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Quiz_4_Mar09key - Quiz 3 EMA 4714 Selection of Materials...

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Quiz 3 Name _______________________ EMA 4714 - Selection of Materials Friday, March 9, 2007 1. [10 points] A cantilever beam is loaded with force P at its free end to produce a deflection δ = PL 3 /3EI. If the beam has a circular cross-section, I = π r 4 /4, develop a “figure of merit” [performance index] for selecting a material that minimizes the weight of the beam for a given stiffness [P/ δ ]. By using the material properties given below, select the best material on the basis of [a] mechanical performance and [b] both mechanical performance and cost. S = [F/ δ ] = 3EI/L 3 = 3E π r 4 /4L 3 ; r 4 = 4L 3 S/3 π E m 2 = π 2 r 4 L 2 ρ 2 ; r 4 = m 2 / π 2 L 2 ρ 2 = 4L 3 S/3 π E m = [S] 1/2 [4 π L 5 /3] 1/2 [ ρ /E 1/2 ]; M 1 = E 1/2 / ρ ; M 2 = E 1/2 / c ρ based on M 1 PI, CFRP is best choice; based on M 2 PI, concrete is better .....
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2. [10 points] You are seized by the noble notion of raising money for charity by traversing a narrow street on a plank resting on the roofs of the houses on either side, a distance L apart. You
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