A4

Engineering 103 -- Section 35 -- Group 12

Background

In this Engineering 103 class, the goal of the term was to build a model bridge out of K'nex pieces with the lowest cost-to-strength ratio. What this means is that the cost of the bridge was to be divided by the number of pounds the bridge could hold before breaking. The lower this number, the stronger and more cost effective the bridge.

Throughout the term, the class learned about effective and ineffective bridge designs, famous bridge failures, how to calculate tension and compression in certain members of the bridge, and how to put all of this information together to build the best possible bridge. The first few weeks of the term were spent familiarizing ourselves with basic truss designs and the West Point Bridge Design software. This software was useful in the beginning because it showed what bridges were realistic, where the bridges would break, and how much tension/compression was on each member. This allowed the class to get a greater understanding of how bridges work before actually modeling, analyzing, and testing one.

After using the West Point Bridge Design software, the class moved on to building a 24-inch bridge out of K'nex pieces. This allowed everyone to see how K'nex differ from theoretical software and understand how things were more likely to break in the medium that we would be using for the final bridge. Working with K'nex also allowed us to examine the bridge after it broke to determine what aspects of the bridge could be improved.

Finally, the class learned how to analyze the physics of bridges to come up with our own compression/tension values and we had to modify our bridge to meet the criteria of the class: at least 36 inches long, 3.5 inches wide, and two inches high. The bridge also could only be supported on each end by the table – no support beams in the middle.

Over the course of the term the class learned how to plan and design a bridge via software and modeling, how to use various bridge design software, the physics behind bridge design, how to determine where the bridge failed and how to fix it. We expanded our knowledge of how the design process works from beginning to end.

Design Process

In the first phase of the design process, each team member worked individually using West Point Bridge Designer. The intention was to make an inexpensive truss bridge that had high compression and tension force to strength ratios on its members. Triangles, the strongest geometrical shape, were used. Constraints included pricing per joint and per member, as well as a restriction to 2 support points allowed, one at each end. The goal was to create a bridge that was inexpensive (goal cost: $200,000 or less), and remain intact through the WPBD’s load test. However, while going through the design process, it was difficult to create a strong bridge that also was inexpensive. However, when the three designs were pooled together for ideas, the group design was close to the goal price.

Once the second phase of the design process began, the goals had to be changed. The West Point Bridge designer was no longer used. Instead, the medium was K’nex building pieces. These pieces behaved very differently from the ideal conditions in the WPBD program. The new goal was clear: build a bridge that balanced structural integrity with low cost. Many individual designs were made, at first by educated guessing, and later with strategic member and joint placement derived from previous test results. Load tests with buckets of sand showed that bridges tended to fail at the gusset plate joints in the center of the bridge, where the load was directly applied. The Method of Joints was applied to a simple, 7-member truss section, and to the K'nex design. The Method of Joints is a system of equations made from free-body diagrams that calculates the force on each member and determines whether the force is tension or compression. Results were then checked using the John Hopkins University Bridge Designer for verification that hand calculations were correct. These calculations showed which members experienced the most force when a certain load was applied, and how the members would react to the applied force. It was useful in predicting how the 

Each phase concluded with the individual designs being brought together in a final design. With the WPBD, the designs could not be combined without sacrificing structural integrity, so one design was picked by all and modified by the group. The K’nex bridge had more combination options. Two designs were made, one spanning 2 feet and the other spanning 3 feet. For the 2-foot bridge, the individual designs were combined so elements from each were included in the final. It followed constrains of a width of at least 3.5” and a height of at least 2” inches, with a space in the middle where cars would fit. For the 3 feet bridge seen in Figures 1 through 6, the constraints were the same, plus the testing site did not have grooved edges as with the previous testing site. The final design for this length was different from the previous one. After much revisiting and editing, the initial 2 feet bridge was exhausted of all options. In an attempt to hold more weight, a more expensive bridge was made that utilized X-cross sections instead of the right triangles previously used. This final design was predicted to fail at 25 pounds, with the middle members dislocating from the gusset plates.

Description of Final Bridge:

Figure 1: Plan Drawing of the Final Bridge Design

Figure 2: Elevation Drawing of the Final Bridge Design

Figure 3: Excel Spreadsheet Bill of Materials

The overall cost of our bridge according to the Truss Bill of Materials (Figure 3) was $342,000.

Figure 4: Plan Photograph of the Final K'nex Bridge

Figure 5: Elevation Photograph of the Final K’Nnex Bridge

Figure 6: Final K’nex Bridge Ready to be Tested

Testing Results

Our final bridge design held 13.6 pounds. Though this was not as great as the predicted carrying capacity of 25 pounds, it still gave us a cost to weight ratio of 25,147.06 dollars/pound. This load at breaking point was not unreasonable low considering the low cost of the bridge. The bridge failed in two places, in each of these two places a member popped out of a joint. The failures occurred at the bottom edge of the middle of the bridge and at the bottom of one of the ends of the bridge. In each of these places the joint that the member popped out of was a 360-grooved gusset plate.  The bridge twisted only slightly when it failed and it did fail graceful as the bridge did not completely fall apart or break in half and no pieces went flying off when the two members popped out. Its only slight twist was a compliment to the stability of the bridge, while many other bridges seemed to twist almost into two pieces.

Conclusions

The bridge behaved as expected. It failed in the middle where the load was applied by members dislocating from the gusset plates. However, it failed much sooner than expected, at 13.6 pounds instead of the expected 25. One reason for this was that the bridge was very box-like. In other words, the only supports came from each face of the rectangular truss. There were no diagonal supports that traversed through the center opening. The bridge would have been far more expensive if these extra supports had been added, but it is possible the design would have held enough weight for the cost to strength ratio to improve, meaning the design was more efficient. It is difficult to know what the other outcomes would have been without more tests. 

Working with both West Point Bridge Designer and the K'nex pieces throughout the design process, it was apparent that the two methods had many differences but also a few similarities. The West Point Bridge Designer has informative stress test simulations and takes multiple factors into account when calculating cost (like material type, length, and density). Members can be any size, made from one of three materials, and can be hollow or solid. All connecting pieces are the same size and weight, but can connect at any angle and it is possible to connect a great number of members to one connecting piece in the drawing board.

K’nex bridges are very different. K’nex pieces are all made from the same solid plastic material. There is a limited variety of members each at a set size that cannot be changed. Connector pieces, known as gussets, are different as well. They have a certain amount of slots at specific angles that fit the member pieces. The K’nex kit has more artistic freedom than the WPBD, since with K’nex a design doesn’t have to be symmetrical on both sides and the perpendicular connecting pieces can be drafted by the user.

There are a few similarities between the two. Both use straight members that can bend a bit to support a design up to a certain breaking point. They both have the possibility to create different shapes not limited to triangles, but triangles are consistently the strongest structures. They both bring new challenges to creating a design that prompt the designer to think things through to determine the best course of action.

Future Work

If our group was to design another version of the bridge, we would completely scrap the design we’ve been trying to work with from the beginning and we would work to make our bridge as strong as it can possibly be. This seems to be the best technique since the average class price ranges from $300,000 dollars to $900,000 dollars, but the weights range from 10 to 100 pounds, and the cost-to-strength ratio was anywhere from $8,000 dollars a pound to $27,000 dollars a pound. With this in mind, it makes more sense to spend the extra few hundred thousand dollars to get 20-40 extra pounds of weight.

Our future bridge design would probably also be less about what we think is unique and might work, and more about strengthening what has been proven to work in the past. These tried and true designs have weathered centuries of use, and thus would likely be a better option than anything our group could think up on the spot.