2-8. Bar AB
is hung by two cables CD and EG. The total weight of the bar is . A vertical force
acts on the bar as shown in the figure.
Assume that the allowable normal stress of the cables is
. If W,
, and
are independent, determine the
diameters 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 below.
,
,
,
,
The stress in cable CD is
Set
, and then
, where
Then,
. We have
.
Thus,
.
Ans.
The stress in cable EG is
Set
, and then
, where
Then,
. We have
.
Thus,
.
Ans.