simplicities sake, were skipping the outer wood bourdry and just going with bent sheet metal with some foam to keep it from going "trapezoidal" on us. As of now it looks like we will be testing our designs next Thursday, and I'll be sure to let you guys know how it went.

 

[Concillian]

Spruce wood is the best strength to weight ratio. But in your case, balsa is probably better if weight is a primary factor.

A good truss that will probably beat most of your classmates is to cut small square pieces of the wood into pieces so that you make equilateral triangles.

Like this
/\/\/\/\/\/\/\/\/

Enough to span the distance you need to span 4 times.

Use wood glue to attach these to both sides of a long flat piece of wood 1" tall and as long as you need it to be. Use wood glue. Wood glue is mostly water and will evaporate. , so it is an excellent strength to weight glue. Since wood is porous, the glue can really get into the wood, making it excellent for these kinds of events.

Make two of those trusses, and connect them with as few crossmembers in between them as you can get away with so it doesn't collapse on itself. Alternate crossmembers so that one is top left to bottom right and the next is top right to bottom left.

You can add flat pieces on the top and bottom to make it sort of an I beam. Or since you know it will be loaded in the center, you can glue an arc piece inside or outside the flat pieces. Do what you need to do to make it able to support your 10 kg weight without breaking.

In a similar competition in high school, I did pretty well with that kind of design. Our rules had a max weight limit such that balsa wood actually made more sense, in your case, where weight is factored in twice, balsa may also be a good option. As I recall my bridge was about 300 grams and supported whatever the max weight was, either 10, 15, or 20kg... that was a long time ago, I don't remember exactly. Our rules were slightly different in that it was a wieght/weight ratio (wight of truss vs. weight held).

The good thing about balsa wood, is that it's pretty cheap too. Find a hobby store and go to town. You can cut it with an x-acto knife.

Since weight seems to be scored twice as much as bend, I'd be very surprised if balsa or spruce is not the best option.

 

[SickBeast]

If you want to win the competition, build a cable-stayed bridge. Goolge "Calatrava bridge". They are highly efficient. Essentially they're just a straight beam running horizontally, with a large tower in the middle of the bridge, with cables hanging from it suspending the bridge. Trust me, there is no beating it.

 

[Concillian]

Originally posted by: byosys
Our assignment is as follows: we are to design and manufacture a "bridge" that will span a 40cm gap between 2 cinder blocks. I say "bridge" because it is more of a beam sitting between 2 cincer blocks. The beam has to be the following:
-65cm length, minimum.
-either 1" square or 1.1" in diameter at the ends (don't ask me why it is in inches and not metric)

I interpreted the 1" square thing meaning that it needed to be that short the whole way across the span, but it only needs to be that short at the ends? If that is the case a cable type bridge (suspension or calatrava as Sick Beast suggested) would probably be better. Kevlar or spectra string (stores that sell stunt kites will have this) is an excellent string for tension strength to weight. Spectra is slightly better than kevlar, I think.

A cable type bridge is signficantly more difficult to construct though.

 

[SickBeast]

Originally posted by: Concillian

Originally posted by: byosys
Our assignment is as follows: we are to design and manufacture a "bridge" that will span a 40cm gap between 2 cinder blocks. I say "bridge" because it is more of a beam sitting between 2 cincer blocks. The beam has to be the following:
-65cm length, minimum.
-either 1" square or 1.1" in diameter at the ends (don't ask me why it is in inches and not metric)

I interpreted the 1" square thing meaning that it needed to be that short the whole way across the span, but it only needs to be that short at the ends? If that is the case a cable type bridge (suspension or calatrava as Sick Beast suggested) would probably be better. Kevlar or spectra string (stores that sell stunt kites will have this) is an excellent string for tension strength to weight. Spectra is slightly better than kevlar, I think.

A cable type bridge is signficantly more difficult to construct though.

Note that a cable stayed bridge is quite different from a suspension bridge and will be considerably more efficient.

 

[byosys]

Our final WWW design is folded sheet metal with some foam (which hardens) in between of the bends in the sheet metal. The foam prevents the truss from twisting and is still extremely light. Concillian: you idea sounds great, but overkill for our project. This isn't AP engineering by any means - more along the lines of the class that all the football guys took b/c they thought a coach was teaching it but didn't turn out that way. Basically, I'm the lone "not dumbass" in my class full of football jocks. From the looks of the other designs, it dosn't look like I've really got anything to worry about. While your idea sounds great (and probably is when constructed), I can't justify the time and energy spent on such a project when I've got more important stuff to do (ie college apps, other "real" courses, etc).

Thanks for all the help guys. Testing (sould) begin on thursday (our next lab day), and I'll be sure to post results.

Edit: compleatly missed the 2nd page. Any cable based bridge is gonna be way overkill. I could probably design one that wouldn't break if a stiff wind blew (bridge building 101), but there is no point. Maybe I'll get to build an "actual" bridge later this year or sometime in college.

PS: The info about cable styled bridges and more complex trusses is exactly why I posted here. Not only do I get a design that I never would have thought up (the WW one), I actually get to learn something that I wouldn't have in class. You guys rock.

 

[byosys]

UPDATE: My team (aka me) won handily. The WW sheet metal design came in a close second behind my orginal design, the metal-wood-metal truss. What is interesting is that the WW design won at all test weights (10-40lbs by 10lb) except for the 20lb test. Since the 20lb is the "10KG" weight that we used (we were using weights from the weight room placed in a paint bucked suspended form the middle of the truss). My designs won by a large margin in all tests. The most telling is the total scores (keep in mind that lower is better). The WW design came in with a total of 2384.93pts and the metal-wood-metal design came in at 2463.73pts. Essentially, they were tied. The 3rd place truss came in at 6272.88pts, almost 3 times that of my designs. To make victory that much sweater, the 3rd place was designed by our teacher and was the heavy favorite to win. Our closeest classmate came in with 6635.78 points. Moral of the story? Weight is key. While my trusses bent a little more than others, the weight savings really made the difference. The metal W came in at 84g and the metal-wood-metal came in at 85g. The next lightest was my bent wood design at 113g followed by a classmates at 120. Despite being 40grmas heavier, my 2 winning designs bent ~ half as much as the next lighest design (excuding my failed bent wood design.) Speaking of the bent wood design, it failed horribly. It was a spring that compressed like no other. I should have tested it with the curve opening upward, not downward like I tested it.

All in all, it was a fun project made better by the fact that I get bragging rights over my teacher until we do our next involved lab. Thanks guys and girls.