If two loads are applied to a cantilever beam as shown in the accompanying drawi
ID: 3320623 • Letter: I
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 is a1X1 + a2X2 X1 aI a2 (a) Suppose that X1 and X2 are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.4 and 2.8 kip, respectively. If a1 = 5 ft and a2 10 ft, what is the expected bending moment? What is the standard deviation of the bending moment? (Give answer accurate to 2 decimal places.) (b) If X1 andX2 are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Give answer accurate to 3 decimal places.)Explanation / Answer
a) here expected bending moment =a1E(X1)+a2E(X2) =5*5+10*10=125
std deviation =(a12Var(X1)+a22Var(X2))1/2 =(25*1.42+100*2.82)1/2 =28.86
b) P(X>75)=P(Z>(75-125)/28.86)=P(Z>-1.7324)=0.958