2-8.  Bar AB is hung by two cables CD and EG. The total weight of the bar is . A vertical force  acts on the bar as shown in the figure. Assume that the allowable normal stress of the cables is . If W, , and  are independent, determine the diameters 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 below.

,     ,   

,     , 

The stress in cable CD is

Set , and then , where

Then, .  We have .

Thus,  .                                                                                                             Ans.

The stress in cable EG is

Set , and then , where

Then, .  We have .

Thus,  .                                                                                                             Ans.