8-10. A steel rod BC with is used as a strongback. A force  is used to slowly lift the weight as shown in the figure. If the modulus of elasticity follows . Determine the probability of failure due to buckling. Assume that E and F are independent.  

Solution:

Joint A :             

:     ,    

:     ,       

Joint B :

:     ,         

The moment of inertia of the rod is

Thus, the buckling load is calculated by

,      where .

Set , then , where

Thus, the probability of failure is

                      Ans.