Problem #8: If two loads are applied to a cantilever beam as shown in the figure

Question

Problem #8: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the loads is al-Y1+, 2 Suppose that Xi and X2 are independent random variables with means 2 and 6 kips, respectively, and standard deviations 0.5 and 1.3 kips, respectively. Suppose that a1 = 5 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 X1 and X2 are normally distributed, what is the probability that the bending moment will exceed 78 kip-ft? Problem #8(a): Problem #8(b): Problem #8(c):

Explanation / Answer

a)here mean =a1E(X1)+a2*E(X2) =5*2+9*6=64

b)std deviation =(a12Var(X1)+a22*var(X2))1/2 =((5*0.5)2+(9*1.3)2)1/2 =11.9641

c) P(X>78) =P(Z>(78-64)/11.9641) =PZ>1.1702)=0.1210

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