|MadSci Network: Engineering|
Hello, Christina! Every year, I attend the awards ceremony for the bridge building contests run by the Illinois Institute of Technology. Some of the bridges these kids have made are fantastic -- a few grams of wood supporting 60-70 kilos! Many of the winners were girls, too. But they've been building bridges all semester, and your class is just doing this for fun at the end of the year. So, a "crash" course in how bridges work: First, like you said, a bridge is a machine that takes a load from where it is and puts it somewhere else, that is, out at the ends. A bridge with no supports under the roadway is called a "simple" bridge. All bridges work by "compression" and "tension" in their members, compression being when the material is being pushed together, and tension being when it's pulled apart. A piece of string under load is in tension; a stack of blocks held horizontally is in compression. The loads on an arch bridge are pretty much uniform all the way across. http://www.technologystudent.com/struct1/arch1.htm (the bottom picture is not an arch bridge!) http://members.cox.net/ksregphotos/Clements_Stone_Arch_Bridgel.html This puts the entire arch in compression. If the load is applied in the center only, the shoulders of the arch (with nothing to hold them down) will flex upwards and fail. If the load is placed only in the center of the span, the best supporting structure would be what's called a kingpost truss.http://www.mnhs.org/places/nationalregister/bridges/nrrk1482/sign.htm l (Also see drawing) The two diagonal members are in compression; the horizontal member is in tension, keeping the bottom end of the diagonals from flying out. Now the thing with compression members is that they fail by buckling. Push down (carefully) on one of your wood pieces. At some point, it will bow sideways. Try this with a long and a shorter piece, and you will see that the longer the member is, the smaller the load it can support before it bows. And, due to the geometery of the triangle, the more acute the angle between the strut and the load vector is, the less load there will be on the strut -- that is, a strut supporting a load at 45 degrees will have to work harder to support it than when the load is at 30 degrees. So there's the design problem: The longer the compression struts, the more acute the angle between them and the load, so the less load on each strut. But, the longer they are, the more likely they are to buckle. Adding bracing from the bottom chord to the struts reduces what engineers call the unbraced length, but it adds weight to the truss. I shouldn't make an out-and-out recommendation as to what kind of bridge you should build. But, the simplest structure would be a kingpost truss in the form of a four-sided triangle, with the load applied at the apex, two long horizontals spanning the gap, and the other two sides the width of the "roadway." The angle of the struts to the bottom chord should be on the order of 45 to 60 degrees. Use bracing struts to reduce the unbraced length of the compression members. One more bit of advice: be very careful in making your joints. That is the most likely point of failure. When you and your friends break your bridges, I strongly recommend that you not only record the weight of the bridge and how much load it carried. Also record the location and type of failure that each bridge experienced. Then, you can build another bridge with the broken part strengthened and other parts lightened. Load that one, and see where the new version breaks. Keep trying, and you may end up with a bridge the equal of the design contest prizewinners! Good Luck! C.H. "Chas" Hague, PE SE
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