8-7.  The force acting on the beam AB follows a normal distribution  and the modulus of elasticity follows another normal distribution. Determine the probability of failure of beam BC caused by x-x axis buckling. The supports at A, B and C are pin connected. Assume that E and P are independent.

Solution:

From the free body diagram of beam AB and BC, we can find the load developed in beam BC

,  

Then, .

The effective length factor of x-x axis buckling is. Thus, the x-x axis critical buckling load can be calculated by

Set , then , where

Thus, the probability of failure of the beam BC caused by x-x axis buckling is

                      Ans.