Bell Weekly Blog- Week 10

In the previous week, the group tested our bridge in the competition. The results of the competition were that it held a total of 29.8 lbs, compared to when we tested this same design in week 8 which held a total of 35 lbs. The major accomplishments that the group has had this past week was placing third in the competition. Although our group didn't hold the most weight, we still had a decent cost to strength ratio. In addition to this, we placed first with the closest guessed weight and actual weight held. Throughout this term, our group has not run into any confrontations or obstacles.

After reading the course goals, I have found out that I have indeed learned many things worthwhile that I can still use later on. First of all, i have learned that teamwork is very essential. Without others, it would make it quite difficult to come up with all of the ideas by yourself. Planning the design was also crucial. Without planning, the building process would be quite difficult. It was also very important to document. Documenting everything made it very easy to refer to in case we needed any information. Probably one of the most important things that we learned was the design process. We learned through ourselves and other classmates the there are multiple designs that could have been built. A lot of thinking and brainstorming had to go into this process to try and come up with the best bridge possible. We went through this process both for the K'nex bridge and the WPBD program. WPBD was a very useful program that I used. The most beneficial aspect of this program was the numerical values that were given at each test. Once we tested these bridges, we were able to find out what was wrong with our design. We tested these K'nex bridges through truss analysis with forces on each member.I feel that the least beneficial aspect of this course was the blog posts. I felt that they had no other purpose other than for the sake of writing. However, this aspect does not include the A1, 2, 3, 4, Truss Analysis, etc., which were very beneficial. Setting the negative things aside, I feel that I enjoy this class as it is and feel no need to make too many changes to this course. The one thing that I would like to change would be the blog posts. Like I said, I think these posts are pointless and serve no meaning. However, this was a very exciting course and I am very pleased with it. 

Staquet Weekly Blog - Week 10

Last week in lab we got the chance to do the official test of our 36" K'Nex bridge.  Seeing as our group had full intentions of winning the competition, I was disappointed that the test results landed us in 3rd place.  During testing our bridge was able to hold 35 pounds but in the competition only made it up to 29.8 pounds before failing.  This was unfortunate but did however make our failure prediction weight of 30 pounds the closest prediction to actual weight held, therefore getting the group an extra credit point.  This week we plan to create the final report blog and submit it as our final assignment.

This term I learned a lot about not only bridge design, but all of the basic things necessary to make the design process possible.  I've gotten the chance to learn hands on about all the the course goals and see how useful each one truly is.  In general, the goals are a system of trial and error that are broken down into the proper things that go with it such as teamwork, planning, documenting, designing, and analyzing.  The group aspect made teamwork a necessity and planning was a must when making sure we were all ready for the upcoming deadlines.  Documentation was a must in terms of blogging, and helped to keep me on top of what was going on with the class.  I learned the design process is much more extensive than most people think and that it requires thinking about every last requirement and constraint involved with the build.  The analyzation of failures and overall bridge design is extremely important; it tells you which parts of the bridge need to be looked over and perhaps redesigned.  The least beneficial portion of this term had to have been the overuse of blogs and the constant comparison of the K'Nex bridge and a real bridge.  They are two entirely different forms of bridges that, in my opinion, should not even be compared when talking about the design and build process.  The most beneficial part of the class for me was actually building the bridges and getting to test them.  The sense of competition made it interesting, and it also gave me a chance to actually see the bridge fail.  Overall I enjoyed the course, but I really hated the blog, especially the whole double submission of assignments that I have already expressed my feelings toward.

Schetley Weekly Blog - Week 10

Last week in class we finally tested our 38" bridge. We expected our bridge to fail at around 30 pounds, and with a cost of $297,000, that would be a cost-to-strength ratio of a little under $10,000 per pound, which we felt would probably be one of the best ratios in the class. It failed because the weight became too much, starting to contort the bridge and it eventually collapsed (a video of that can be seen here). We actually expected the bridge to fail at the joints on the bottom like it usually did, so we weren't expecting that to happen. To stop that from happening, it would probably require us to strengthen the top of the bridge, or extend the top level of our bridge a bit farther across the bridge.

This being the final weekly blog post of this course, the weekly question we were asked was to look at the course goals listed on the class blog and discuss what we learned from each topic, what was the most beneficial, and what was the least beneficial of all the topics. I didn't really learn much about teamwork since I have been working in group projects since grade school, but I did learn a bit about each of the other topics, especially anything to do with the physical design of the bridge, such as physical modeling, and static analysis of the bridge. These were the most useful of the topics presented, as they provided me hands-on experience (in the case of the physical modeling) and an application of some topics I had been learning about for a while (when using static analysis). The latter answered the question that so many students ask: "Why do we need to learn this?" and that was very beneficial in my opinion. To me the least beneficial topic covered in the course was the topic of computer software. Looking back on it we used four programs: Blogger (which most people, including myself, already know), West Point Bridge Designer (a very basic bridge design software), Bridge Designer (an even more basic bridge software, this one doing load calculations), and Excel (which I knew how to use even better than Blogger before starting the course). This was also somewhat useless since most of these softwares we were introduced to for a week, then we moved on from them and went to work with physical bridges and physical modeling. If I could offer a suggestion, I would either change the amount of computer software lab lessons (I would make it less since I like working with my hands more) and remove the lesson on teamwork, because, as I mentioned, we've been doing group projects since roughly grade school so we should be quite familiar with group dynamics by now.

A4 - Section 35 Group 04

Below is the three previous assignments that each of us have done prior to this, detailing some of the steps we took to get to this final bridge:
A1 (West Point Bridge Design Bridge) - Bell, Schetley, Staquet

A2 (Individual 24" Bridge Designs and Cost)- Bell, Schetley, Staquet

A3 (Method of Joints Analysis) - Bell, Schetley, Staquet

Background:

Assignment 4 of Engineering 101–Bridge Design was for each group to design and construct a truss bridge using K’Nex which could be tested to determine its overall weight capacity.  The K’Nex pieces were each given individual prices and the group with the best bridge was determined based off its cost to weight capacity ratio.  The bridge had to have a clear span of 36” and be at least 3.5” in width.  A continuous clearing, 3” wide by 2” high, had to run through the bridge to simulate a roadway.  The bridge was tested by centering an 11” by 6” piece of plywood on top of the bridge; this piece was to act as a washer for a metal rod that ran through the bridge and suspended a bucket to be filled with sand.  Understanding how truss bridges are designed and how they react to stress  was an important aspect of this project and made it possible to build a cost effective bridge that could also hold a relative amount of weight.

Design Process:

In the beginning we did not have any specific goals besides designing and building a bridge with the best cost to weight ratio in the class.  We kept this mindset throughout our time of working on the assignment and never once discussed 2^nd place.  West Point Bridge Designer played a major role in determining a basic design for our bridge; it showed us where an overhead truss bridge experienced tension and compression forces as well as the best way to orient the interior cross members.  During lecture we learned how to analyze a truss which is a way of calculating the exact amount of force each truss member experiences when a given load is placed on the bridge.  This analysis also aided in how we placed the interior cross members.  We did not design individual bridges, instead we came together as a group and designed one bridge.  This eliminated having to pick through multiple designs and allowed us work together as a team.  Our bridge was designed during the construction process due to the use of fixed length K’Nex members as well as gusset connection pieces that limited angles to increments of 45 degrees.  During the open testing time we had in lab, our bridge was able to hold 35 pounds so to be safe we predicted that the bridge would fail at 30 pounds.

Description of Final Bridge:

Our bridge is a 38-inch, three levels high bridge utilizing many triangles throughout the bridge. The members are designed to push the force on the bridge outwards towards the edges of the bridge. There is more strength on the center of the bridge to accommodate for more force on the middle of the bridge. We wanted to add additional levels on the bridge because we figured that one tier would leave the bridge too weak in the middle, especially as more weight was added onto the bridge. You can see a hand drawn sketch and a photograph of the bridge (as well as the final cost of the bridge and the number of pieces in the bridge) below.

Figure 1: Plan/Elevation Drawing

Figure 2: Bridge Picture During Testing

Figure 3: Bridge Cost and Materials

Testing Results/Conclusions About Bridge Design:

For the most part, our bridge design was successful. We made a very accurate prediction as to how much weight the bridge held. Based on our design and previous test runs, we predicted the bridge to hold a total of 30 lbs. We also made this assumption based on our truss analysis we composed a few weeks ago. Once the bridge was tested in the final competition, the bridge was found out to have held a total of 29.8 lbs. We think that having only a 0.2 lb. difference was a very accurate assumption.  Even though the bridge held almost the exact guessed weight, we still were partially incorrect in terms of the failure mode. In the precious bridge designs and the one tested in the competition, we predicted the bridge to fail by the joints on the bottom of the bridge being disconnected from the members, usually towards, but not quite at, the ends of the bridge. Now, the bridge did indeed fail by this method. But, this wasn’t the only factor in the failure of the bridge. We took a video of the competition, revealing how our bridge might have failed in case we missed it. We played the video back in slow motion. We then found out that a major factor in the failure in our bridge was that the bridge started to contort and twist, meaning one side twisted clockwise and the other side twisted counter-clockwise. The point in which these two opposites met was not in the middle, but slightly offset from the middle. So, we were right in every aspect in terms of load and failure mode except the one aspect of the failure mode where the bridge started to contort. You can see a video of the bridge failing below.

Bridge Failure Video

Future Works:

Every group was going to fail at some point; and every group, including ourselves, could make some changes to improve the bridge either with weight or the cost to strength ratio. We feel that we could to two things to our bridge that would put the design to its full potential. We also would have stuck with the same/similar design if we were to create another version. We felt that the design we had had an adequate cost to strength ratio. The first change that we would make would be to add various pieces to the bridge to help with the tension problem, specifically at the bottom. Throughout this term, the main problem we have been facing was the tension along the bottom. If we were to decrease the rate of failure due to tension at the bottom of the bridge, the next main mode of failure would be contortion and twisting of the bridge. The easiest and most effective way to fixing this problem would be to add lateral cross members to the bridge. This would give strength to the bridge so that contortion would be much more difficult. Even though these two modifications would be a little costly, they would in turn cause the bridge to hold much more weight. Ultimately, these modifications should help improve the cost to strength ratio. 

Staquet Weekly Blog - Week 9

Last week we given most of the class period to work with the K'Nex and build our 36" span bridge.  Our group also had the chance to test the bridge to get an idea for how much weight it would be able to suspend.  With spending only $297,000 in K'Nex pieces, our bridge was able to hold 35 pounds before breaking.  My group and I have decided that for this coming week we will win the bridge competition for the second time and continue our reign as the Bridge Design Masters.  As a group we were faced with an issue on deciding on a specific design, but after testing we were able to settle with what we think is the better bridge.

During this term I have learned a lot about the design of bridges as well as some of the techniques used to test these designs.  Though there are many different types of bridges, this class dealt more specifically with truss bridge design and I was able to learn about how one can be constructed.  The top pieces of the truss are called top cords while the bottom ones are referred to as bottom cords.  The inner members are usually oriented in the form of triangles for strength purposes, and are crucial to the overall strength of the entire bridge.  I also learned that truss bridges experience tension on their lower most cords, and the force of compression on the top cords; whether the bridge is an overhead design or below deck design.  I was able to learn a lot about the behavior of bridges under stress thanks to the West Point Bridge Designer, which then aided in the design of my group's K'Nex bridges.  The combination of this program and the K'Nex bridges showed me a lot of different aspects that a truss bridge must be able to withstand when undergoing the force of a load.  One of the main things I learned from this class that designing a bridge is not an easy process, and that it requires a lot of thinking about anything and everything a fully constructed bridge will be faced with.  Most importantly I learned that bridges are in no way intended to fail to ensure the safety of anyone on or around it; Meaning a real bridge will be checked, double checked, tested, and re-tested, and  looked over by multiple engineers until it is perfect in all aspects of its design.

Schetley Weekly Blog - Week 9

The past week involved our group designing our final 36-inch bridge for competition this coming week. We had to think of what was going to span that amount, keep our cost down, and still remain strong enough to hold a decent amount of weight. When we did our final design, we kept the same basic design as the 24-inch bridge except extended it to 36 inches, reinforced the middle, and added a structure to the top to help distribute the weight better. This was actually the hardest part of the conversion from a 24-inch span to a 36-inch span. Simply extending the bridge weakens it in the middle, so it requires extra support in the middle, and how to efficiently add that support was a bit challenging. When we tested the bridge in class, it held 35 pounds, and with a cost of $297,000, this gave us a ratio of 8.49, a ratio that I hope ends up being one of the better ratios in the class. Hopefully, when we test the bridge again in class this week, the bridge holds as much weight as it did in our test last class.

Now that the bridge design part of this course has come to an end, I have learned a few things about bridge design itself. First and foremost, I learned about the method of joints for calculating the forces on individual members. I had an idea that the calculations would be very similar to the Physics 101 concept of sum of forces, but I wasn't completely sure. The calculations for member tension and compression are actually a lot simpler than I thought they would be, requiring only basic knowledge of trigonometry. Another thing that was reinforced was the strength of triangles in structures. When initially playing around with the K'Nex, it noticed that squares were a bit weaker and gave more than triangles, so it makes sense that we utilized them in our bridge. Finally, another thing I noticed was that more gusset plates and members doesn't necessarily translate to a better bridge overall. The thing that makes bridges more efficient is the placement of the members and gusset plates to distribute the force on the bridge better, not overloading on one point to make it strong when it might not need to be anyway, as not that much force is applied at that point.

Bell Weekly Blog- Week 9

In week 8, the group constructed and tested our bridge that spanned 36”. We had the idea in our heads but never actually put anything to the test until week 8’s class. During this test, we analyzed our results to see which bridge had the best cost to strength ratio. The first 36” bridge seemed to have a better ratio than the second 36” bridge, but only slightly. The final bridge design held 35 lbs. and cost $297,000. Considering the large span that the bridge had to reach, I feel that our bridge held a significant amount of weight. In this coming week (week 9), our group has agreed to continue the analysis of our bridge. If need be, we will make slight adjustments to improve our design. The major accomplishments for our group for the week include constructing a bridge with a good cost to strength ratio. Constructing a bridge that spans 36” was difficult enough; having a good cost to strength ratio was the challenging part. Some issues that the team might run into could be differing opinions on what types of adjustments we should make to our bridge. If we disagree, we will have to try and see if we can work something out that most, and hopefully everyone can agree on.

There are many things that I have learned about in my bridge design. The very first thing I learned about bridges was the term “truss.” Trusses are the building blocks to a successful bridge. Furthermore, we learned how to apply these trusses in in different orientations. It was good that the groups got to play around with the K’nex to get some ideas about what makes a good, strong, yet serviceable bridge. We also learned about which members experience tension and which experience compression. In WPBD, our group played around with changing materials and thicknesses to max out the most members possible with tension and compression. This was done because the goal of this whole project is to have a serviceable bridge that was as cheap as possible. Throughout the weeks, I learned especially that the main focus needs to be in the center of the bridge. The center will have the majority of the weight, so more thought must be given to it. More specifically in our class, there were different things to consider, being that we used K’nex pieces instead of cement, steel, etc. (real bridge materials) So, like I have said in multiple previous posts, the part where the bridge always gives out is the bottom part of the bridge where the members connect to the joints. This was ultimately due to the exceeding tension force. However, throughout this term, I have gained quite a large deal of knowledge about bridges.

Staquet Weekly Blog - Week 8

In the lab last week we were introduced to the "Method of Joints" which we made use of in completion of the A-3 assignment.  As a group, we also went over some ideas for the design of our 36" bridge that we will be working on in the coming lab.  We agreed that we will continue to brainstorm ideas and hopefully have a completed bridge by the end of this week's class.

Clearly this single method of analysis, the "Method of Joints," is not sufficient for a real bridge for numerous reasons.  A real bridge would have to be tested and analyzed in many more ways than just a single downward force on a single connection joint, and the bridge design itself would never be so simple.  A real bridge needs to not only hold its own weight but also has to deal with dynamic loads and things like side pushing from the side and even up drafts from underneath.  Also, a real bridge would be composed of two sides that would have to have some type of lateral connection that, in the end, would play a large roll in the behavior of the bridge.  I am not saying that the "Method of Joints" is not used at all, because I believe it is, but It would be done on a much more advanced level and have to take some of the earlier mentioned aspects into account.  This method would only be one of many that are used to analyze bridges and in my mind would not be enough for a real bridge.  The only thing I would like to further analyze would be the exact failure point of the K'Nex gussets when they are experiencing tension forces.  This information could be gathered using an automated stress analyzer that would give a readout of the amount of force that caused the K'Nex to fail.  This could then be taken into account when building the new 36" bridge that we will be designing and building.  

Bell Weekly Blog- Week 8

In this past week, the group started to work on our A3 assignment. In addition, the group started tossing around some ideas regarding the 36" bridge that will be constructed this week. We didn't actually construct anything, but got an idea. Our team has agreed that, in the coming week, we will begin constructing our 36" bridge. We plan to use a very similar design that we used for the 24" bridge. We figured that since this bridge worked quite well, it was worth a shot to see if it would span another foot, with some modifications of course. The major accomplishment that our team has achieved this week was having a basic concept on what we are going to be doing for our 36" bridge. Creating an idea could have been challenging, but our group seemed to do just fine. Our team faces no current issues at the moment. The only issue that I could think of would be having conflicting ideas about how the members and joints should be used/oriented; and the overall structure.

Basing my decision off of the Bridge Designer program, I believe that this method of analysis is indeed sufficient enough for a real bridge. Had we not had the numerical values of the tension/compression values of the members, I would say otherwise. Having the numbers handy enables you to visualize how close a member is to breaking (and how much weight it is taking). The one thing that I would like to know about the K'nex bridge is the value of the breaking point between the member and the joint. With the K'nex bridge, this point is the only problem that we are having. Having these numbers could enable us to further analyze our bridge and make thee appropriate adjustments.

Schetley Weekly Blog - Week 8

The past week was a lot more calculation and math than actual physical building, if not all. We learned about the method of joints calculation, which takes each individual joint on the bridge and makes it a free body diagram. At this point, we simply have to measure the tension force from each member on the joint, which is a simple sum of forces problem. There really was no problem with this part of the assignment A3. The only hard part of that was finding the angles of all the triangles of the bridge, and even that was not that difficult. In the next week we will probably use this calculation method for a couple members and joints in an attempt to make the 36-inch bridge we must design for the following week better.

We were using the method of joints to find the force on the K'Nex bridge, but this calculation method could also be used on real bridges. The only difference between the calculations we just did on the small bridge and the ones that would be performed on larger bridges is the calculations would have to account for greater forces on more points, since there is rarely a case where there is only one measurable load on a bridge at any given point. Other than that minor detail, this method would be sufficient for a real bridge, in my opinion. As for things I could further analyze, there is nothing really that I don't know right now that I would like to. For the projects we are currently involved in, all the tools and calculation methods are sufficient to get things done.

A3- Bell

For this assignment, the task was to analyze a truss bridge so we could get an idea of how much force of compression/tension was on each member. For my truss, it was said to be 24 inches long, 6 inches high, and to have a load held from the center at the bottom of 10 pounds. It was just simple trigonometry and force diagrams to figure out the force on each member both in pounds and in newtons. The results of my truss analysis is as follows:

Figure 1: The front page of the truss analysis

At the top of this page, I have the initial truss design. Then, I go into more detail about each individual triangle, finding out the lengths of the members and the angle of the joints. At the bottom, I was able to find out the weight that the two end joints receive when the load is in place. 

Figure 2: The back page of the truss analysis

This page includes all the weights/forces on each member. Across from their calculations is a free body diagram of the joint with all the appropriate forces labeled. At the bottom is all the forces on the members in Newtons and pounds.

In order to ensure that these calculations are bother accurate and indeed correct, an online program (Bridge Designer) has been created to do all this work for us. Just by simply drawing the bridge with your specific measurements, the program returns numbers on each member in pounds. In addition, the final results are color coated; red codes for tension and blue codes for compression (as seen in the figure):

Figure 3: Truss analysis using Bridge Designer

As you can see in the picture, my results that I received from Bridge Designer were very similar to that of my hand-written truss analysis. The advantage to this program is that my truss doesn't have to be to scale with the actual dimensions. 

In my truss analysis, I had to scale the bridge. Regardless, I still kept the same shape of the truss, so the design/dimensions wouldn't change. Each block in the Bridge Designer truss analysis is 3 inches. As long as everything is scaled correctly, everything should come out as the same numbers as the hand-written analysis. 

Figure 4: K'nex bridge analysis using Bridge Designer 

In this image, we have the K'nex bridge design that we have been testing in class for the past week or two. However, it is not exact. The member that seems to be missing in the middle is due to the limitations of the Bridge Designer program. Nonetheless, this program still comes in handy. Now, we can analyze which member is the weakest or closest to its breaking point. Through this program, we can make accurate modifications to our bridge to improve its durability and ability to hold weight. 

A3 - Staquet

For assignment three I analyzed the given truss design using the "Method of Joints;" the process to find the force running through each member of a truss based off of the joints that connect it.  My calculations can be seen below in Figure 1.

Figure 1.

With the above calculated forces I was able to draw a diagram of the bridge showing the force on each individual member.  This can be seen in Figure 2 and please note that these forces are in pounds.

Figure 2.

Next I used the online Bridge Designer to further replicate my analysis.  Figure 3 shows the analysis done on the same bridge as seen earlier though the forces are slightly off.  I would have to say that this minimal error is due to the Bridge Designer having a poor grid system with no labeled increments and the use of the mouse arrow/pointer to place the nodes rather than a cross hair or x.  Another problem was the fact that my bridge was 36" long and 10" tall, causing its triangles to have irregular angles and making it slightly tougher to scale than a bridge made of 45, 45, 90 triangles.  Non the less, with the right scaling and proportionality I was able to get most of the figures correct by hand and the figures that didn't match up were only about a half a pound off.

Figure 3.

I have also included the analysis, done with the online Bridge Designer, of the group bridge that was built out of K'Nex.  We completed this as a group and a screenshot is provided in Figure 4.

Figure 4.

This type of analysis can be useful in improving our K'Nex bridges because it gives a great visual of which pieces are undergoing compression forces and which are experiencing tension forces.  The numbers associated to the forces can be loosely used as a reference due to the change in design for the 36" bridge as well as how the force acts on the K'Nex during testing.  The K'Nex bridge does not experience a force on its underside, nor is it applied at a single joint.  Overall, the "Method of Joints" is a useful tool in the design of a bridge or any structure composed of joints that will be undergoing forces.  

A3 - SCHETLEY

In this assignment we used starting calculating the actual amount of force that is on a bridge, beginning with a simple bridge made up of three triangles. My personal assignment was to perform a truss analysis on a bridge spanning 36 inches with a height of 10 inches and a load of 20 pounds. I was able to calculate the force on each member pretty easily, as they are all just simple sum of forces problems. When I calculated the force on each member, I calculated the amount of force in Newtons, because the video that taught me how to do truss analysis (seen here) used Newtons and in physics, when learning sum of forces problems, all weights needed to be first converted to Newtons. The results of my calculations can be seen here:

Figure 1: Truss Analysis - Page 1

Figure 2: Excel Worksheet Calculating Angles

Figure 3: Truss Analysis - Page 2

Figure 4: Truss Analysis - Page 3

The final results for all the forces on the members can be seen below, labeled in both Newtons and pounds of force:

Figure 5: Forces in Individual Truss Members

There is also a program online called Bridge Designer that does a very basic analysis of bridges, shown below. All you need for this program is a few nodes, some connecting members, a load (or more than one load) and the program calculates all the numbers for you. I designed a bridge in the program like the one I just did an analysis on by hand and it produced the following results:

Figure 6: Bridge Designer Analysis of Three Triangle Bridge

As you can see in the image, the results I obtained in my hand-written analysis are the same numbers as the results from Bridge Designer. I think this has to do with the fact that I used a load of 20 (it isn't incredibly visible in the screenshot) and I scaled my bridge to the bridge I was analyzing (1 block on Bridge Designer was equivalent to 2 inches). I think that I got the same results because the force on the bridge does not have as much to do with the size of the bridge but rather the angles of the members and the weight of the bridge. Since I attempted to scale my bridge on Bridge Designer as accurately as possible, I ended up getting the same results.

We also had to do a Bridge Designer Analysis of the K'Nex Bridge from a couple weeks ago that spanned 24 inches and held the load of 39.2 pounds. We had to apply a load of 20 to the bridge, and the results are below:

Figure 7: Bridge Design Analysis of K'Nex Bridge

As you can see from the results from the Bridge Designer, a majority of the force and weight was being applied to the middle members. This was scaled properly to one block for every inch, so the loads on each member are probably very accurate. However, as you can see in the picture, the middle member of our bridge is missing. The program believes, for a bridge to be "stable," the number of members plus three must be equal to the twice the number of nodes. In our actual design, there is a total of 28 members and 15 nodes, so the program can't run this simulation, deeming that the bridge would be unstable, when it clearly is not. This forced us to remove the middle member, as it would give as a "stable" bridge while keeping it symmetric and taking away one of the least essential members (we think).

We can now calculate the forces that are on the bridge given a certain load, and there is a study that was done on the tensile strengths of K'Nex here. Knowing this, we can design our K'Nex bridge so that the pieces do not experience more than the given amount of tensile strength listed on the page. This would be beneficial so we would be able to know exactly what the breaking points of certain places would be, so we could adjust our members to compensate for the loads they will experience.

Bell Weekly Blog- Week 7

In the previous week, our group kept the design of our bridge that we had made in week 5. We felt like our design had the best cost to strength ratio possible. In week 6, our group actually put our design to the true test. Our bridge held a total of 39.2 lbs. It also broke between the joint and the member, as expected. In the coming week, our group has agreed to keep the design that we currently have. This week in lab, the group will start to construct a bridge that spans 3 feet instead of 2 feet. We have agreed to use the same design as the 2 foot bridge because we feel that the design will suffice with another foot to add on. We have also agreed to make the bridge higher for maximum strength. Our major accomplishments for the week have been being constructing a bridge that was able to hold a lot of weight. The only issue that our team might have would be the argument over different designs. On person might think a certain design would be better while the other two members don't.

When we were using WPBD, the group was able to analyze what pieces had more tension/compression and exactly how much. Based on these block box answers, the group was able to change the material and thickness of the member accordingly. Once we started to use K'nex, the only thing we can use to analyze anything was with our eyes. we could physically see where it broke, but that's about it. Another thing that would be nice to have with K'nex is ability to choose the length of the members, the amount of members attached to a joint, the angle at which you can connect members to joints etc. But, none of that is possible, because everything in K'nex is fixed and can not be changed. If I could choose any results to show up as numbers, I would choose the breaking point between the member and the joint. 99/100 times, the breaking point will occur at the connection point between the joint and the member. I wouldn't really worry about buckling too much. The strength of the solid plastic is far more than the strength between the member and the joint. As seen in our test in week 6, the only numbers we would like to view are the connection of the joint to the member. More specifically, we would like to see the block box answer for the joint to member connection for the second joint in on the bottom on the bridge (total of 4). These 4 points seem to be the first to give throughout all of our tests.

Staquet Weekly Blog - Week 7

Last week in lab each group was required to test their K'Nex bridge to see how much weight it would be able to suspend.  After testing, each group completed a survey on their bridge regarding how much weight the bridge held, its cost, how many pieces it was made of, a short description of the bridge design as well as why/how it failed.  Our bridge was able to hold 39.1 pounds while only costing $133 thousand, making it the strongest bridge in the class in terms of the cost to weight ratio.  This was a major accomplishment for our group, but I think that constructing the 3' span bridge will be much more difficult for not only our group, but for the class as a whole.  This week in lab we will be learning more about the structural analyzation of trusses and be able to gather some figures in reference to the weight capabilities of a specific design.

Working on the K'Nex bridge design without any numbers hasn't been too much of a problem up to this point.  Knowing the length of the members was obviously important in making sure the bridge would be able to span 24", but as far as weight goes, the exact numbers had not been a serious necessity.  Now that the bridge will have to span 36" I think some figures regarding failure in the K'Nex pieces will be much more useful.  The true challenge will be the fact that the bridge will still be experiencing the same 8" of force, only now it will be 6" farther away from each end.  I think the most important number to know will be the maximum tension force a K'Nex gusset plate can withstand before it lets go of the straight member connected to it.  It could be calculated by doing a number of stress tests on a simple connection and getting an average reading for the force required for the connection to fail.  This test would have to be evaluated for a number of different scenarios based on not just the orientation of the gusset piece, but the kind being used; whether it is a 360,180, 90, or 45 degree connector as well as how many members are being connected to it.  Another interesting number to know would be the length that a gusset piece adds to a straight member when they are connected. This can be easily found with the use of a ruler, and I honestly am unsure as to why our group has yet to calculate it.  The more important number is the failure point of the gusset pieces due to tension, because this is the primary reason that bridges collapsed during the lab.  Compression is not an issue with the K'Nex because they will fail elsewhere from tension forces before compression becomes a factor.

Schetley Weekly Blog - Week 7

Within the past week we got our first formal test of our bridge that we designed last week, and it actually held a lot of weight for it's shape and cost. The bridge held a weight of 39.1 pounds for only $133,000 worth of materials, resulting in a cost to weight ratio of 3.40 thousand dollars for every pound of sand held by the bridge, the lowest ratio in the class. I believe our bridge performed well because we had a feeling where the most weight and pressure would be on the bridge, so we put more members in those places to account for that. We also refrained from using grooved gusset plates. These gusset plates are weaker because as opposed to snapping in place like the other plates, one part simply slides into another, making these pieces (once again) weaker, but more expensive. In the next week I hope to learn about the ways of calculating stress and weight placed on the gussets and members in class, and I feel like that will be useful in attempting to improve our bridge.

The software we used before (West Point Bridge Design) gave us all the data we needed to analyze our bridge. It gave us compression and tension data automatically without having to turn on any special settings or run some ridiculous and tedious simulation to get the data, we just had to simply place a member, then run the general simulation to get the data. Unfortunately, using the K'Nex pieces don't readily give us any kind of data of how much weight is on each member when sand is loaded into the apparatus. That being said some of the data I would like to see for our design is firstly how much weight is on each member when sand is being loaded into the bucket. I know there is a way to calculate that number, but I'm not sure of how to do that yet, if it is possible at all. Another calculation I want to know is the breaking point of each gusset plate and I feel like that is something we are going to learn in class this week. It probably has something to do with the basic sum of forces concept we learned in Physics I, but I once again I suspect we will learn that in class this week. Finally, if this is even possible, I wonder if there is a way to see the amount of wear and tear is on some of the pieces from previous tests. While they don't break at the slightest amount of weight, these K'Nex pieces are still under a pretty decent amount of stress when these tests are administered. Each time a test is run the pieces get weaker and weaker, and if that has a significant impact on our bridge strength within a couple tests, I would like to know to be able to swap out those pieces.

Staquet Weekly Blog - Week 6

Last week in lab, as a group, we were given time to basically play with K'Nex in order to come up with ideas for our bridge that will be tested in the upcoming lab.  After building a few different designs and testing their weight capacities we were able to find a design that seemed to hold a decent amount of weight in comparison to its cost.  We made a few minor changes to the design while away from lab and have now finalized our bridge that will be tested in class.  During this class my team members and I hope to get a better idea of what other teams are doing, as well as what their cost to weight ratios are looking like in comparison to ours.

After working with the K'Nex this week I feel as though my opinion of the comparison between them and building a real bridge is about the same.  While the K'Nex are very convenient and easily constructed in comparison to an actual bridge, they are still extremely limiting in terms of their length and gusset angles.  There are a wide variety of differences between this plastic 24 inch bridge and a full scale steal construction bridge spanning 20 feet.  To me, the main difference is the simple fact that a 20 foot span, steal truss bridge would be designed and built with a purpose other than seeing how much weight can hang from it.  I would believe that the full scale bridge would have to have some kind of road surface or rail system running across it so that it can be used as an actual passage to move over an obstacle.  With this being said, the design of a "real" bridge would have to allow for something to pass through it without hitting any structural members, and also have to meet specific codes and regulations.  Another key difference is that a real bridge would have to be designed around the environment in which it will be built with materials and coatings that can allow for it to be safe and maintainable for years to come.  Designing a K'Nex bridge and designing a full scale bridge can be viewed similarly in the sense that they are both bridges that have a basic truss format and are designed to hold weight, but the differences between the two are endless and depend a lot on the situation in which a bridge is needed.

Schetley Weekly Blog - Week 6

In the last week we designed our bridge for initial testing in lab this week. We all designed our own bridge and worked off the one that held the most weight (around 33 pounds). We modified the middle of the bridge to hold more weight, adding a couple more members and gussets, since that is the area the bridge failed when we tested it. Adding up all the parts resulted in a total of $133,000, which is a bit more expensive than our initial design, but hopefully more stable. This week when testing the bridge we will be filling the bucket with sand, a more uniform weight distribution, allowing for equal stress to be placed on more members instead of more weight on less members and gussets.

Our bridge design did not change much compared to our designs last week, so we can't really address that question. However, in response to the other question, designing a K'Nex bridge spanning two feet is a lot different than spanning a steel bridge spanning twenty for a couple reasons. First of all, a K'Nex bridge experiences the most weight and stress on the gussets, since a K'Nex member is relatively strong. Steel bridges, depending on the strength of the welds and members, will be more inclined to have stress throughout the bridge. This is actually a reason why designing these K'Nex bridges are more difficult, because more emphasis needs to be placed on the gussets. Another difference is steel is, of course, a much, much stronger material the K'Nex, allowing it to hold more weight, but then again, no cars are going to be driving over a K'Nex bridge anytime soon. Since steel is also stronger, less material can be used for a given area in the bridge,  probably resulting in a better cost to strength ratio.

Bell Weekly Blog- Week 6

In the prior week, the group each constructed a bridge out of K'nex. We each built one to get some different ideas out onto the table. After we each had our bridge built, we each tested our bridge with weights. For the bridge that held the most weight, we took that bridge design and built off of that. We decided to take that design home with us for some analysis and construction. As a team, we have agreed to keep the bridge design that we already have. The tasks we will cover in the coming week will consist of changing minor things on our bridge to help reinforce its structure. The major accomplishment our group had in the week was having a bridge that was able to hold nearly all the weight that was available (about 33 lbs.). Some issues that might come up throughout the next week might be an argument over different structures on different parts of the bridge. 

Compared to last week, I would say that our group made little to no changes to our design. If we were to make a steel bridge that spanned 20', many things would change. First of all, we would need way less material because steel is way stronger than many materials. Second of all, the steel bridge would be able to hold a lot more weight proportionally because the joints on the steel bridge would probably be welded. The K'nex bridge always fails at the joints.

Staquet Weekly Blog - Week 5

Last week we were instructed on how the competition will be set up and in what ways our bridges will be tested.  We found out that the bridge will need an area relatively close to the center in order to fit a metal rod through, as well as a portion of the top of the bridge that is flat for about 8 inches.  These requirements are so an 8 inch piece of wood in which a metal rod is attached can be placed on top of the bridge.  The metal rod will run through the bridge from top to bottom where it will then be attached to a bucket that will be slowly filled with weight, ultimately determining the strength of the bridge.  The strength of the bridge is then compared to its cost and the team with the lowest cost to weight ratio is the winner.  As a group we were given about an hour to work with the K'Nex and get an idea of their sizes and how they fit together.  This week we plan to collaborate and decide on a basic bridge design to work off of.  We are hoping to get the chance to build more bridges and get more hands on experience with the K'Nex.  As a group I feel we may run into an issue with having enough time in the lab to build and test our designs.  It is a competition that relies a lot on trial and error and in our case, building and testing over and over again.  With everyone in the lab doing this the testing station could begin to get congested and cause a bit of standing around.

While West Point Bridge Design and building bridges out of K'Nex may seem to be very similar, they are completely different at the same time.  WPBD has a lot more options in not only materials but the orientation of members as well.  With K'Nex you are limited to building off of gussets that only come in 45 degree increments, unlike WPBD which allows you to connect to anchor points in anyway you choose.  Another huge difference is the materials; in WPBD you are able to change between hollow and solid members, choose any length of member, and the type of material while K'Nex come in limited sizes and only one material.  The comparison between the two methods will continue to show that the K'Nex are more limiting in any aspect.  Another big difference is that in WPBD the goal was to be as cheap as possible and still have the truck drive over the bridge.  Now the competition is dependent on a rate of cost to weight.  This makes the competition a little more challenging in terms of comparison to other groups because the weight is no longer held constant.

A2 -Staquet

My bridge is designed to be very cost effective while also being as strong as possible.  I used a simple truss design that should be relatively strong in supporting loads during the competition.  The bridge measures roughly 3.5 inches tall, 5 inches wide, and spans a total of 24 inches.  It is an overhead truss design with the bottom cord running the entire span, and the top cord resembling that of a trapezoid.  The interior bracing is composed of a series of triangles to give the bridge needed strength.  The cross members that spread the width of the bridge and are shown to be snapped into the gussets in a perpendicular fashion.  Figure 1 shows the bridge from the top view as well as the side view.  Figure 2 is a list of the amount and type of truss members and gusset plates needed to construct the bridge.  A final materials cost is also listed at the bottom of this figure.

Figure 1.

Figure 2.

 My bridge didn't experience much change during the design process besides the fact that the K'Nex gussets only allow for connections in 45 degree increments, a detail my prior designs weren't limited to.  I also was unaware of the dimensions of the K'nex gusset pieces seeing as they are not given, nor did I bring my set from home to reference.  This made it difficult to determine a proper geometrical layout for the bridge  that will actually work when I am in the lab.  I found that designing the bridge was difficult without the actual pieces.  This competition, being that it is so small scale, is something that will require a lot of trial and error; hands-on building and testing in the lab rather than drawing and typing.

Schetley Weekly Blog - Week 5

In this past week we each made our individual preliminary K'Nex designs. All of us made our designs on pen and paper, actually making very similar designs. The basic concept was to utilize triangles as much as possible, making many isosceles triangles and trying to avoid the longer members when possible. In the class last week, we also got a bunch of the K'Nex pieces to mess around with, get some initial visualization with the parts, and see what members work with what to see what shapes could be made. This coming week we will take the best of each design and collaborate on a better design. The main problem our group could run into is disagreements on which features to use in our bridge, but I am sure we can get past those.

This last week we starting moving from using the CAD software West Point Bridge Design to the physical K'Nex pieces. These are somewhat similar in that they allow you to use different length members and things of that, but that is where the similarities stop with the two. WPBD allows for more freedom when designing a bridge than K'Nex, to start with, because only angles possible with K'Nex are 45 and 90 degrees. This makes it extremely difficult to make arch K'Nex bridges, which in my opinion is a much stronger bridge than the one I designed my previous blog post. Another difference is the fact that WPBD disregards the gussets in bridge testing. In the software, when a bridge fails the members are what break, but with these K'Nex pieces the members won't be easily broken, so the first to fail is going to be the connector pieces. This means we will have to focus more on gusset strength in these K'Nex tests as opposed to member strength if we want our bridge to be able to minimize its cost-to-strength ratio.

Bell Weekly Blog- Week 5

In the previous week, our group started to actually get some hands-on experience with our bridge materials that we will be using for the competition. We didn't actually start working on our final design, or any design for that matter. We were just getting to know the pieces and how they could be oriented for a bridge. During the coming week, the group will start putting our ideas into an actual bridge. By now, we probably have a good idea as to what kind of bridge we want to build. A major accomplishment that the group has completed this week was truly starting to come on a consensus on what we want to construct. On that note, we might also disagree on what we want to do as well. There is really no way to tell what everyone will want to do during the process. For example; someone might come up with an idea that the other(s) might not like. However, I am confident that our group will not run into too many of these arguments.

The similarities and differences between K'nex and WPBD favor in the differences. The main similarity between these two are the fact that the orientation is pretty much the same. There are joints and different length members. As for the differences, for one, the lengths of the members and angle of the members connecting to the joints can be anything in WPBD. In K'nex, there are only four or so set joint/member pieces. The other difference between the two is the breaking point. In WPBD, the breaking point was due to the overpowering tension/compression on the members. For this competition with the K'nex, I am almost positive that the members will not be the first to go. It will almost always be the connection of the joints to the members. That being said, I feel that our main focus should differ than WPBD. We should have more focus on the connection points between the joints and the members.

A2-SCHETLEY

 Below is my initial bridge design drawn by hand, scaled as best I could. The bridge is just a combination of triangles, the strongest shape. I wanted to concentrate more members in the middle because that's where the most tension and compression on the bridge will be in the bridge. I might add members on the sides to give the bridge more support, but at this point I will see how the bridge hold up. Below is the design of my bridge and the cost of the bridge, which comes out to be $98,000.

Figure 1: Top and Side View of Bridge Design

Figure 2: Bridge Materials Cost

Since this was a preliminary design, it didn't change much, if at all. I felt like it was extremely difficult to visualize the bridge on paper without the bridges in front of time. There were times when it took me a second to know which member would go in the place (if there was even a member size that would fit it). The thing that I learned about while designing this bridge is the application of geometry. If you aren't using the right size members, you're bridge will not be able to fit or be built.

A2- Bell

For my A2 bridge design, I chose to go with a more simplistic design. There are only 8 diagonal members in the whole design (excluding the 2 on the very end). What is unclear and hard to interpret is that the diagonal trusses on the inside are alternating orientation from front to back. In other words, the middle diagonal members coming out of the 135 degree pieces form a "W" on one side (either on the close side or far side). The opposite side would be every other truss. Overall, I learned from designing this bridge that it is harder that I thought to make the bridge geometrically sound. Lots of members needed to be changed. The first time around, I found myself trying to fit different members in different places because my specific shape didn't allow what I initially wanted.

 Figure 1: The drawing of my bridge; plan on top, and elevation on the bottom

Figure 2: The K'nex pieces bill of materials chart

Bell Weekly Blog- Week 4

In week three, the group was given a challenge to make the cheapest, but still serviceable bridge my the end of class. We learned quite a few things about what makes the best design, the best materials, and the best diameter of the members; meaning we were able to get the members as close to their breaking point without breaking. In the coming week, the group will learn more aspects about bridges that will help us in the future have a better understanding about bridge designs. The one major accomplishment that our group had this week was building a decently cheap, yet serviceable bridge. Some issues that the team might run into could be arguing over different bridge designs.

I think that, for the most part, West Point Bridge Design is very realistic. Not only do you just connect members to pivot points, but you also change the material and thickness of the members. The program also allows you to reduce the cost as much as you can by maxing out the tension/compression values for each member for the cheapest cost.

Schetley Weekly Blog - Week 4

This week we worked on our bridge in West Point Bridge Designer, trying to prefect our bridge design to maximize strength while at the same time reducing cost. I, personally am getting more and more comfortable with the West Point software, so it is getting easier to use and really analyze what the data from the software is telling me. For the coming week, my group and I plan to learn even more about bridges, continue to prefect our design, and overall make progress with this project. I feel like we still can lower the cost by adjusting material type and size in the future, and hopefully we can without drastically altering the design of the bridge. As for West Point Bridge Designer itself, I feel like it is a good representation for the bridge design process with the many different features of the software, such as the ability to alter concrete type, anchor points, number of piers, and number of lanes, and those features are just the setup before the actual design of the bridge. Once in the actual design part, the ability to alter member size, placement, and material really gives a good look at bridge designing complexity. While I do think that it is a good software, I feel that it is a good basic software. The software to me is not as intricate and realistic as bridge design could be. When the animation plays, the bridge sags much, much more than a realistic bridge would (actual bridges sag fractions of an inch, if at all), and I feel like that takes a bit away from the realism of the system. I also feel like bridge design is more complex than place a connector at a point in space, connect a few members, repeat, then a bridge is made. But as I mentioned earlier, WPBD is a good basic, introductory software for bridge design.

Staquet Weekly Blog - Week 4

Last week, as a group, we worked on the computer with the West Point Bridge Design program to try and make our bridges from last week more cost effective.  We ended up designing a whole new bridge, keeping in mind the fact that with less weight and material comes a cheaper bridge.  As a team we were able to design a bridge that costed less than any of our previously designed bridges and I think this is due to the fact that we were able to put all of our thoughts together to accomplish the task.  In the coming week we plan to learn more about bridge design to see what combinations to work better than others so we can design a really good bridge for the K'Nex competition.  We will also learn from the questions being answers by the research librarian.  I believe that West Point Bridge Designer is a great demonstration of the bridge design phase in a real life situation.  There are all types of bridges to choose from and after that it is all up to the designer.  It gives you the ability to change a lot parameters right from the start including bridge span, anchor points, number of piers, road deck material, and even how many lanes wide it will be.  It gives you the opportunity to see what the relative cost of that type of bridge would be and can be very insightful as to what is safe and what is not.  While all of these aspects are great, the program does leave out a lot of crucial pieces to building an actual bridge like the ground type, dynamic side loads like wind, and even what type of environment the bridge will be standing in (corrosive, salt ridden air for example).  It also does not give you an estimate for the actual construction cost of building the designed bridge.  Although it is not the perfect program it is extremely useful for students in an entry level bridge design course, and it gave me the chance to learn a lot about truss bridges and their core design.  

Bell Weekly Blog- Week 3

Throughout this week, our group basically learned the basics of the West Point Bridge Design program. We learned how to created a serviceable bridge, while keeping the cost in mind by not adding meaningless members. This week, our group has accomplished one bridge design each that was able to be serviceable to the truck. In the upcoming week, our group will mess around with some different materials and sizes of the members. 

Questions:

1.  Which materials are strongest for tension and compression?

2.  Which bridge design is better; a bridge with trusses under the asphalt or a bridge with trusses above the asphalt?

3.  What is the longest bridge ever made?

Staquet Weekly Blog - Week 3

The three questions I have prepared for our research librarian, Mr. Jay Bhatt, are as follows.  Roughly how many bridges in the United States are currently considered to be structurally deficient?  How much money will It cost the U.S. to repair or replace these structurally deficient bridges?  What is the length of the largest pier to pier bridge span ever built in the world?
Last week in class we learned about truss bridge design and how it relates to the bridges we are designing.  As a group we were given some time to work on possible designs by using West Point Bridge Design.  This week we will learn about researching bridges, a lecture that will be lead by Mr. Bhatt, our research librarian.  After learning about research tactics, we plan to meet as a group and further our bridge design, and work on making it cost as little as possible.

Schetley Weekly Blog - Week 3

This week was mostly learning how to use the CAD software West Point Bridge Design. This is the software that will be used to design and test the bridge before it will be "field tested." It was very easy to learn and is a very user-friendly software. I, personally, haven't dabbled adjusting the materials, size, and other options like that. I want to first get comfortable with the program before I get advanced with lowering costs and changing materials. I'm unsure of what we will do in the coming week, since we seem to still be in the introductory phase of the class. This week we might learn more about the different materials and hollow versus solid members. I am looking forward to learning more about bridges in this class this week.

Also, the three questions I would ask Mr. Bhatt these three things when he visits:
1) What is the strongest shape in bridges?
2) What is the strongest material in bridges?
3) What is the most-cost effective material in bridges?

A1-BELL

For my bridge design, I felt that it would be appropriate to create an arch that stretched from one end to the other facing up. The advantage to this design is that a semi-circle is a very strong shape. When the asphalt  part of the bridge bows in, the arch in my bridge design compresses each piece equally. If it were any other shape, some pieces would have not compression or tension, while other take all of the compression and tension. As for everything else inside the arch, i felt the best way to create strength to the bridge was to simply create multiple triangular trusses along the length of the bridge. Finally, I have vertical members to support the weight of the arch. In terms of change in design, I never actually changed the physical layout of the design. I only changed the thickness and materials of certain members. Members that had high compression (arch of bridge) were changed from carbon steel to quenched and tempered steel, which is a better material for compression. Members with high compression also had thickness added to them. The cost of my bridge after all the corrections have been made came to a total of $364,160. Through research and analysis of my bridge design, I am confident that I could knock off at least $50,000, using different dimensions and materials. Throughout my bridge design, I learned that the top of the bridge needs the most focus because it has more compression than any other part of the bridge. The three following figures show the 2D model of the bridge, the table of the test results, and a 3D model of the bridge with the truck in the middle of the bridge.

 Figure 1: 2D Model

 Figure 2: Table of Test Results

Figure 3: 3D Model

A1 -STAQUET

The goal of this bridge design is to build a safe bridge that is as cost effective as possible.  I choose to design my bridge with all of the steel members being above the roadway deck in a relatively arch shaped pattern.  I then integrated interior cross members in the form of triangles to give the bridge added strength.  I decided to use this shape bridge because I personally believe that an arch is the strongest shape possible for this type of construction, and the addition of triangular internal truss members only makes the design stronger.  I did not have too many design changes during my time I spent creating the bridge up to this point, only slight arch angle changes.  In the future I plan on experimenting with the different available materials and changing between hollow and solid materials to get my bridge to cost as little as possible.  My bridge currently costs $298,000, and with future work and experimentation I plan to get the bridge to cost under $250,000.  During this design process I learned that bridges are extremely expensive, and involve a lot of time and effort outside of the actual construction process.  Below, Figure 1 shows a 2-D view of the bridge in the drawing board view, Figure 2 shows the simulated truck in the middle of the bridge, and Figure 3 shows the load test results of the bridge.  

Figure 1

Figure 2

Figure 3

A1-SCHETLEY

My initial bridge design is just a simple arch bridge design with triangular truss members I settled on this after realizing that other shapes weren't as strong as a combination of arches and triangles. The initial design is very simple, which is expected since I am relatively new to not only West Point Bridge Design but bridge design in general. Initially I tried to incorporate two equally sized arches across the bridge, but I could not get the bridge to support itself, even without the truck on it. I actually realized that in order for there to be multiple arches, there must be a center column in the water. Right now the bridge costs $334,495.95, but as I become more comfortable with the program, the strengths and weaknesses of certain materials, and what is the best shapes for bridges, I feel like the bridge can go below a cost of $300,000, possibly even $250,000. Below are pictures of the bridge's 2-D design, its 3-D design, and the test results of the bridge.

Figure 1: 2-D Design

Figure 2: 3-D Design

Figure 3: Test Results