Question

If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is2 Ху a2 0 (a) Suppose that x, and x2 are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.3 and 2.6 kip, respectively. If a17 ft and a214 ft, what is the expected bending moment and what is the standard deviation of the bending moment? (Round your standard deviation to three decimal places.) expected bending moment standard deviation kip-ft kip-ft (b) If X1 adX2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.) (c) Suppose the positions of the two loads are random variables. Denoting them by A and A2, assume that these variables have means of 7 and 14 ft, respectively, that each has a standard deviation of o.5, and that all A/'s and Xs are independent of one another. What is the expected moment now? kip-ft (d) For the situation of part (c), what is the variance of the bending moment? (Round your answer to two decimal places.) kip-ft (e) If the situation is as described in part (a) except that Corr(X1, X2) = 0.5 (so that the two loads are not independent), what is the variance of the bending moment? kip-ft2

Answer 1

a)

expected bending moment =7*5+14*10 =175

std deviation =sqrt((7*1.3)²+(14*2.6)²)=37.520

b)

P(X>75)=P(Z>(75-175)/37.520)=P(Z>-2.67)=0.9962

c)

expected bending moment =175

d)

variance =1441.13

e)

variance =1739.01