Q1. A column of a high-rise building is supported by a pile group consisting of

Question

Q1. A column of a high-rise building is supported by a pile group consisting of two piles. The load carrying capacity of each pile, C, is the sum of two independent contributions, namely: frictional resistance, F, along the pile length and the end bearing resistance, B, at the pile tip. Suppose F and B are both normally distributed with mean values of 200 and 300 kN and coefficients of variation of 0.2 and 0.3, respectively. (10%) a) Determine the mean and c.o.v. of the load carrying capacity, C, of one pile. What is the distribution of C? Why? Explain. (10%) b) Determine the mean and c.o.v. of the total load carrying capacity, T, of the pile group consisting of two piles if the capacities between the two piles are correlated with a correlation coefficient of = 0.25. (10%) c) If the maximum load applied on the pile group, L, is also normally distributed with a mean value of 500 kN and a c.o.v. of 0.3, what is the probability of failure of this pile group? Assume the total capacity and load to be statistically independent. Assume also the total load carrying capacity to be normally distributed.

Explanation / Answer

a) Determine the mean and c.o.v. of the load carrying capacity, C, of one pile. What is the distribution of C? Why? Explain.

since C=F+B

& both F & B follow normal dist so by rule their sum will also follow Normal distribution with:

mean = (200+300) = 500 KN

since SD of F= c.o.v * mean = 0.2*200 = 40

SD of B= c.o.v * mean = 0.3*300 = 90

SD of C= sqrt(SD_B^2 + SD_F^2 ) = sqrt(40^2 + 90^2) = 98.49 KN

Since F & B are independent so no covariance term will appear here.

so, COV= sigma/mean = 98.49/500 = 0.197

b) Determine the mean and c.o.v. of the total load carrying capacity, T, of the pile group consisting of two piles if the capacities between the two piles are correlated with a correlation coefficient of = 0.25

mean=500kn

sd= sqrt(40^2 + 90^2+2*.25*40*90) =107.23 kn

cov= 107.23/500=0.214

c) Since total capacity =500 kn

& load=500 kn

thus prob of failure will be 50%

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