2-10. A wooden beam is subjected to a normally distributed load , where . The beam has a cross-sectional area  and a modulus of elasticity  ksi. The length is  ft. If the allowable displacement of  is  in, what is the probability of failure? 

Solution:

The load is calculated by

The displacement of B is then given by

The probability of failure of the beam due to excessive deformation is

 follows a normal distribution .

Thus,

Ans.