Word%20Pro%20-%20q3spr2005_key4714

Word%20Pro%20-%20q3spr2005_key4714 - failure, which of the...

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Quiz 3 EMA 4714 - Materials Selection and Failure Analysis KEY Monday, February 21, 2005 1. [10 points] Show that the lightest cantilever beam of length L and square section [free] which will not fail during application of an end load F is that made of the material with the largest value of M 2 = σ 2/3 / ρ [neglect self-weight]. Select the optimum material from the following table. Objective:m = t 2 L ρ ; t 2 = m/L ρ F max = [I/y m ][ σ f /L]; I = t 4 /12, y m = t/2; I/y m = t 3 /6; F max = t 3 σ f /6L; t 3 = 6LF max / σ f ; [t 3 ] 2/3 = t 2 = [6LF max / σ f ] 2/3 = m/L ρ solving for m, = [6F max ] 2/3 [L] 5/3 [ ρ / σ f 2/3 ]; M 2 = σ f 2/3 / ρ QED best material in Table is CFRP 2. [10 points] For a 2 m long beam, supporting an end load F of 1000N without failure, what will be the mass and the dimension of the square section? *************************************************************************** m = [6000] 2/3 [2] 5/3 [7.652x10 -6 ] = 8.02x10 -3 Mg [~ 17.6 lbs] t = [8.02x10 -3 /2/1.2] 1/2 = 5.78x10 -2 m = 5.78 cm on a side 3. [10 points] For a 2 m long beam, supporting an end load F of 1000N, deflecting 5 cm without
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Unformatted text preview: failure, which of the materials listed in the table would be the optimum choice? *************************************************************************** m 2 = [6F max ] 2/3 [L] 5/3 [ ρ / σ f 2/3 ] = m 1 = [ 4F/ δ min ][L 5/2 ][ ρ /E 1/2 ] [ σ f 2/3 / ρ ]/[E 1/2 / ρ ] = 0.825 δ max /[F max 1/3 L 5/6 ] = 0.002315; CC[CFRP] closest but not very close- going to have to decrease load/increase deflection contraints or look for materials with better combinations of properties closer to the design coupling constant. 9.9 24.26 2.45 1,103 116 4.4 Ti-6Al-4V 9.58 72.14 7.53 1,240 145 1.6 CFRP 10.13 13.07 1.29 62.1 2.38 1.2 polycarbonate M 2 /M 1 M 2 , σ t 2/3 / ρ M 1 , E 1/2 / ρ tensile strength, σ t , MPa elastic modulus, E, GPa density, Mg/m 3 material...
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This note was uploaded on 10/19/2011 for the course EMA 4714 taught by Professor Staff during the Spring '08 term at University of Florida.

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