Probability, Statistics, and Decision For Civil Engineers by Jack R. Benjamin & C. Allin Cornell

Author:Jack R. Benjamin & C. Allin Cornell [Jack R. Benjamin & C. Allin Cornell]
Language: eng
Format: epub
Publisher: Dover Publications, Inc
Published: 2014-08-17T16:00:00+00:00

3.23. Consider the simple model shown of a flexible (long-span) structure resting on two footings. The foundation engineer’s concern is in the relative deflection of the ends of the structure:

Fig. P3.23

Assume that flexibilities (the reciprocals of the stiffnesses) f1 and f2 of the two soil and footing systems are jointly distributed random variables with common mean m and common variance σ2, and with covariance ρσ2, where ρ is the correlation coefficient, a measure of the dependence between flexibilities, and hence a measure of lateral homogeneity of the soil. Find

(a) The expected value of ∆.

(b) The variance and standard deviation of ∆. (Note the relationship between variance and the soil homogeneity measure ρ. It is unlikely that ρ would ever be negative.)

(c) If f1 and f2 are jointly normally distributed (bivariate normal), with Q = 1000 kips, σ = 0.002 in./kip, and ρ = 0.9, find

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