70. A 500-mm-long strip is subjected to a torque  shown in the figure. The strip has a rectangular cross section with a width of  and a thickness of . If the allowable shear stress is , estimate probability of failure using the First Order Second Moment Method. Note that  and  are independent.

Solution

For a rectangular section strip in torsion, the maximum shearing stress is given by

Thus the limit-state function is the maximum shearing stress subtracted from allowable one. Failure occurs when

where .

Using FOSM, we have

The probability of failure is then given by

Ans.