Embedded Files
As an introduction to the mathematical calculations for the members of a bridge, we used a simple lever-based testing machine and test specimens made from file folders to calculate the theoretical yield of structural members. We followed the directions listed out in activity 2 of the WPBD series (a pdf of which can be found in the google drive folder below). After conducting all of the tests, we organized our information in a spreadsheet, calculated the tensile/compressive strength, and created a graph.
Construction of structural members:
We used the laser cutter to make our test members so that they would all be uniform. It took some time to figure out exactly how to design the members on Inkscape, but after creating the first tube, the rest were easy. I first drew a rectangle with the dimensions of all the sides added together (ex. for the 10mm x 10mm tubes the rectangle was 46mm wide and either 5, 10, or 16 cm long) and then converted all measurements to inches. Inside the rectangle I drew four lines and positioned them according to the dimensions of the tube by typing in a specific value for the x-coordinate. Thus, the lines ended up the correct distance apart. I used the picture below as a guide:
In the laser cutting settings, we turned color mapping on in order to use different power and speed on different lines. We made the outer rectangles of each member red, and under the color red, we set the speed low and the power high so that it would cut all the way through. For the interior lines, we made them blue and set the speed higher and the power lower so that it would not cut all the way through, which would allow us to fold them and make the tubes. The svg files are uploaded in the google drive folder above and shown below are screenshots of our designs.
10mm x 10mm tubes:
10mm x 6mm tubes:
4mm, 6mm, and 8mm bars:
Pictures of setup/testing:
Compression setup:
*we stacked books so that the lever would be level at the beginning when no weight was added
Tension setup:
Similar to the compression setup but specimen was put on the other side of the pivot
Tension specimens after testing: Compression specimens after testing:
Examples of collapsed test members:
Examples of broken test members from tension:
Results and graphs:
Analyzing the results:
We used what we previously knew about what influences tensile strength (only cross sectional area and material) and what influences compressive strength (length, shape, cross sectional area, and material) to make the experiment most efficient. Because the thickness of the bars and material was kept the same, only the width would change the cross sectional area and thus the tensile strength. To test compressive strength we used two tubes with different shapes and cross-sectional areas and for each type of tube we tested three different lengths.
As we would expect, in the tensile strength graph, we see an upward trend. As the width increases, so does the cross-sectional area, and therefore, the tensile strength also increases. If we had more time, it would have been better to test more members of each type, which would have eliminated some of the overlap between the data points.
The compressive strength graph had more going on since more variables were involved. The red dots represent 6mm x 10mm rectangular test members while the blue dots represent 10mm x 10mm square test members. What we observed was expected since an increase in cross-sectional area and a square shape instead of a rectangular shape should increase compressive strength. The effect length had on the members was a little less clear since there was so much overlap. Once again, a large sample of members would have resulted in more precise graphs.
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