Problem #8: Tf two loads are applied to a cantilever beam, as shown in the figur

Question

Problem #8: Tf two loads are applied to a cantilever beam, as shown in the figure below, the bending moment at 0 due to the loads is a1X1 + a2X2 S2 21 Suppose that X1 and X2 are independent random variables with means 2 and 5 kips, respectively, and standard deviations 0.7 and 1.2 kips, respectively. Suppose that a 6 ft and a2-9 ft. (a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) If Xi and X2 are normally distributed, what is the probability that the bending moment will exceed 69 kip-ft?

Explanation / Answer

a) expected value E(X)=a1*E(X1)+a2*E(X2) =6*2+9*5=57

b) std deviation =(a12*Var(X1)+a22*Var(X2))1/2 =(62*0.72+92*1.22)1/2 =11.5879

c) probability =P(X>69)=P(Z>(69-57)/11.5879)=P(Z>1.0356)=1-0.8498=0.1502

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