2-9. Bar AB, which is hung by a cable CD, is used to support a load. The weight of the bar is negligible. Force  acts on the bar at point B to support the load that acts at point A. Assuming that the allowable normal stress of the cable is , and that , , and  are independent, determine the diameter of the cable to make sure that the probability of failure is less than 10^-4.

Solution:

The internal force developed in cable CD is shown below.

,     ,   

The stress in cable CD is

Set , and then , where

Then, .  We have .

Thus,  .                                                                                                             Ans.