23. A tension rod is subjected to a load of . It has a diameter of   and a length of . The Poission ratio is  and the modulus of elasticity is . Determine the mean and standard deviation of the change in rod diameter using the First Order Second Moment Method. Note that ,  and  are independent.

Solution

The applied tensile stress is

And the corresponding axial strain is given by

Then the lateral strain is

Thus the change in rod diameter is expressed as

Let

where .

Using FOSM, we have