33. A bar is subjected to a tensional force . The bar includes a round cross section with diameter  and length . And it has a tapered portion of length  and a diameter  of the end circular cross section. The modulus of elasticity is . If  and   are independent, determine the mean and standard deviation of total axial elongation using the First Order Second Moment Method. Note that the elongation of tapered portion is .

Solution

For the section with constant diameter, the axial elongation is

For the tapered portion, the elongation is given by

Thus the total axial elongation is expressed as

Let

where .

Using FOSM, we have

Ans.