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MAE455 hw 2 solution

# MAE455 hw 2 solution - MAE 4550 Intro to Composites Fall...

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MAE 4550 – Intro to Composites Fall 2009 HW 2 Steps for finding ρ and x 0 : 1) Arrange strengths (x) from least to greatest (MPa) 2) Calculate F i for each piece of data where F i = (i-0.5)/n 3) Plot x vs. Fi 4) Find x 0 from plot where F=0.632 5) Plot ln(x/x 0 ) vs. ln(-ln(1-Fi)) 6) Find ρ from slope of plot Carbon 10mm x (MPa) Fi ln(x/xo) ln(-ln(1-Fi) 2982 0.02 -0.27985 -3.90194 2992 0.06 -0.27651 -2.78263 3130 0.1 -0.23142 -2.25037 3160 0.14 -0.22188 -1.89165 3167 0.18 -0.21966 -1.61721 3233 0.22 -0.19904 -1.39247 3375 0.26 -0.15605 -1.2003 3427 0.3 -0.14076 -1.03093 3437 0.34 -0.13785 -0.87824 3457 0.38 -0.13205 -0.73807 3547 0.42 -0.10635 -0.60747 3560 0.46 -0.10269 -0.48421 3641 0.5 -0.08019 -0.36651 3698 0.54 -0.06466 -0.25292 3699 0.58 -0.06439 -0.14214 3870 0.62 -0.01919 -0.03295 3933 0.66 -0.00305 0.075858 3978 0.7 0.00833 0.185627 3989 0.74 0.011092 0.297935 3994 0.78 0.012344 0.41484 4033 0.82 0.022062 0.539296 4401 0.86 0.109383 0.676058 4447 0.9 0.119781 0.834032 4777 0.94 0.191364 1.034398 4789 0.98 0.193873 1.364055

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Plot of x vs. Fi y = 0.00055663x - 1.56432256 0 0.2 0.4 0.6 0.8 1 1.2 0 1000 2000 3000 4000 5000 6000 0.632= .00055663x-1.56432256 x 0 =3945 MPa Plot of ln(x/x 0 ) vs. ln(-ln(1-Fi)) y = 8.6767x + 0.0475 -5 -4 -3 -2 -1 0 1 2 3 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 ρ = 8.6767
Carbon 100mm X (MPa) Fi ln(x/xo) ln(-ln(1-Fi)) 2101 0.02 -0.51714 -3.90194 2103 0.06 -0.51619 -2.78263 2231 0.1 -0.4571 -2.25037 2265 0.14 -0.44198 -1.89165 2346 0.18 -0.40684 -1.61721 2813 0.22 -0.2253 -1.39247 2982 0.26 -0.16696 -1.2003 2989 0.3 -0.16461 -1.03093 3129 0.34 -0.11884 -0.87824 3139 0.38 -0.11565 -0.73807 3168 0.42 -0.10645 -0.60747 3201 0.46 -0.09609 -0.48421 3231 0.5 -0.08676 -0.36651 3252 0.54 -0.08028 -0.25292 3316 0.58 -0.06079 -0.14214 3394 0.62 -0.03754 -0.03295 3439 0.66 -0.02437 0.075858 3742 0.7 0.060069 0.185627 3761 0.74 0.065134 0.297935 3821 0.78 0.080961 0.41484 3836 0.82 0.084879 0.539296 3864 0.86 0.092152 0.676058 3969 0.9 0.118963 0.834032 4003 0.94 0.127493 1.034398 4513 0.98 0.247411 1.364055

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Plot of x vs. Fi y = 0.000441x - 0.922012 0 0.2 0.4 0.6 0.8 1 1.2 0 1000 2000 3000 4000 5000 0.632= .000441x-922012 x 0 =3524 MPa Plot of ln(x/x 0 ) vs. ln(-ln(1-Fi)) y = 5.6582x + 0.0555 -5 -4 -3 -2 -1 0 1 2 -0.6 -0.4 -0.2 0 0.2 0.4 ρ = 5.6582
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MAE455 hw 2 solution - MAE 4550 Intro to Composites Fall...

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