4-9. A beam is subjected to a
normally distributed force 
lb/ft as shown. The
beam has a square cross-section and 
. If the allowable
bending stress is 
ksi, and the allowable shear
stress is 
psi, what is the minimum length of b
for a probability of failure due to excessive bending stress less than 10-4
and a probability of failure due to excessive shear stress less than 10-4
? Assume 
, 
, and 
are independent.
(Ans. 
)
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