ec1 - Lotfi Limouni MEM 230 Extra Credit 1 11/16/2010...

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Lotfi Limouni MEM 230 Extra Credit 1 11/16/2010
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figure 1 figure 2 From “figure 1” and by using geometry we can see that eq.1 the negative sign in ‘y’ ensures that is negative when the fiber is above the neutral axis (contracting), and positive when under the neutral axis (stretching). Working eq.1 and because the angle is so small we get Thus, Dividing both sides by “”. having an infinitesimally small element we proceed to take the limit approaching “zero”. So, eq.2
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And by definition the strain eq.3 From “ figure 2 ” and by using geometry methods similar to ones used in “eq.1” we get Rearranging and taking the limit we get So, eq.4 Substituting eq.3 and eq.4 into eq.2 we obtain “figure 3”
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From Hook’s Law along with the assumption that the longitudinal fibers either extend or contract, and are made of linear elastic material. We can directly obtain the following equation: Which is equal to: eq.5 Note : from figure 3 we notice that since the stress distribution is linear the greatest stresses occur in the
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ec1 - Lotfi Limouni MEM 230 Extra Credit 1 11/16/2010...

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