12.
A shaft with a round cross section is designed to tranismit a power at .
The diameter and the allowabe shear stress of the shaft are
and
, respectively. If the maximum
probability of failure is desinged to be
, estimate the maximum power that the
shaft can transimit using the First Order Second Moment Method. Note that
and
are independent.
Solution
The transmitted power is given by
Thus
And the maximum shear stress is
The
limit-state function is the maximum shear stress subtracted from the allowable
stress. Failure occurs when.
where
.
Using FOSM, we have
The probability of failure is then given by
Thus
Solving
for yields
Ans.