3. The distribution of force P is , and the strength of the cable is normally distributed with . P and are independent. Determine the distribution of the resultant force at A, and the probability of failure of the cable.

Solution

1)

Thus

So we have

The distribution of the resultant force at A is . Ans.

2)

From 1), we know

So the distribution of T is . Also, we know the strength of the cable is normally distributed with .

Suppose , we can find and

Ans