8-11. Bar BC is pin-connected at its ends. Load is applied to pin B. If the modulus of elasticity follows . Determine the distribution of the critical buckling load about the y-y axis. Also determine the probability buckling of Bar BC. Assume that E and F are independent.

Solution:

Section Properties

By analyzing the equilibrium of joint B, we have

Thus, the compressive force developed in the bar BC is .

The critical buckling load about y-y axis is

;       .

Since , we have

Thus, the critical buckling load follows .                                       Ans.

Set , then , where

Thus, the probability of failure is

                     Ans.