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.

(a) Suppose that X₁ and X₂ are independent rv's with means 5 and 10 kips, respectively, and standard deviations 1.5 and 3.0 kip, respectively. If

a₁ = 10 ft and a₂ = 20 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	kip-ft
standard deviation	kip-ft

(b) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? (Round your answer to four decimal places.)

Answer 1

From the given information we have

Let

.

So expected bending moment is

and variance of expected moment is

So standard deviation of expected moment is

(b)

The z-score for B = 75 is

Using z table, the required probability is