52. A force  is applied to a cantilevered tube as shown in the figure. The tube has an outside diameter of  and inside diameter of . The lenghth of the tube is  and the modulus of elasticity is . Assume that the allowable transverse deflection is  and the maximum probability of failure is designed to be , estimate the inside diameter of the tube. Note that the maximum deflection is

Solution

The maximum deflection happens at O and is given by

The limit-state function is the maximum deflection subtracted from allowable transverse deflection. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by

Thus

Solving for  yields

Thus  can be used.                                                                                                          Ans.