Overview

Recently in our Honors Physics Class, we were tasked with the job of creating a bridge to show our knowledge of how forces on a two dimensional scale work. Split into two groups of three, our class of six was to make bridges that were the most efficient under a certain set of rules. After a number of days of learning the basics and designing through simulations, we were to have a few days to actually build the bridges, and then finally test out until they broke. What follows will be a rather in depth look at the entire project within our group, consisting of Jon Scibelli, Ian Thorp, and myself, ZAC Corriveau.

Phases:

1. Rules and Guidelines
2. Materials
3. Concepts
4. Design and Construction
5. Results and Comparison
6. Resources

Before starting any kind of learning, planning, or building, the entire class came together and decide upon what we needed to focus on for this challenge. Obviously, it had to do with bridges. After much debate, we decided upon this, and set off to get down and dirty with the bridges.This was summed up in this essential question:

How do we design the most efficient bridge by assessing certain materials and by ensuring the support of a weight load?

All material and content on this blog is that of ZAC 2013

Rules and Guidelines

As with any good competition, there should be rules to make sure each team doing the same thing. While the rules were our biggest obstacle in hindsight, I can begrudgingly see the need, as they tested our ability to design and plan with limitations, thus making the whole challenge a little harder. In the end, we made some serious rules outlining the entire challenge. 

The Challenge:

Design and construct a bridge that will support the greatest weight possible in the most efficient way, using the provided materials and adhering to the rules.

Rules:

• Each bridge will only be made up of the following materials: Toothpicks, Skewers, Straws, and Glue.
• The bridge must be free standing in design. It cannot be attached to the surface in any way, and is only allowed to rest between the edges of the gap.
• The bridge must cover a gap of at least 40cm.
• The bridge must have a width of at least 5cm to 10cm. 
• No lamination is allowed. Lamination is defined as five or more of any type of materials layered in a parallel direction and only separated by glue.
• A budget will be in place, where each unit of material is assigned a cost. Only materials used in the final design will add to this cost. When "buying" a material, the entire unit is bought. Glue is free.
• The Budget will be limited to: $2500

Materials

Each team was only given four different types of materials. Each unit of one material had a price. The only other stipulation was we couldn't "laminate"- layer 5 or more of any material. That turned out to be a problem, but more on that later. Here they are, also found on the resource page here. Anyways, our first task when given the materials was not instantly how to put them together- it was how strong were they? We then preformed a number of strength tests on each material. This consisted of a electronic force meter (in Newtons) being applied to the material until it broke. Unfortunately, due to limitations in our hardware, these results were not the most useful, as our meter only would read up to 55 Newtons of force.

Toothpicks

Cost: $18 per toothpick

Strength: ~55N (vertical)
              ~21 N (horizontal)
Mass: ~1g

Pros: Very inexpensive, strong for the size

Cons: Very small, Points on the end make for bad joints

Skewers

Cost: $97
Mass:~14g
Strength: ~55N (vertical)
              ~21N (horizontal)
Pros: Long and Strong
Cons: The most expensive

Straws

Cost: $55
Mass: Unknown

Strength: ~16N (vertical)
              ~ 3N (horizontal)

Pros:...none

Cons: Very weak, very expensive

Glue

Cost: $0

Strength: Unknown
Mass: Unknown
Pros: Can be pored over joints, holds somewhat well, free
Cons: Messy, takes multiple hours to dry

After looking at all this data, we concluded that excluding straws would be our best bet, as they were expensive and weak.

How we determined strength 

For those curious people out there, you may be wondering how exactly we determined the vertical and horizontal strengths. One of the best ways to find these out, especially if you have lots of extra materials, is to stress test them until they break. Most places have very sophisticated equipment to do this, but being a small rural school, we lack these. So we came up with our own methods. Using digital sensors to measure the forces, we pushed on the materials until they snapped. The vertical force was pushing down on the material from the round ends, while horizontal was applying pressure to create bends in the material. However, these were not all that accurate, so we use "~" to designate this. This is mostly because of the force scale only reading up to 55N. So, it is my assumption that our skewers and toothpicks are much stronger than they are shown to be here.


In the end, we made up our designs with toothpicks and skewers in mind, simply because they would be the strongest and easiest to work with. 

Concepts

As this is a project for a Honors Physics Class, we had to look at all the in depth physics that goes into making a bridge, and what happens when a load is put on it. Here are some of the Laws, Equations, and Rules we had to consider regarding the physics part of all this.

Forces: 

There are different types of forces in physics, always denoted as f (usually with a subscript). They are separated into two different categories- field and contact. Field forces are things like electromagnetism, but for this project, we don't look into how they effect our bridges. The other, contact, is our style. The affect a single point. These can also be called support forces, and include things like the normal force, which is the tension that holds up a surface, which deals with compression. more on that later. 

Weight:

Weight is a pretty simple concept. In a mathematical model, it is the mass times the acceleration. In this case, since nothing is moving, it is always the mass times the acceleration due to gravity- 9.8m/sec^2. It is almost always thought to be "negative" in a simulation. In our project, weight was the only example of a shearing force, in which the load forces in a direct "slice", creating the shearing affect.

Equilibrium:

When talking about weight, another concept that comes up is equilibrium, which is when all the forces- the net force- equals 0N. An equilibrium exists when an object is static, has no motion, or when it is moving at a constant velocity, known as dynamic. This is a very useful tool to know when building bridges, because it allows us, as long as there is a non moving weight on the bridge, to know that as long as the bridge is still standing, the bridge has a total of 0N on it. In simple terms, the "negative" weight cancels out with the "positive" support forces of the bridge. 

Torque:

Torque is force applied to a lever arm, or T=fl. the lever arm is always perpendicular to the surface on which the force is applied. For a bridge with uneven weight, this allows us to find how much force is on each side of the bridge.

Hooke's Law:

In having to do with how much force an object can take, you use Hooke's Law, known as f=Kx. Simply put, that is the force applied equals the change in position times its constant of elasticity. It is constant until a point, in which the material breaks or becomes deformed. We did not really use this here, but in bridge force diagrams, it is very useful. here is a pretty decent example:

Depending on where the load is one the bridge, the forces acting on the sides are different. This is turned into a lever arm, so hookes law can apply the distance the load is from the fulgrim and the amount of force on the lever into how much force is on each side. The forces on each side, regardless of if the bridge holds or not, will experince the force of the load.

Compression and Tension

Perhaps the most important thing that we saw was the difference between compression and tension. Compression is when two or more forces come together and push toward the center of and object. Tension is the opposite, as forces push towards the edges of the object. In dealing with bridges, these forces act at the same time on different parts of the materials, like so.

Moving on!

Design and Construction

Design

Ready to start the hands on part of building a bridge, our class looked at the different designs that had been used in the past, and took heavy consideration into what had and hadn't worked. Here are some common designs that we looked into.

Ah. This example might be a bit small. Here is some detail. These might not be all of the types of bridges out there, but they are the most common.

Beam

Pretty much what it sounds like. All of the load is transferred onto beams that touch the bottom of whatever the bridge is spanning. As a result, they cannot hold up as much as others, since the force causes the beams to bend dramatically. Also, our bridges were not allowed to touch the bottom, so they were ruled out.

Truss

This was one of the more common bridges. The used multiple bracing throughout the bridge to push the forces against each other. Compression and tension here were moved to the outside, so the only place for failure resulted in the strength of the joints and materials used. However, this bridged used a lot of parts at varying angles. I didn't want to use it, as liquid glue would make this very tricky.

Arch

One of the most reliable bridges in history has been the arch bridge. These puppies use the arch and the sides of the gap- the compression from the load on the arch equals out the tension on the top part of the bridge, and over all work very well. 

Suspension

The end all be all of bridges. the suspension bridge is renowned for being the best for spanning large gaps and carrying large loads. They work by transferring the load to large cables that are anchored on the side of the gaps, with the cables resting upon the pillars. This allows the bridge to sway as well.

Cable Stayed

Sometimes confused with the suspension bridge, a cable stayed bridge is only similar in that it uses cables. However, instead of large cables running horizontally the bridge with smaller ones holding up the base of the bridge, a cable stayed bridge has the cables attached to the pillars, and not to counter weights on the edges. Again, this design was ruled out due to it needing cables. 

After looking at many many pictures of bridges, and thoroughly understanding the concepts behind them, we quickly jumped to the suspension bridge for our first design. It was almost drilled into us that it was the best design- it cost less than fancy truss bridges And hey, it even looked nicer!

However! We soon had a problem with that- we had nothing to use for cables. While we could have worked around it, maybe by hanging something, but that would have become quite messy. When then looked at arches. They were indeed strong, and much simpler than a suspension bridge.However, due to the materials, all being very straight and having low elasticity, did not suit a arch. In the end, we we almost forced into a truss bridge, the one thing I wanted to avoid. 

After a number of simulations, it was pretty much decided that a truss would be the best. We would uses small triangles- the strongest of all the geometric shapes- for the inside trusses. This would make the compression resulted from the load put tension on the main part of the bridge, thus holding a large amount of weight. After pages of sketches with lots of triangles, we came up with this:

Excuse the poor drawing. Paint is really terrible.

So, pretty simple, but hopefully very effective. Time to build. We also used this simulator to help in our design process. While this may have not gone as I would have thought in the simulator, it still worked while we built it.

Construction

One of the challenges that I tackled was with the materials. Since we decided as a group to stick to toothpicks and skewers, one of the biggest problems was that they were round, and round surfaces make it hard attach angled joints to. Also, as single units, they were tough to arrange together in a way that seemed strong enough.

My solution was to bundle skewers and toothpicks into threes. This would make them stronger and easier to connect to each other, as well as give them three times the strength, hopefully. For example, we tested one of the bamboo skewers against my new tri-skewer. After one kilogram of weight, the skewer bent and bowed inward toward the weight. This is how the tri-skewer preformed:

That is about 6 kilograms of mass on one of our supports. In our design, we used shortened tri skewers (and the cut of ends in the trusses) as the bottom "bed", hoping that these super strong beams would gives us much more support. The rest of the build was rather simple after that. We used toothpick bundles and the mini-skewers in the trusses, and a few going across the width of the bridge to hold everything together. 

One hard part about this style was joining the two bundles of skewers on the end. We used leftover skewer to hold them together on a flat face. Due to the limitation of lamenting  we could use only one, whereas we planned for three.

Everything was held together with Elmer glue, which from a DIY standpoint is a fickle substance. It holds very well and has a high elasticity, but is a liquid and takes a long time to become solid. We waited about 24 hours for the glue to get a good hold. It was still very messy and time consuming. 

One of our processes that was used in the gluing process was clamping. We made one truss at a time, then clamped the top to the main skewers on the bottom. This was along the lines of of pressure treated concrete or pressure treated wood. If we could get the materials to form under such pressures, than maybe they might stand up to higher forces acting on them. 

In the end we got this:

Notice one change to our design- we added a small truss underneath. We had leftovers and didn't really see why not. In hindsight, we really didn't need it, or at least I don't think we did. 

As for prices, this is what we had in the end:

Toothpicks: 66.....$864

Skewers: 12........$1164

For a grand total of: $2028

Which is under $2500, so under budget!

As for mass, we came in at 48.7g

Results and Comparison

Competition 

By the end of the third day of construction, we were left with this: 

Where as the other team had constructed this beauty.

 

As per pre-decided rules, mass would be added to the bridge until it broke. Our team went first with the weight being supported by triangle in the middle. 

.........


      In the end, our bridge held 2970.9g! In terms of efficiency  which is what our competition was about, our bridge, which was 48.7g, held 6186% or its own weight. I was very impressed!

      However, then the other team went. Without being too critical, I was not expecting much of their bridge. I had heard of their budget problem.  It was 35.8g, had little or no trusses, looked very flimsy. However, it kept going, and held 2690.9g! We were shocked to discover that because of their low mass, they had an efficiency of 7278%! 

So they won.

Analysis

Our bridges were then examined afterword. Here was ours:

       You may notice that the flaw was in the side support. The bridge twisted itself, broke a single truss, and slipped a few centimeters to its doom. Nothing else, not one material, snapped- it was only the glue. I thought that was a huge success on its own. The forces that this broke down to were that the compression on the top beam (the mini skewers), which moved them sideways. Our bridge was not built for this kind of sideways z-axis force, so it collapsed. Up until then, however, there was very little bend in it, and it held up well.

        But there were some big differences that I would like to bring up between the two bridge designs. When weight was added to their design, it bent instantly. It bent more with every single addition of weight as well, and by the end looked like a "u". Ours, however did not, and remained straight until it gave out. I think that that makes ours a better bridge in general, as it resisted the impact of the downward forces more than the other bridge. This made it sturdier, and it even held more. This is all not to mention that it was also way under budget. 

So there.

But I guess by the rules, we have to admit they won. Shame is upon my family. 

Some Closing Calculations

       Just thought it would be interesting to reflect back on some of our calculations. Let's say that we really wanted our bridge to win this little competition, based on efficiency. Now we can't really add much more weight to our bridge without it snapping, unless we rebuilt the entire thing with a better design. However, we can change the second part- the mass of the bridge. 

       Let's say we just remove some unnecessary components. In our bridge, i would remove the truss on the bottom. By numbers, the eliminates...12 tooth picks, and one piece of a skewer, which I would judge, thickness wise, as about two more toothpicks. In total, 14 tooth picks. With our measurement of one toothpick having a mass of about .5 grams (they are very light) that would eliminate a total of 7 grams from our bridge, bringing our mass to 41.7g. Assuming that that truss had little to no affect on the bridge, we can do a hypothetical re-evaluation. 2970.9g divided by 41.7g and times 100....is.....7124.5%, just 100 percent shy of the other bridge. Hmmm.....

The question now becomes, how much would we have to remove to get past the other team, in terms of efficiency? Simply equation here: 2690.9/35.8 = 2970.9/x, with x coming out to be...39.5g. So we would have had to sacrifice a little less than 10g to equal out to or opponents. An interesting thought.

Resources

Throughout this entire project, we used a ton of different simulators and other various resources to both design and create our bridge. Here is a nice concise list of everything that was used. Feel free to explore and use them for your own nefarious purposes.

Simulators:

1. Some fun little Flash bridge games
2. The West Point Bridge designer Software (Download)

Materials:

1. Skewers
2. Straws
3. Toothpicks
4. Glue

Information/Concepts:

1. PBS: Building Big (Very helpful, also includes Simulator)
2. A useful page

Other Blogs on the same topic:

• Ryan
• Jon
• Ian
• Devon
• Luke