14. A hollow steel shaft is subjected to a torque . The allowabe torsional stress is . If the inside diameter is designed to be 80% of the outiside diameter and the probability of failure is designed to be , determine the size of  shaft and choose a preferred one using FOSM. Note that  and  are independent.

Solution

For a shaft in torsion, the maximum torsional stress is given by

Thus the limit-state function is the maximum torsional stress subtracted from the allowable one. 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.