2-7. Bar AB
is hung by two cables CD and EG. The total weight of the bar is . A vertical force
acts on the bar at the middle
point. Assume that the allowable normal stress of the cables is
. If W,
, and
are independent, determine the
cross-cectional area of the cables to make sure that the probability of failure
of each cable is less than 10-4.
Solution:
The internal forces developed in cables CD and EG are shown in the free-body diagram below.
,
,
,
,
The stress in cables CD and EG is
Set
, and then
,
where
Thus,
.
We
have . Ans.