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problemset_2008-5_key

# problemset_2008-5_key - Problem Set 5 EMA 4714 Materials...

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Problem Set 5 EMA 4714 - Materials Selection and Failure Analysis Due Wednesday, February 20, 2008 – 8:30 am 1. The following 4 problems [lifted from Ashby, Materials Selection in Mechanical Design] all involve cantilever beams, but with different loading configurations or design objectives/constraints. Read carefully .... ******************************************************** The constraint equation in all 4 cases is the same as is the 2nd area moment [inertia]; δ = FL 3 /[C 1 EI] I = t 4 /12 a. Show that the best material for a cantilever beam of length L and given [i.e. fixed] square section [t x t] which will deflect least under a given end load F is that with the largest value of the index M = E, where E is Young’s Modulus [neglect self-weight]. ******************************************************

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L 3 /[2Et 4 ]; m = Lt 2 ? ; Substituting value for m into expression for ? min , ? min = [3/2][L 4 /t 2 ][ ? /E]; M δ min = 12FL 3 /[3Et 4 ] = 4FL 3 /[Et 4 ] = [4F]][L 3 /t 4 ][1/E]; M 1 = E QED b. Show that the best material choice for a cantilever beam of a given length L and with a given square section [t x t] which will deflect
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problemset_2008-5_key - Problem Set 5 EMA 4714 Materials...

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