6-5. A mechanical component is subject to a random force . There is a circular groove in the component as shown in the figure. Neglect the effect of stress concentration. Determine the distribution of the maximum tensile stress.

Solution:

The distance between P and O is 

Let M denote the moment developed in the component, then

;  ; 

The maximum tensile stress is given by

Since , we have

Thus, the maxmium tensile stress follows a normal distribution of .

Ans.