1-13. The chandelier is hung from the ceiling using two
rods. Rod AB has a diameter of 
=
4 mm, and rod BC has a diameter of 
=
6 mm. The allowable stress in either rod follows the distribution 
MPa. If the mass of the
chandelier follows the distribution of 
kg,
what are the probabilities of failure of the two rods? Assume 
and m are independent.
Solution
Free Body Diagram
Determine the forces in the two rods in terms of m.
Determine the area of each rod
m2
m2
Determine the equation for normal stress in each rod
The probability of
failure in a single rod is
. Let 
, then
Then, 
for a single
rod is written as 
. Because normal random
variables and m are independent, 
also follows a normal
distribution, 
.
MPa
MPa
MPa
MPa
Thus
