1-2. The two aluminum rods support the vertical force
of 
. The allowable tensile stress for
the aluminum is 
. Determine the diameters
of the two rods to make sure that the probabilities of failure of them both are
less than 
. Assume that P and Sa
are independent.
Solution
Internal Loadings:
The force developed in each rod can be determined by using the method of
joints. Consider the equilibrium of joint A as shown in Fig. 1.2.2,
; 
;
; 
;
For rod AB, the probability of
failure 
is
(1)
Since
,
,
and P and Sa are independent, Y
also follows a normal distribution, 
.
(2)
(3)
Equation (1) can be written as
Therefore, 
(4)
From (1), (2) and (3), we
can get 
. Ans.
Similarly, For rod AC,
the probability of failure is
(5)
we can get 
.
Ans.