46. A cylindrical tube is subjected to an internal pressure . The tube has an inside diameter of  in and the allowable tangential stress is . If the maximum probability of failure is designed to be , determine the minimum thickness of the tube using the theory of thin-walled vessels. Note that  and  are independent.

Solution

Applying the theory of thin-walled vessels, the maximum tangential stress is expressed as follows:

The limit-state function is the maximum tangential stress of the vessel subtracted from the allowable tangential stress. 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.