11. A rectangular shaft is designed to transimit a torque  shown in the figure. It has a rectangular cross section with a width of  and a thickness of . The shear modulus is . If the allowable angle of twist is  and the proability of failure is designed to be , determined the maximum length of the shaft. Note that and  are independent.

Solution

For a rectangular shaft in torsion, the maximum angle of twist is given by

where  is a function of  and it is 0.228 in this case.

Thus the limit-state function is the maximum angle of twist subtracted from 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.