7-2. A sportsman is performing a pole vault, and the minimum radius of curvature of the pole is estimated to be 5 m. The pole has a diameter of 42 mm and its material has a Young’s modulus of. If the allowable bending stress of the pole is, determine the probability of failure. Assume E and  are independent.

Solution:

Moment-Curvature Relationship could be calculated by

,     in which  .

Thus,                           

Set , then , where

The probability of failure of the pole is then calculated by

Ans.