29. An axial force  is applied to a solid circular shaft that has a diameter of  and a length of . If the modulus of elasticity is , determine the mean and standard deviation of the tensile spring constant using the First Order Second Moment Method. Note that ,   and  are independent.

Solution

The total extension of the shaft is 

Thus the spring constant of the axially loaded shaft is expressed as

Let

where .

Using FOSM, we have