30. A cantilever bar is subjected to a torsion  at the end. The bar has a round cross section with a diameter of  and a length of . The shear modulus of the bar is . If  and  are independent, what is the mean and standard deviation of strain energy for torsion using the First Order Second Moment Method?

Solution

The strain energy for torsion is given by 

Let

where .

Using FOSM, we have