Technical Report for Balsawood Bridge

EDITOR'S NOTE: For a change, the comments are being left ON. I welcome and would appreciate your thoughts -- this technical report has not been scored yet, so it will be interesting for your feedback to compare & contrast with the judges. Just keep it constructive, if you'll pardon the pun! :D

Design Philosophy and Construction Procedure
As stated in the introduction, we used the Warren Truss, with slight alterations, for our design. Even before we began our research, our design was based on common sense, intuition and prior experience. With force being applied to the truss we knew that we had to build a design where it was distributed and transferred to the supports with as little stress as possible to the bridge. The top of the bridge is where the compression is located when force is applied, and if not handled appropriately the bridge will snap inwards; while if there’s too much tension, on the bottom of the bridge, it will slide apart and buckle. Knowing this, we decided to use equilateral and isosceles triangles, with 60-60-60 and 90-45-45 degrees to dissipate the force being placed on the bridge by both gravity and the machine.
The force of gravity (weight) is equal to the product of the mass of the bridge times the acceleration due to gravity, in accord with Newton’s 2nd law of motion (Fnet=ma). According to the 3rd law of motion, the bridge tester will exert a normal force back on the bridge that is equal in force to weight but opposite in direction. The bridge testing machine will apply force equal to the product of pressure times area (P = F/A or F = PA). The pressure will also be equal to the work done by the tester over the volume of the bridge, where work is the product of force times distance time cosine of the angle relative to the direction of motion (W=Fd cos θ), and volume is area times depth (V=Ad). So (P = W/V = Fd cos θ/Ad). As the crusher does it’s work, the force of the load is transmitted along our beams. That stress will cause deformation from shearing and strain of extension and compression as previously stated once we pass the point of elasticity (Young’s modulus).
Our first design used the triangular method, with two sides at an angle connected by a roadway, but on our bottom beam we had vertical pieces of would which we soon realized would snap under the stress of compression and used too much wood. Our second design consisted of three major triangles with one smaller one inside of the middle triangle all at 60 degrees. The change leading to our third and last design was adding another beam for more support and changing our corresponding triangles to equal angles with our major ones being isosceles or equilateral.
Although it may’ve been better to stand the whole bridge at an angle, we have it at 90 degrees, with space between, hopefully to displace the force with greater efficacy. The goal of our BBB bridge is to attain the highest amount of efficiency possible with the given materials. Efficiency is measured by taking the ratio of the mass of the bridge itself compared to the mass that the bridge can hold. That number is then multiplied by 100 to discover the percent of efficiency. A highly efficient bridge would have its own weight at minimum and the amount of weight it could hold, at maximum.

Bridge Construction
After the team agreed to on final design, we gathered the needed materials necessary to construct the bridge: one-quarter by one-quarter inch (¼” x ¼”) balsa wood thirty-six inches long (36”) provided for us by our SECME coordinator, and we began to cut the pieces. Beam lengths were as determined by competition rules (EX: no member shorter than two inches (2”)). Angles were joined at 60-60-60 and 90-45-45 degrees. Pieces were adhered together with cyanoacrylate glue. We allowed the glue time to dry with each piece so it would not compromise the structure of the bridge.

Top view: roadway span: 45 cm in length by 4.5 cm in width
End view: roadway span: 4.5 cm in width by 1.3 cm in depth, attached to truss 18 cm in height by 4.5 cm in width
Side view: total bridge height of 18 cm, with central truss height clearance of 2 cm and width clearance of 45 cm

Conclusion
As foreboding as this task was in the beginning, we predict that our bridge will do pretty well. With an understanding of how the force of gravity and the testing machine cause tension and compression on the bridge, we presume to have designed and built a bridge to withstand the stress, strain and sheering being placed on it. However, if we were to voice concern over possible failure areas it would be at the intersection of our 45/60 degree angles. Seeing as how the force is being directed towards the center of the bridge there’s a fear that tension will occur resulting in movement of supporting beams.

Selected Bibliography
- NOVA Online | Super Bridge. (n.d.). PBS. Retrieved February 22, 2010, from http://www.pbs.org/wgbh/nova/
- "BrainPOP | Technology | Learn about Bridges." BrainPOP - Animated Educational Site for Kids - Science, Social Studies, English, Math, Arts. Web. 18 Jan. 2012. http://www.brainpop.com/technology/scienceandindustry/bridges/.