2-7.  Bar AB is hung by two cables CD and EG. The total weight of the bar is . A vertical force  acts on the bar at the middle point. Assume that the allowable normal stress of the cables is . If W, , and  are independent, determine the cross-cectional area of the cables to make sure that the probability of failure of each cable is less than 10^-4.

Solution:

The internal forces developed in cables CD and EG are shown in the free-body diagram below.

,     ,   

,     , 

The stress in cables CD and EG is

Set , and then , where

Thus, .

We have   .                                                                                   Ans.