1-6.  A vertical force of  is applied to the bell crank. Assuming that the allowable normal stress at the 10-mm diameter rod CD is , and the allowable shear stress at the 6-mm diameter pin B, subjected to double shear is . If and are independent, determine the probabilities of failure of rod CD and pin B.

Solution

Referring to the free-body diagram of the bell crank shown in Fig. 1.6.1.

;

Thus, the force acting on pin B is .

Since pin B is in double shear, we have .

The cross-section area of rod CD is  , and the area of the shear plane of pin B is . We obtain the normal stress  at rod CD and shear stress  at pin B as follows

,        .

Set , then , where

.

Thus, the probability of failure of rod CD is

.

Similarly, set , then , where

.

Thus, the probability of pin B is

.              Ans.