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geometric arrangement of the members into the triangle. The triangle then must be an |
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inherently stable structure. |
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With that in mind let's take another look at the other polygonal shapes to see how they |
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might be made stable. For example let's place an additional member in the parallelogram |
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so that it joins two of its opposite joints together as shown in Fig. 122 a). This action, called |
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triangulation since we are dividing the polygon into two triangular shaped sections, makes |
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the parallelogram stable and forms it into a square. Let's do the same for the pentagon. |
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First we insert one extra member so as to form a triangle with any two adjacent edges of |
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the pentagon as shown in Fig. 122 b) above. This helps stabilize part of the structure but |
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the other three members can still move. We add another member forming three triangular |
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sections in all. The pentagon is now stable also. Finally, we triangulate the hexagon in a |
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similar manner and find that it takes a minimum of three extra members to make it stable |
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(Fig. 122 c). In each of these examples, the rigidity imparted to the polygon is due only to |
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the fact that it was triangulated since all of its joints are hinged. Triangulation changed |
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them from being inherently unstable to being inherently stable. |
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Using such hit and miss methods ancient builders eventually discovered the principle of |
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triangulation in their attempts to build stable structures. But structural engineers do not |
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like being eaten by wolves any more than the third little pig did. So they wisely use a |
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mathematical equation, attributed to Euler, that gives a good indication if a polygonal |
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structure with flexible joints is inherently stable or not. And if it is not stable the equation |
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predicts how many additional bracing members it takes to stabilize it: |
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M = 2 J - 3 where M = members |
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J = joints |
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Back to Knowhere |
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