homework_08

homework_08 - V f c = 0.1. Find in approximation the mean...

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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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1.010 Fall 2008 Homework Set #8 Due November 13, 2008 (in class) 1. A concrete column has square cross-section with side length 0.5m. The column is subject to a random axial stress S contributed by two random loads W 1 and W 2 , i.e. S = W W 1 2 where A is the cross-sectional area of the column. The mean value and + A A coefficient of variation of W 1 are m W 1 = 2500kN and V W 1 = 0.2, whereas for W 2 , m W 2 = 3000kN and V W 2 = 0.15. W 1 and W 2 have correlation coefficient " = 0.5. The compressive strength of concrete, f c , is also random and independent of W 1 and W 2 , with mean value m f c = 30000 kN/m 2 and coefficient of variation
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Unformatted text preview: V f c = 0.1. Find in approximation the mean value and variance of the safety factor SF = f c / S . 2. Daily temperature and humidity are measured each day of a week in August, and the resulting sample is: T ( o F) H(%) 70 81 84 86 79 90 65 77 68 78 86 95 77 86 (a) Plot the sample (Plot H against T). (b) Estimate the mean values and variances of T and H. (Replace the expectation in the definition of m and ! 2 with the sample average) (c) Find the covariance and correlation coefficient between T and H. (Again replace the expectation in the definition of m and ! 2 with the sample average) (d) Suppose that one day temperature is reported to be 80 o F. What would you expect the humidity to be? How much uncertainty would you have on H?...
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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homework_08 - V f c = 0.1. Find in approximation the mean...

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