3-3. A coupling connects the two shafts as shown. The
torque applied on the shafts
follows a normal distribution of
. Each bolt has a
diameter
, and the bolts are uniformly distributed
at the radius
. If the allowable shear stress
of the bolt is
, determine how many bolts the
coupling should have to make sure that the probability of failure of each bolt
is less than
. Assume that
and
are independent, and the shear stress in
the bolts is uniform. (Ans.
)