2-1.  Bar AB is hung by a cable at C. The total weight of the bar is . A vertical force  acts on the bar at point B. Assuming that the allowable normal stress of the cable is . If W and P are independent, determine the cross-cectional area of the cable to make sure that the probability of failure of the cable is less than 10^-4.

Solution

From the diagram, we can find force F in the cable using

,    ,   .

Stress in the cable is

Set , then , where

Thus, .

We have   .                                                                                 Ans.